Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition t1 is true if proposition t2 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition q is true if proposition t0 is true. Proposition v4 is true if proposition w4 is not true. Proposition t4 is true if proposition t5 is true. Proposition v6 is true if proposition w6 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition w1 is true if proposition v1 is not true. Proposition t3 is true if proposition t4 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition v5 is true if proposition w5 is not true. Proposition w0 is true if proposition v0 is not true. Proposition w6 is true if proposition v6 is not true. Proposition t2 is true if proposition t3 is true. Proposition w5 is true if proposition v5 is not true. Proposition w2 is true if proposition v2 is not true. Proposition v1 is true if proposition w1 is not true. Proposition w4 is true if proposition v4 is not true. Proposition t5 is true if proposition e8 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v3 is true if proposition w3 is not true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition w3 is true if proposition v3 is not true. Proposition e0 is true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition t0 is true if proposition t1 is true. Proposition v7 is true if proposition w7 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition w7 is true if proposition v7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition t1 is true if proposition t2 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition q is true if proposition t0 is true. Proposition v4 is true if proposition w4 is not true. Proposition t4 is true if proposition t5 is true. Proposition v6 is true if proposition w6 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition w1 is true if proposition v1 is not true. Proposition t3 is true if proposition t4 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition v5 is true if proposition w5 is not true. Proposition w0 is true if proposition v0 is not true. Proposition w6 is true if proposition v6 is not true. Proposition t2 is true if proposition t3 is true. Proposition w5 is true if proposition v5 is not true. Proposition w2 is true if proposition v2 is not true. Proposition v1 is true if proposition w1 is not true. Proposition w4 is true if proposition v4 is not true. Proposition t5 is true if proposition e8 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v3 is true if proposition w3 is not true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition w3 is true if proposition v3 is not true. Proposition e0 is true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition t0 is true if proposition t1 is true. Proposition v7 is true if proposition w7 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition w7 is true if proposition v7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition t1 is true if proposition t2 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition q is true if proposition t0 is true. Proposition v4 is true if proposition w4 is not true. Proposition t4 is true if proposition t5 is true. Proposition v6 is true if proposition w6 is not true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition w1 is true if proposition v1 is not true. Proposition t3 is true if proposition t4 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition v5 is true if proposition w5 is not true. Proposition w0 is true if proposition v0 is not true. Proposition w6 is true if proposition v6 is not true. Proposition t2 is true if proposition t3 is true. Proposition w5 is true if proposition v5 is not true. Proposition w2 is true if proposition v2 is not true. Proposition v1 is true if proposition w1 is not true. Proposition w4 is true if proposition v4 is not true. Proposition t5 is true if proposition e8 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v3 is true if proposition w3 is not true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition w3 is true if proposition v3 is not true. Proposition e0 is true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition t0 is true if proposition t1 is true. Proposition v7 is true if proposition w7 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition w7 is true if proposition v7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition w2 is true if proposition v2 is not true. Proposition e0 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition w0 is true if proposition v0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition v3 is true if proposition w3 is not true. Proposition t3 is true if proposition e8 is true. Proposition t1 is true if proposition t2 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition s1 is true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition w4 is true if proposition v4 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition v1 is true if proposition w1 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w5 is true if proposition v5 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v2 is true if proposition w2 is not true. Proposition t0 is true if proposition t1 is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w6 is true if proposition v6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition w2 is true if proposition v2 is not true. Proposition e0 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition w0 is true if proposition v0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition v3 is true if proposition w3 is not true. Proposition t3 is true if proposition e8 is true. Proposition t1 is true if proposition t2 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition s1 is true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition w4 is true if proposition v4 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition v1 is true if proposition w1 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w5 is true if proposition v5 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v2 is true if proposition w2 is not true. Proposition t0 is true if proposition t1 is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w6 is true if proposition v6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition w2 is true if proposition v2 is not true. Proposition e0 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition w0 is true if proposition v0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition v3 is true if proposition w3 is not true. Proposition t3 is true if proposition e8 is true. Proposition t1 is true if proposition t2 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition s1 is true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition