text stringlengths 1 1k | source stringlengths 31 152 |
|---|---|
3
x
+
2
y
≤
12
2
x
+
3
y
... | https://en.wikipedia.org/wiki/Integer_programming |
er with the coordinate axes define the polyhedron of the LP relaxation, which is given by the inequalities without the integrality constraint. The goal of the optimization is to move the black dashed line as far upward while still touching the polyhedron. The optimal solutions of the integer problem are the points
... | https://en.wikipedia.org/wiki/Integer_programming |
rom minimum vertex cover to integer programming that will serve as the proof of NP-hardness.
Let
G
=
(
V
,
E
)
{\displaystyle G=(V,E)}
be an undirected graph. Define a linear program as follows:
... | https://en.wikipedia.org/wiki/Integer_programming |
≥
1
∀
u
,
v
∈
E
... | https://en.wikipedia.org/wiki/Integer_programming |
ligned}}}
Given that the constraints limit
y
v
{\displaystyle y_{v}}
to either 0 or 1, any feasible solution to the integer program is a subset of vertices. The first constraint implies that at least one end point of e... | https://en.wikipedia.org/wiki/Integer_programming |
v
{\displaystyle y_{v}}
we have also found the minimum vertex cover.
== Variants ==
Mixed-integer linear programming (MILP) involves problems in which only some of the variables,
x
i
... | https://en.wikipedia.org/wiki/Integer_programming |
U
⌋
+
1
{\displaystyle \lfloor \log _{2}U\rfloor +1}
binary variables:
x
=
x
1
+
2
x
2
... | https://en.wikipedia.org/wiki/Integer_programming |
oor \log _{2}U\rfloor }x_{\lfloor \log _{2}U\rfloor +1}.}
== Applications ==
There are two main reasons for using integer variables when modeling problems as a linear program:
The integer variables represent quantities that can only be integer. For example, it is not possible to build 3.7 cars.
The integer variab... | https://en.wikipedia.org/wiki/Integer_programming |
e objective is to maximize the total production, without exceeding the available resources. In some cases, this can be expressed in terms of a linear program, but the variables must be constrained to be integer.
=== Scheduling ===
These problems involve service and vehicle scheduling in transportation networks. For ... | https://en.wikipedia.org/wiki/Integer_programming |
order to plan some operations while considering different criteria or constraints. Some requirements for this problem are: contiguity, compactness, balance or equity, respect of natural boundaries, and socio-economic homogeneity. Some applications for this type of problem include: political districting, school distric... | https://en.wikipedia.org/wiki/Integer_programming |
=== Cellular networks ===
The task of frequency planning in GSM mobile networks involves distributing available frequencies across the antennas so that users can be served and interference is minimized between the antennas. This problem can be formulated as an integer linear program in which binary variables indicate ... | https://en.wikipedia.org/wiki/Integer_programming |
, if the ILP has the form
max
c
T
x
{\displaystyle \max \mathbf {c} ^{\mathrm {T} }\mathbf {x} }
such that
A
... | https://en.wikipedia.org/wiki/Integer_programming |
x
{\displaystyle \mathbf {x} }
be an arbitrary basic feasible solution . Since
x
{\displaystyle \mathbf {x} }
is feasible,
we know that
A
x
=
... | https://en.wikipedia.org/wiki/Integer_programming |
j
]
{\displaystyle \mathbf {x} _{0}=[x_{n_{1}},x_{n_{2}},\cdots ,x_{n_{j}}]}
be the elements corresponding to the basis columns for the basic solution
x
{\displaystyle \mathbf ... | https://en.wikipedia.org/wiki/Integer_programming |
aystyle B}
is square,
B
{\displaystyle B}
is nonsingular,
and therefore by assumption,
B
{\displaystyle B}
is unimodular and so
det
(
B
)
=
±
1
... | https://en.wikipedia.org/wiki/Integer_programming |
a
d
j
det
(
B
)
=
±
B
... | https://en.wikipedia.org/wiki/Integer_programming |
⇒
B
−
1
=
±
B
... | https://en.wikipedia.org/wiki/Integer_programming |
is integral.
⇒
Every basic feasible solution is integral.
... | https://en.wikipedia.org/wiki/Integer_programming |
are a variety of algorithms that can be used to solve integer linear programs exactly. One class of algorithms are cutting plane methods, which work by solving the LP relaxation and then adding linear constraints that drive the solution towards being integer without excluding any integer feasible points.
Another class... | https://en.wikipedia.org/wiki/Integer_programming |
nd methods can be used to return multiple optimal solutions.
=== Exact algorithms for a small number of variables ===
Suppose
A
{\displaystyle A}
is an m-by-n integer matrix and
b
{\displaystyle \mathbf {b} }
i... | https://en.wikipedia.org/wiki/Integer_programming |
er of variables) is a fixed constant, then the feasibility problem can be solved in time polynomial in m and log V. This is trivial for the case n=1. The case n=2 was solved in 1981 by Herbert Scarf. The general case was solved in 1983 by Hendrik Lenstra, combining ideas by László Lovász and Peter van Emde Boas. Doigno... | https://en.wikipedia.org/wiki/Integer_programming |
with no dependence on
V
{\displaystyle V}
.
In the special case of 0-1 ILP, Lenstra's algorithm is equivalent to complete enumeration: the number of all possible solutions is fixed (2n), and checking the feasibility of each solution can be done in time poly(m, log V). In the g... | https://en.wikipedia.org/wiki/Integer_programming |
case, the problem is reduced to a bounded number of lower-dimensional problems. The run-time complexity of the algorithm has been improved in several steps:
The original algorithm of Lenstra had run-time
2
O
(
n
... | https://en.wikipedia.org/wiki/Integer_programming |
O
(
1
)
{\displaystyle n^{O(n)}\cdot (m\cdot \log V)^{O(1)}}
.
Frank and Tardos presented an improved algorithm with run-time
n
2.5
n
⋅
... | https://en.wikipedia.org/wiki/Integer_programming |
⋅
(
m
⋅
log
V
)
O
(
1
)
{\displaystyle n^{n}\cdot 2^{O(n)}\cdot (m\cdot \log V)^{O(1)}}
.
Reis and Rothvoss presented an improved algorith... | https://en.wikipedia.org/wiki/Integer_programming |
ec.5 has run-time
2
O
(
n
3
)
⋅
p
o
l
y
(
d
,
L
)
... | https://en.wikipedia.org/wiki/Integer_programming |
n
)
{\displaystyle 2^{O(n\log n)}}
or to
n
n
{\displaystyle n^{n}}
.
=== Heuristic methods ===
Since integer linear programming is NP-hard, many prob... | https://en.wikipedia.org/wiki/Integer_programming |
roblem). Finally, long-term memory can guide the search towards integer values that have not previously been tried.
Other heuristic methods that can be applied to ILPs include
Hill climbing
Simulated annealing
Reactive search optimization
Ant colony optimization
Hopfield neural networks
There are also a variety of oth... | https://en.wikipedia.org/wiki/Integer_programming |
matrix has a block structure, which is the case in many applications. The sparsity of the matrix can be measured as follows. The graph of
A
{\displaystyle A}
has vertices corresponding to columns of
A
{\displaystyle A}
, and two col... | https://en.wikipedia.org/wiki/Integer_programming |
Let
a
{\displaystyle a}
be the numeric measure of
A
{\displaystyle A}
defined as the maximum absolute value of any entry of
A
{\displaystyle A}
. Let
n
... | https://en.wikipedia.org/wiki/Integer_programming |
,
d
)
n
k
{\displaystyle f(a,d)n^{k}}
. In particular, the time is independent of the right-hand side
b
{\displaystyle b}
and objective function
c
... | https://en.wikipedia.org/wiki/Integer_programming |
998). Theory of linear and integer programming. John Wiley and Sons. ISBN 978-0-471-98232-6.
Laurence A. Wolsey (1998). Integer programming. Wiley. ISBN 978-0-471-28366-9.
Dimitris Bertsimas; Robert Weismantel (2005). Optimization over integers. Dynamic Ideas. ISBN 978-0-9759146-2-5.
John K. Karlof (2006). Integer prog... | https://en.wikipedia.org/wiki/Integer_programming |
Integer Optimization: Theory and Practice. CRC Press. ISBN 978-1-498-71016-9.