w4 is true if proposition v4 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition v1 is true if proposition w1 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w5 is true if proposition v5 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v2 is true if proposition w2 is not true. Proposition t0 is true if proposition t1 is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w6 is true if proposition v6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition w2 is true if proposition v2 is not true. Proposition e0 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition w0 is true if proposition v0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition v3 is true if proposition w3 is not true. Proposition t3 is true if proposition e8 is true. Proposition t1 is true if proposition t2 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition s1 is true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition w4 is true if proposition v4 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition v1 is true if proposition w1 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w5 is true if proposition v5 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v2 is true if proposition w2 is not true. Proposition t0 is true if proposition t1 is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w6 is true if proposition v6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition w2 is true if proposition v2 is not true. Proposition e0 is true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition t2 is true if proposition t3 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition w0 is true if proposition v0 is not true. Proposition v6 is true if proposition w6 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition v3 is true if proposition w3 is not true. Proposition t3 is true if proposition e8 is true. Proposition t1 is true if proposition t2 is true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition s1 is true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition w4 is true if proposition v4 is not true. Proposition v5 is true if proposition w5 is not true. Proposition w1 is true if proposition v1 is not true. Proposition v7 is true if proposition w7 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition v1 is true if proposition w1 is not true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition s0 is true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition v4 is true if proposition w4 is not true. Proposition w3 is true if proposition v3 is not true. Proposition w5 is true if proposition v5 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition v2 is true if proposition w2 is not true. Proposition t0 is true if proposition t1 is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition w6 is true if proposition v6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition v7 is true if proposition w7 is not true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition w1 is true if proposition v1 is not true. Proposition etrue is true. Proposition w2 is true if proposition v2 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition v4 is true if proposition w4 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition s1 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition s0 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w6 is true if proposition v6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w4 is true if proposition v4 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition q is true if proposition e8 is true and proposition wide is true and proposition etrue is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e0 is true. Proposition w0 is true if proposition v0 is not true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition v3 is true if proposition w3 is not true. Proposition w3 is true if proposition v3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition v7 is true if proposition w7 is not true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition w1 is true if proposition v1 is not true. Proposition etrue is true. Proposition w2 is true if proposition v2 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition v4 is true if proposition w4 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition s1 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition s0 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w6 is true if proposition v6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w4 is true if proposition v4 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition q is true if proposition e8 is true and proposition wide is true and proposition etrue is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e0 is true. Proposition w0 is true if proposition v0 is not true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition v3 is true if proposition w3 is not true. Proposition w3 is true if proposition v3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition v7 is true if proposition w7 is not true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition w1 is true if proposition v1 is not true. Proposition etrue is true. Proposition w2 is true if proposition v2 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition v4 is true if proposition w4 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition s1 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition s0 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w6 is true if proposition v6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w4 is true if proposition v4 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition q is true if proposition e8 is true and proposition wide is true and proposition etrue is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e0 is true. Proposition w0 is true if proposition v0 is not true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition v3 is true if proposition w3 is not true. Proposition w3 is true if proposition v3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition v7 is true if proposition w7 is not true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition w1 is true if proposition v1 is not true. Proposition etrue is true. Proposition w2 is true if proposition v2 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition v4 is true if proposition w4 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition s1 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition s0 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w6 is true if proposition v6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w4 is true if proposition v4 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition q is true if proposition e8 is true and proposition wide is true and proposition etrue is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e0 is true. Proposition w0 is true if proposition v0 is not true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition v3 is true if proposition w3 is not true. Proposition w3 is true if proposition v3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition v7 is true if proposition w7 is not true. Proposition e7 is true if proposition e6 is true and proposition w6 is true. Proposition e2 is true if proposition v1 is true and proposition e1 is not true. Proposition e7 is true if proposition v6 is true and proposition e6 is not true. Proposition w1 is true if proposition v1 is not true. Proposition etrue is true. Proposition w2 is true if proposition v2 is not true. Proposition e3 is true if proposition v2 is true and proposition e2 is not true. Proposition e8 is true if proposition e7 is true and proposition w7 is true. Proposition v4 is true if proposition w4 is not true. Proposition e1 is true if proposition v0 is true and proposition e0 is not true. Proposition e1 is true if proposition e0 is true and proposition w0 is true. Proposition s1 is true. Proposition e6 is true if proposition v5 is true and proposition e5 is not true. Proposition e8 is true if proposition v7 is true and proposition e7 is not true. Proposition v5 is true if proposition w5 is not true. Proposition v1 is true if proposition w1 is not true. Proposition v6 is true if proposition w6 is not true. Proposition w5 is true if proposition v5 is not true. Proposition s0 is true. Proposition e3 is true if proposition e2 is true and proposition w2 is true. Proposition w6 is true if proposition v6 is not true. Proposition w7 is true if proposition v7 is not true. Proposition w4 is true if proposition v4 is not true. Proposition e6 is true if proposition e5 is true and proposition w5 is true. Proposition e4 is true if proposition v3 is true and proposition e3 is not true. Proposition q is true if proposition e8 is true and proposition wide is true and proposition etrue is true. Proposition e4 is true if proposition e3 is true and proposition w3 is true. Proposition v0 is true if proposition w0 is not true. Proposition e2 is true if proposition e1 is true and proposition w1 is true. Proposition e0 is true. Proposition w0 is true if proposition v0 is not true. Proposition e5 is true if proposition v4 is true and proposition e4 is not true. Proposition v2 is true if proposition w2 is not true. Proposition e5 is true if proposition e4 is true and proposition w4 is true. Proposition v3 is true if proposition w3 is not true. Proposition w3 is true if proposition v3 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition a2 is true if proposition h2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition qcore is true if proposition h0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition etrue is true. Proposition h2 is true if proposition a2 is not true. Proposition s3 is true. Proposition t0 is true if proposition t1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h0 is true if proposition a0 is not true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition h1 is true if proposition a1 is not true. Proposition s0 is true. Proposition t1 is true if proposition qcore is true. Proposition s2 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition a2 is true if proposition h2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition qcore is true if proposition h0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition etrue is true. Proposition h2 is true if proposition a2 is not true. Proposition s3 is true. Proposition t0 is true if proposition t1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h0 is true if proposition a0 is not true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition h1 is true if proposition a1 is not true. Proposition s0 is true. Proposition t1 is true if proposition qcore is true. Proposition s2 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition a2 is true if proposition h2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition qcore is true if proposition h0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition etrue is true. Proposition h2 is true if proposition a2 is not true. Proposition s3 is true. Proposition t0 is true if proposition t1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h0 is true if proposition a0 is not true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition h1 is true if proposition a1 is not true. Proposition s0 is true. Proposition t1 is true if proposition qcore is true. Proposition s2 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition a2 is true if proposition h2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition qcore is true if proposition h0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition etrue is true. Proposition h2 is true if proposition a2 is not true. Proposition s3 is true. Proposition t0 is true if proposition t1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h0 is true if proposition a0 is not true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition h1 is true if proposition a1 is not true. Proposition s0 is true. Proposition t1 is true if proposition qcore is true. Proposition s2 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition a2 is true if proposition h2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition qcore is true if proposition h0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition etrue is true. Proposition h2 is true if proposition a2 is not true. Proposition s3 is true. Proposition t0 is true if proposition t1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h0 is true if proposition a0 is not true. Proposition s1 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition h1 is true if proposition a1 is not true. Proposition s0 is true. Proposition t1 is true if proposition qcore is true. Proposition s2 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition a2 is true if proposition h2 is not true. Proposition q is true if proposition t0 is true. Proposition h0 is true if proposition a0 is not true. Proposition qcore is true if proposition h0 is true. Proposition h1 is true if proposition a1 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t0 is true if proposition t1 is true. Proposition t3 is true if proposition qcore is true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition t1 is true if proposition t2 is true. Proposition t2 is true if proposition t3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition a2 is true if proposition h2 is not true. Proposition q is true if proposition t0 is true. Proposition h0 is true if proposition a0 is not true. Proposition qcore is true if proposition h0 is true. Proposition h1 is true if proposition a1 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t0 is true if proposition t1 is true. Proposition t3 is true if proposition qcore is true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition t1 is true if proposition t2 is true. Proposition t2 is true if proposition t3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition a2 is true if proposition h2 is not true. Proposition q is true if proposition t0 is true. Proposition h0 is true if proposition a0 is not true. Proposition qcore is true if proposition h0 is true. Proposition h1 is true if proposition a1 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t0 is true if proposition t1 is true. Proposition t3 is true if proposition qcore is true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition t1 is true if proposition t2 is true. Proposition t2 is true if proposition t3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition a2 is true if proposition h2 is not true. Proposition q is true if proposition t0 is true. Proposition h0 is true if proposition a0 is not true. Proposition qcore is true if proposition h0 is true. Proposition h1 is true if proposition a1 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t0 is true if proposition t1 is true. Proposition t3 is true if proposition qcore is true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition t1 is true if proposition t2 is true. Proposition t2 is true if proposition t3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition a2 is true if proposition h2 is not true. Proposition q is true if proposition t0 is true. Proposition h0 is true if proposition a0 is not true. Proposition qcore is true if proposition h0 is true. Proposition h1 is true if proposition a1 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t0 is true if proposition t1 is true. Proposition t3 is true if proposition qcore is true. Proposition h2 is true if proposition a2 is not true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition t1 is true if proposition t2 is true. Proposition t2 is true if proposition t3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition t4 is true if proposition t5 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition h2 is true if proposition a2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition a2 is true if proposition h2 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition qcore is true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition qcore is true if proposition h0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition t4 is true if proposition t5 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition h2 is true if proposition a2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition a2 is true if proposition h2 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition qcore is true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition qcore is true if proposition h0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition t4 is true if proposition t5 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition h2 is true if proposition a2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition a2 is true if proposition h2 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition qcore is true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition qcore is true if proposition h0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition t4 is true if proposition t5 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition h2 is true if proposition a2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition a2 is true if proposition h2 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition qcore is true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition qcore is true if proposition h0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition t4 is true if proposition t5 is true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition h2 is true if proposition a2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition a2 is true if proposition h2 is not true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t3 is true if proposition t4 is true. Proposition t5 is true if proposition qcore is true. Proposition t0 is true if proposition t1 is true. Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h1 is true if proposition a1 is not true. Proposition qcore is true if proposition h0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition t0 is true if proposition t1 is true. Proposition s1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition h2 is true if proposition a2 is not true. Proposition qcore is true if proposition h0 is true. Proposition t1 is true if proposition t2 is true. Proposition h1 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition t3 is true if proposition qcore is true. Proposition s3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition t0 is true if proposition t1 is true. Proposition s1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition h2 is true if proposition a2 is not true. Proposition qcore is true if proposition h0 is true. Proposition t1 is true if proposition t2 is true. Proposition h1 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition t3 is true if proposition qcore is true. Proposition s3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition t0 is true if proposition t1 is true. Proposition s1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition h2 is true if proposition a2 is not true. Proposition qcore is true if proposition h0 is true. Proposition t1 is true if proposition t2 is true. Proposition h1 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition t3 is true if proposition qcore is true. Proposition s3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition t0 is true if proposition t1 is true. Proposition s1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition h2 is true if proposition a2 is not true. Proposition qcore is true if proposition h0 is true. Proposition t1 is true if proposition t2 is true. Proposition h1 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition t3 is true if proposition qcore is true. Proposition s3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition t0 is true if proposition t1 is true. Proposition s1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition s2 is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition s0 is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h0 