== External links ==
A Tutorial on Integer Programming
Conference Integer Programming and Combinatorial Optimization, IPCO
The Aussois Combinatorial Optimization Workshop | https://en.wikipedia.org/wiki/Integer_programming |
Programming is a form of music production and performance using electronic devices and computer software, such as sequencers and workstations or hardware synthesizers, sampler and sequencers, to generate sounds of musical instruments. These musical sounds are created through the use of music coding languages. There are... | https://en.wikipedia.org/wiki/Programming_(music) |
own level of difficulty and function.
=== Alda ===
The music coding language Alda provides a tutorial on coding music and is, "designed for musicians who do not know how to program, as well as programmers who do not know how to music". The website also has links to install, tutorial, cheat sheet, docs, and community... | https://en.wikipedia.org/wiki/Programming_(music) |
development comes with more function and utility and each decade tends to favor a certain program and or piece of equipment.
=== MUSIC-N ===
The first digital synthesis family of computer programs and languages being MUSIC-N created by Max Mathews. The development of these programs, allowed for more flexibility and ... | https://en.wikipedia.org/wiki/Programming_(music) |
===
Around the time of the 1950s, electric rhythm machines began to make way into popular music. These machines began to gain much traction amongst many artists as they saw it as a way to create percussion sounds in an easier and more efficient way. Artists who used this kind of technology include J. J. Cale, Sly Ston... | https://en.wikipedia.org/wiki/Programming_(music) |
. Some notable artists who used the LM-1 were Peter Gabriel, Stevie Wonder, Michael Jackson, and Madonna. These developments continued to happen in future decades leading to the creation of new electrical instruments such as the Theremin, Hammond organ, electric guitar, synthesizer, and digital sampler. Other technolog... | https://en.wikipedia.org/wiki/Programming_(music) |
usic was made and recorded began to change. For instance, many artists began to record their beats by programming instead of recording a live drummer.
=== Music programming in the early 2000s ===
Today, music programming is very common, with artists using software on a computer to produce music and not actually using... | https://en.wikipedia.org/wiki/Programming_(music) |
Pro, Ableton Live, Presonus Studio One, Magix Samplitude Pro X, Cockos Reaper, Propellerhead Reason, Steinberg Cubase Pro, GarageBand, and Bitwig Studio.
== Equipment ==
Technology: digital audio workstation, drum machine, groovebox, sampler, sequencer, synthesizer and MIDI
== References ==
== External links ==
D... | https://en.wikipedia.org/wiki/Programming_(music) |
Fetal programming, also known as prenatal programming, is the theory that environmental cues experienced during fetal development play a seminal role in determining health trajectories across the lifespan.
Three main forms of programming that occur due to changes in the maternal environment are:
Changes in development... | https://en.wikipedia.org/wiki/Fetal_programming |
tch famine of 1944–45. The famine caused severe malnutrition among the population, including women in various stages of pregnancy. The Dutch Famine Birth Cohort Study examined the impact of lack of nutrition on children born during or after this famine. It showed that throughout their life, these children were at great... | https://en.wikipedia.org/wiki/Fetal_programming |
gh nutrition. This leads to increased risk of metabolic syndrome.
== Nutritional status ==
The developing fetus forms an impression of the world into which it will be born via its mother's nutritional status. Its development is thus modulated to create the best chance of survival. However, excessive or insufficient n... | https://en.wikipedia.org/wiki/Fetal_programming |
systems of the fetus, and renders it impossible to maintain normal blood pressure levels.
=== Insufficient nutrition ===
Pre-eclampsia, involving oxygen deprivation and death of trophoblastic cells that make up most of the placenta, is a disease which is often associated with maladaptive long-term consequences of ina... | https://en.wikipedia.org/wiki/Fetal_programming |
uld be altered by the mental state of the mother, due to affected glucocorticoid transfer that takes place across the placenta.
=== Thyroid ===
Thyroid hormones play an instrumental role during the early development of the fetus's brain. Therefore, mothers suffering from thyroid-related issues and altered thyroid hor... | https://en.wikipedia.org/wiki/Fetal_programming |
ental effects during prenatal development, excess cortisol exposure has deleterious effects on fetal growth, the postnatal function of physiological systems such as the hypothalamic-pituitary-adrenal axis and brain structure or connectivity (e.g., amygdala).
During gestation, cortisol concentrations in maternal circul... | https://en.wikipedia.org/wiki/Fetal_programming |
fetus in the uterus, predominantly via hormones and genetics. The mother's mood, including maternal prenatal anxiety, depression and stress during pregnancy correlates with altered outcomes for the child. That being said, not every fetus exposed to these factors is affected in the same way and to the same degree, and ... | https://en.wikipedia.org/wiki/Fetal_programming |
environment for the baby whilst the mother suffers from depression.
=== Psychological stress ===
Maternally experienced psychological stress that occurs either before or during gestation can have intergenerational effects on offspring. Stress experienced during gestation has been linked with preterm delivery, low bi... | https://en.wikipedia.org/wiki/Fetal_programming |
al and/or early postnatal exposure to alcohol (ethanol) has been found to hurt a child's neuroendocrine and behavioral factors. Alcohol passes through the placenta on being ingested by the mother during her pregnancy, and makes its way to the baby in utero. Changes posed to the fetus through ethanol exposure may signif... | https://en.wikipedia.org/wiki/Fetal_programming |
e (MTSE), can contribute towards various problems in babies of smoking mothers. About 20% of mothers smoke whilst pregnant and this is associated with increased risk of complications, such as preterm birth, decreased fetal growth leading to lower birth weight, and impaired fetal lung development.
=== Drugs ===
There ... | https://en.wikipedia.org/wiki/Fetal_programming |
Fetal Programming's website. | https://en.wikipedia.org/wiki/Fetal_programming |
Logic programming is a programming, database and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical form, representing knowledge about some problem domain. Computation is performed by applying logical reasoning to that knowledge, to solve problems in the domain. M... | https://en.wikipedia.org/wiki/Logic_programming |
clauses), all of the A, B1, ..., Bn are atomic formulae of the form p(t1 ,..., tm), where p is a predicate symbol naming a relation, like "motherhood", and the ti are terms naming objects (or individuals). Terms include both constant symbols, like "charles", and variables, such as X, which start with an upper case lett... | https://en.wikipedia.org/wiki/Logic_programming |
For example, the definition of sibling uses a negative condition, where the predicate = is defined by the clause X = X :
Logic programming languages that include negative conditions have the knowledge representation capabilities of a non-monotonic logic.
In ASP and Datalog, logic programs have only a declarative read... | https://en.wikipedia.org/wiki/Logic_programming |
ield of logic programming has been concerned with trying to develop a logical semantics for negation as failure and with developing other semantics and other implementations for negation. These developments have been important, in turn, for supporting the development of formal methods for logic-based program verificati... | https://en.wikipedia.org/wiki/Logic_programming |
programming language that places no constraints on the order in which operations are performed.
Logic programming, with its current syntax of facts and rules, can be traced back to debates in the late 1960s and early 1970s about declarative versus procedural representations of knowledge in artificial intelligence. Adv... | https://en.wikipedia.org/wiki/Logic_programming |
e. goal-reduction or backward chaining) and from assertions (i.e. forward chaining). The most influential implementation of Planner was the subset of Planner, called Micro-Planner, implemented by Gerry Sussman, Eugene Charniak and Terry Winograd. Winograd used Micro-Planner to implement the landmark, natural-language u... | https://en.wikipedia.org/wiki/Logic_programming |
eille was working on natural-language understanding, using logic to represent semantics and using resolution for question-answering. During the summer of 1971, Colmerauer invited Kowalski to Marseille, and together they discovered that the clausal form of logic could be used to represent formal grammars and that resolu... | https://en.wikipedia.org/wiki/Logic_programming |
1974.
Colmerauer, with Philippe Roussel, used the procedural interpretation as the basis of Prolog, which was implemented in the summer and autumn of 1972. The first Prolog program, also written in 1972 and implemented in Marseille, was a French question-answering system. The use of Prolog as a practical programming la... | https://en.wikipedia.org/wiki/Logic_programming |
amming to develop advanced Artificial Intelligence applications on massively parallel computers. Although the project initially explored the use of Prolog, it later adopted the use of concurrent logic programming, because it was closer to the FGCS computer architecture.