is true if proposition a0 is not true. Proposition h2 is true if proposition a2 is not true. Proposition qcore is true if proposition h0 is true. Proposition t1 is true if proposition t2 is true. Proposition h1 is true if proposition a1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t2 is true if proposition t3 is true. Proposition t3 is true if proposition qcore is true. Proposition s3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition t1 is true if proposition qcore is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t0 is true if proposition t1 is true. Proposition h1 is true if proposition a1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition qcore is true if proposition h0 is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition h2 is true if proposition a2 is not true. Proposition etrue is true. Proposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition h0 is true if proposition a0 is not true. Proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition t1 is true if proposition qcore is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t0 is true if proposition t1 is true. Proposition h1 is true if proposition a1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition qcore is true if proposition h0 is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition h2 is true if proposition a2 is not true. Proposition etrue is true. Proposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition h0 is true if proposition a0 is not true. Proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition t1 is true if proposition qcore is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t0 is true if proposition t1 is true. Proposition h1 is true if proposition a1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition qcore is true if proposition h0 is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition h2 is true if proposition a2 is not true. Proposition etrue is true. Proposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition h0 is true if proposition a0 is not true. Proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition t1 is true if proposition qcore is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t0 is true if proposition t1 is true. Proposition h1 is true if proposition a1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition qcore is true if proposition h0 is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition h2 is true if proposition a2 is not true. Proposition etrue is true. Proposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition h0 is true if proposition a0 is not true. Proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition t1 is true if proposition qcore is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition t0 is true if proposition t1 is true. Proposition h1 is true if proposition a1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition qcore is true if proposition h0 is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition h2 is true if proposition a2 is not true. Proposition etrue is true. Proposition s0 is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition h0 is true if proposition a0 is not true. Proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h0 is true if proposition a0 is not true. Proposition s0 is true. Proposition h1 is true if proposition a1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition qcore is true if proposition h0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h0 is true if proposition a0 is not true. Proposition s0 is true. Proposition h1 is true if proposition a1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition qcore is true if proposition h0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h0 is true if proposition a0 is not true. Proposition s0 is true. Proposition h1 is true if proposition a1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition qcore is true if proposition h0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h0 is true if proposition a0 is not true. Proposition s0 is true. Proposition h1 is true if proposition a1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition qcore is true if proposition h0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition etrue is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition h2 is true if proposition a2 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition h0 is true if proposition a0 is not true. Proposition s0 is true. Proposition h1 is true if proposition a1 is not true. Proposition a2 is true if proposition h2 is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s1 is true. Proposition qcore is true if proposition h0 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition s2 is true. Proposition s1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition qcore is true if proposition h0 is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition t1 is true if proposition qcore is true. Proposition s0 is true. Proposition a2 is true if proposition h2 is not true and proposition h3 is not true. Proposition h4 is true if proposition a4 is not true. Proposition a4 is true if proposition h4 is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition h2 is true if proposition a2 is not true. Proposition s3 is true. Proposition a3 is true if proposition h3 is not true and proposition h4 is not true. Proposition h0 is true if proposition a0 is not true. Proposition h3 is true if proposition a3 is not true. Proposition t0 is true if proposition t1 is true. Proposition h1 is true if proposition a1 is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition s2 is true. Proposition s1 is true. Proposition a0 is true if proposition h0 is not true and proposition h1 is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition qcore is true if proposition h0 is true. Proposition a1 is true if proposition h1 is not true and proposition h2 is not true. Proposition t1 is true if proposition qcore is true. Proposition s0 is true. Proposition a2 is true if proposition h2 is not true and proposition h3 is not true. Proposition h4 is true if proposition a4 is not true. Proposition a4 is true if proposition h4 is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition h2 is true if proposition a2 is not true. Proposition s3 is true. Proposition a3 is true if proposition h3 is not true and proposition h4 is not true. Proposition h0 is true if proposition a0 is not true. Proposition h3 is true if proposition a3 is not true. Proposition t0 is true if proposition t1 is true. Proposition h1 is true if proposition a1 is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.