However, the committed choice feature of concurre... | https://en.wikipedia.org/wiki/Logic_programming |
independently of the FGCS project. In particular, although Prolog was developed to combine declarative and procedural representations of knowledge, the purely declarative interpretation of logic programs became the focus for applications in the field of deductive databases. Work in this field became prominent around 1... | https://en.wikipedia.org/wiki/Logic_programming |
2001, the journal was renamed The Journal of Logic and Algebraic Programming, and the official journal of ALP became Theory and Practice of Logic Programming, published by Cambridge University Press.
== Concepts ==
Logic programs enjoy a rich variety of semantics and problem solving methods, as well as a wide range ... | https://en.wikipedia.org/wiki/Logic_programming |
gy by using different logical representations.
The two main problem-solving strategies are backward reasoning (goal reduction) and forward reasoning, also known as top-down and bottom-up reasoning, respectively.
In the simple case of a propositional Horn clause program and a top-level atomic goal, backward reasoning de... | https://en.wikipedia.org/wiki/Logic_programming |
are considered at a time. For example, subgoals can be solved in parallel, and clauses can also be tried in parallel. The first strategy is called and-parallel and the second strategy is called or-parallel. Other search strategies, such as intelligent backtracking, or best-first search to find an optimal solution, are ... | https://en.wikipedia.org/wiki/Logic_programming |
s is a sensible problem-solving strategy. Here is another example, where forward reasoning beats backward reasoning in a more conventional computation task, where the goal ?- fibonacci(n, Result) is to find the nth fibonacci number:
Here the relation fibonacci(N, M) stands for the function fibonacci(N) = M, and the pr... | https://en.wikipedia.org/wiki/Logic_programming |
ontrast, forward reasoning generates the sequence of fibonacci numbers, starting from 0 and 1 without any recomputation, and its complexity is linear with respect to n.
Prolog cannot perform forward reasoning directly. But it can achieve the effect of forward reasoning within the context of backward reasoning by means ... | https://en.wikipedia.org/wiki/Logic_programming |
s relations.
Compared with relational syntax, functional syntax is more compact for nested functions. For example, in functional syntax the definition of maternal grandmother can be written in the nested form:
The same definition in relational notation needs to be written in the unnested, flattened form:
However, nes... | https://en.wikipedia.org/wiki/Logic_programming |
mming languages in the sense of this article.
However, the relational language RML is an imperative programming language
whose core construct is a
relational expression, which is similar to an expression in first-order predicate logic.
Other relational programming languages are based on the relational calculus or rela... | https://en.wikipedia.org/wiki/Logic_programming |
as providing a separate proof-theoretic (or operational) semantics for logic programs. But from a logical point of view, they are proof methods, rather than semantics.
The other approach to the declarative semantics of Horn clause programs is the satisfiability semantics, which understands solving a goal as showing tha... | https://en.wikipedia.org/wiki/Logic_programming |
also has an alternative, more mathematical characterisation as the least fixed point of the function that uses the rules in the program to derive new facts from existing facts in one step of inference.
Remarkably, the same problem-solving methods of forward and backward reasoning, which were originally developed for t... | https://en.wikipedia.org/wiki/Logic_programming |
s 0, 1, 2, ... as a sequence of terms of the form 0, s(0), s(s(0)), .... In general, the term s(X) represents the successor of X, namely X + 1. Here are the standard definitions of addition and multiplication in functional notation:
X + 0 = X.
X + s(Y) = s(X + Y).
i.e. X + (Y + 1) = (X + Y) + 1
X ×... | https://en.wikipedia.org/wiki/Logic_programming |
= 5 is true. But with the satisfiability semantics, there is only one model, namely the standard model of arithmetic, in which 2 + 2 = 5 is false.
In both semantics, the goal ?- add(s(s(0)), s(s(0)), s(s(s(s(s(0)))))) fails. In the satisfiability semantics, the failure of the goal means that the truth value of the goal... | https://en.wikipedia.org/wiki/Logic_programming |
y of reasoning with the logical consequence semantics using the completion of a logic program in first-order logic.
Completion amounts roughly to regarding the set of all the program clauses with the same predicate in the head, say:
A :- Body1.
...
A :- Bodyk.
as a definition of the predicate:
A iff (Body1 or... | https://en.wikipedia.org/wiki/Logic_programming |
t cannot be shown that tom is a minor.
If, however, we receive new information that tom is indeed a minor, the previous conclusion that tom should be punished is replaced by the new conclusion that tom should be rehabilitated:
This property of withdrawing a conclusion when new information is added, is called non-monot... | https://en.wikipedia.org/wiki/Logic_programming |
ntics, negation is interpreted according to the classical definition of truth in an intended or standard model of the logic program.
In the case of logic programs with negative conditions, there are two main variants of the satisfiability semantics: In the well-founded semantics, the intended model of a logic program i... | https://en.wikipedia.org/wiki/Logic_programming |
r sanctioning thieves is (locally) stratified, and all three semantics for the program determine the same intended model:
Attempts to understand negation in logic programming have also contributed to the development of abstract argumentation frameworks. In an argumentation interpretation of negation, the initial argum... | https://en.wikipedia.org/wiki/Logic_programming |
where true represents an empty conjunction, and (B,C) is a composite term representing the conjunction of B and C. The predicate clause(A,B) means that there is a clause of the form A :- B.
Metaprogramming is an application of the more general use of a metalogic or metalanguage to describe and reason about another lan... | https://en.wikipedia.org/wiki/Logic_programming |
, are "very similar" to logical conditionals, but they are simpler and have greater psychological plausibility (page 51). Among other differences between logic and rules, he argues that logic uses deduction, but rules use search (page 45) and can be used to reason either forward or backward (page 47). Sentences in logi... | https://en.wikipedia.org/wiki/Logic_programming |
asoning, and goal-reduction - are also defining characteristics of logic programming. This suggests that Thagard's conclusion (page 56) that:
Much of human knowledge is naturally described in terms of rules, and many kinds of thinking such as planning can be modeled by rule-based systems.
also applies to logic progra... | https://en.wikipedia.org/wiki/Logic_programming |
o code "temporal notions in natural language by looking at the way human beings construct time".
=== Knowledge representation ===
The use of logic to represent procedural knowledge and strategic information was one of the main goals contributing to the early development of logic programming. Moreover, it continues to... | https://en.wikipedia.org/wiki/Logic_programming |
se states that a fact holds immediately after an event initiates (or causes) the fact. The second clause is a frame axiom, which states that a fact that holds at a time continues to hold at the next time unless it is terminated by an event that happens at the time. This formulation allows more than one event to occur a... | https://en.wikipedia.org/wiki/Logic_programming |
le and a red block is stacked on the green block (like a traffic light). At time 0, the red block is moved to the table. At time 1, the green block is moved onto the red block. Moving an object onto a place terminates the fact that the object is on any place, and initiates the fact that the object is on the place to wh... | https://en.wikipedia.org/wiki/Logic_programming |
, when logic programs are used to represent the existing, explicit rules of a business organisation or legal authority.
For example, here is a representation of a simplified version of the first sentence of the British Nationality Act, which states that a person who is born in the UK becomes a British citizen at the ti... | https://en.wikipedia.org/wiki/Logic_programming |
l rule base in the world.
== Variants and extensions ==
=== Prolog ===
The SLD resolution rule of inference is neutral about the order in which subgoals in the bodies of clauses can be selected for solution. For the sake of efficiency, Prolog restricts this order to the order in which the subgoals are written. SLD... | https://en.wikipedia.org/wiki/Logic_programming |
the top of the stack, and retrying the attempted solution of the selected subgoal in the previous goal clause using the next clause that matches the selected subgoal.
Backtracking can be restricted by using a subgoal, called cut, written as !, which always succeeds but cannot be backtracked. Cut can be used to improve ... | https://en.wikipedia.org/wiki/Logic_programming |
ge of state:
The sequence of move events and the resulting locations of the blocks can be computed by executing the query:
Various extensions of logic programming have been developed to provide a logical framework for such destructive change of state.
The broad range of Prolog applications, both in isolation and in c... | https://en.wikipedia.org/wiki/Logic_programming |
program, but are predefined by some domain-specific model-theoretic structure or theory.
Procedurally, subgoals whose predicates are defined by the program are solved by goal-reduction, as in ordinary logic programming, but constraints are simplified and checked for satisfiability by a domain-specific constraint-solver... | https://en.wikipedia.org/wiki/Logic_programming |
queries the database to find out when john both taught logic and was a professor:
The solution
2010 ≤ T, T ≤ 2012
results from simplifying the constraints
2005 ≤ T, T ≤ 2012, 2010 ≤ T, T < 2014.
Constraint logic programming has been used to solve problems in such fields as civil engineering, mechanical engineeri... | https://en.wikipedia.org/wiki/Logic_programming |
ons as part of the database itself.
It was recognized early in the development of relational databases that recursive queries cannot be expressed in either relational algebra or relational calculus, and that this defficiency can be remedied by introducing a least-fixed-point operator. In contrast, recursive relations c... | https://en.wikipedia.org/wiki/Logic_programming |
ling gives the same answers and terminates without looping.
=== Answer set programming ===
Like Datalog, Answer Set programming (ASP) is not Turing-complete. Moreover, instead of separating goals (or queries) from the program to be used in solving the goals, ASP treats the whole program as a goal, and solves the go... | https://en.wikipedia.org/wiki/Logic_programming |
tion of this constraint, the problem now has only two solutions:
The addition of constraints of the form :- Body. eliminates models in which Body is true.
Confusingly, constraints in ASP are different from constraints in CLP. Constraints in CLP are predicates that qualify answers to queries (and solutions of goals). C... | https://en.wikipedia.org/wiki/Logic_programming |
c problem solver, such as the DPLL algorithm or a Boolean SAT solver. However, some implementations, such as s(CASP) use a goal-directed, top-down, SLD resolution-like procedure without
grounding.
=== Abductive logic programming ===
Abductive logic programming (ALP), like CLP, extends normal logic programming by all... | https://en.wikipedia.org/wiki/Logic_programming |
case a solution is a plan for achieving the goal.
We can use the rules for cause and effect presented earlier to solve the goal, by treating the happens predicate as abducible:
ALP solves the goal by reasoning backwards and adding assumptions to the program, to solve abducible subgoals. In this case there are many al... | https://en.wikipedia.org/wiki/Logic_programming |
(ILP) is an approach to machine learning that induces logic programs as hypothetical generalisations of positive and negative examples. Given a logic program representing background knowledge and positive examples together with constraints representing negative examples, an ILP system induces a logic program that gener... | https://en.wikipedia.org/wiki/Logic_programming |
ation:
Stuart Russell has referred to such invention of new concepts as the most important step needed for reaching human-level AI.
Recent work in ILP, combining logic programming, learning and probability, has given rise to the fields of statistical relational learning and probabilistic inductive logic programming.
... | https://en.wikipedia.org/wiki/Logic_programming |
procedurally, when there are several clauses whose heads H match a given goal, then all of the clauses are executed in parallel, checking whether their guards G1, ... , Gn hold. If the guards of more than one clause hold, then a committed choice is made to one of the clauses, and execution proceeds with the subgoals B1... | https://en.wikipedia.org/wiki/Logic_programming |
of | in the second and third clauses is the list constructor, whereas the second occurrence of | is the commitment operator.) The program can be used, for example, to shuffle the lists [ace, queen, king] and [1, 4, 2] by invoking the goal clause:
The program will non-deterministically generate a single solution, for... | https://en.wikipedia.org/wiki/Logic_programming |
rd, which is a set of constraints that may block the applicability of the clause. When the guards of several clauses are satisfied, concurrent constraint logic programming makes a committed choice to use only one.
=== Higher-order logic programming ===
Several researchers have extended logic programming with higher-o... | https://en.wikipedia.org/wiki/Logic_programming |
LO, Lolli, ACL, and Forum. Forum provides a goal-directed interpretation of all linear logic.
=== Object-oriented logic programming ===
F-logic extends logic programming with objects and the frame syntax.
Logtalk extends the Prolog programming language with support for objects, protocols, and other OOP concepts. It ... | https://en.wikipedia.org/wiki/Logic_programming |
nce (includes Formal methods)
Logic programming languages
Programmable logic controller
R++
Reasoning system
Rule-based machine learning
Satisfiability
Syntax and semantics of logic programming
== Citations ==
== Sources ==
=== General introductions ===
Baral, C.; Gelfond, M. (1994). "Logic programming and knowle... | https://en.wikipedia.org/wiki/Logic_programming |
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