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Most philosophers (including Hintikka) have attacked this axiom, since numerous examples from everyday life seem to invalidate it. In general, axiom 5 is invalidated when the agent has mistaken beliefs, which can be due for example to misperceptions, lies or other forms of deception. Axiom B states that it cannot be th... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Knowledge versus Belief | 316 | 1,260 | null |
Section: Epistemic Logic > Axiomatization. The Hilbert proof system K for the basic modal logic is defined by the following axioms and inference rules: for all j ∈ A G T S {\displaystyle j\in AGTS} , The axioms of an epistemic logic obviously display the way the agents reason. For example, the axiom K together with the... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Axiomatization | 223 | 775 | null |
The following proof systems for L EL {\displaystyle {\mathcal {L}}_{\textsf {EL}}} are often used in the literature. We define the set of proof systems L EL := { K , KD45 , S4 , S4.2 , S4.3 , S4.3.2 , S4.4 , S5 } {\displaystyle \mathbb {L} _{\textsf {EL}}:=\{{\textsf {K}},{\textsf {KD45}},{\textsf {S4}},{\textsf {S4.2}... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Axiomatization | 295 | 669 | null |
Moreover, for all H ∈ L EL {\displaystyle {\mathcal {H}}\in \mathbb {L} _{\textsf {EL}}} , we define the proof system H C {\displaystyle {\mathcal {H}}^{\textsf {C}}} by adding the following axiom schemes and rules of inference to those of H {\displaystyle {\mathcal {H}}} . For all A ⊆ A G T S {\displaystyle A\subseteq... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Axiomatization | 347 | 805 | null |
{\displaystyle {\textsf {S4}}\subset {\textsf {S4.2}}\subset {\textsf {S4.3}}\subset {\textsf {S4.3.2}}\subset {\textsf {S4.4}}\subset {\textsf {S5}}.} So, all the theorems of S4.2 {\displaystyle {\textsf {S4.2}}} are also theorems of S4.3 , S4.3.2 , S4.4 {\displaystyle {\textsf {S4.3}},{\textsf {S4.3.2}},{\textsf {S4.... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Axiomatization | 245 | 527 | null |
Many philosophers claim that in the most general cases, the logic of knowledge is S4.2 {\displaystyle {\textsf {S4.2}}} or S4.3 {\displaystyle {\textsf {S4.3}}} . Typically, in computer science and in many of the theories developed in artificial intelligence, the logic of belief (doxastic logic) is taken to be KD45 {\d... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Axiomatization | 221 | 775 | null |
Br {\displaystyle {\textsf {Br}}} has been propounded by Floridi as the logic of the notion of 'being informed’ which mainly differs from the logic of knowledge by the absence of introspection for the agents. For all H ∈ L EL {\displaystyle {\mathcal {H}}\in \mathbb {L} _{\textsf {EL}}} , the class of H {\displaystyle ... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Axiomatization | 286 | 827 | null |
Then, for all H ∈ L EL {\displaystyle {\mathcal {H}}\in \mathbb {L} _{\textsf {EL}}} , H {\displaystyle {\mathcal {H}}} is sound and strongly complete for L EL {\displaystyle {\mathcal {L}}_{\textsf {EL}}} w.r.t. the class of H {\displaystyle {\mathcal {H}}} –models, and H C {\displaystyle {\mathcal {H}}^{\textsf {C}}}... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Axiomatization | 210 | 500 | null |
Section: Epistemic Logic > Decidability and Complexity. The satisfiability problem for all the logics introduced is decidable. We list below the computational complexity of the satisfiability problem for each of them. Note that it becomes linear in time if there are only finitely many propositional letters in the langu... | Wikipedia - Dynamic epistemic logic - Epistemic Logic > Decidability and Complexity | 155 | 710 | null |
Section: Adding Dynamics. Dynamic Epistemic Logic (DEL) is a logical framework for modeling epistemic situations involving several agents, and changes that occur to these situations as a result of incoming information or more generally incoming action. The methodology of DEL is such that it splits the task of represent... | Wikipedia - Dynamic epistemic logic - Adding Dynamics | 238 | 1,251 | null |
Section: Adding Dynamics > Public Events. In this section, we assume that all events are public. We start by giving a concrete example where DEL can be used, to better understand what is going on. This example is called the muddy children puzzle. Then, we will present a formalization of this puzzle in a logic called Pu... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Public Events | 321 | 1,398 | null |
States s , t , u , v {\displaystyle s,t,u,v} intuitively represent possible worlds, a proposition (for example p {\displaystyle p} ) satisfiable at one of these worlds intuitively means that in the corresponding possible world, the intuitive interpretation of p {\displaystyle p} (A is dirty) is true. The links between ... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Public Events | 348 | 1,501 | null |
This suppression is what we call the update. We then get the model depicted below. As a result of the announcement, both A and B do know that at least one of them is dirty. We can read this from the epistemic model. Now suppose there is a second (and final) announcement that says that neither knows they are dirty (an a... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Public Events | 301 | 1,338 | null |
We define the language L P A L {\displaystyle {{\mathcal {L}}_{PAL}}} inductively by the following grammar in BNF: L P A L : ϕ ::= p ∣ ¬ ϕ ∣ ( ϕ ∧ ϕ ) ∣ K j ϕ ∣ [ ϕ ! ] ϕ {\displaystyle {{\mathcal {L}}_{PAL}}:\phi ~~::=~~p~\mid ~\neg \phi ~\mid ~(\phi \land \phi )~\mid ~K_{j}\phi ~\mid ~[\phi !]\phi } where j ∈ A G T S... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Public Events | 231 | 623 | null |
The truth condition for the new dynamic action modality [ ψ ! ] ϕ {\displaystyle [\psi !]\phi } is defined as follows: where M ψ := ( W ψ , R 1 ψ , … , R n ψ , I ψ ) {\displaystyle {\mathcal {M}}^{\psi }:=(W^{\psi },R_{1}^{\psi },\ldots ,R_{n}^{\psi },I^{\psi })} with W ψ := { w ∈ W ; M , w ⊨ ψ } {\displaystyle W^{\psi... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Public Events | 321 | 661 | null |
The formula [ ψ ! ] ϕ {\displaystyle [\psi !]\phi } intuitively means that after a truthful announcement of ψ {\displaystyle \psi } , ϕ {\displaystyle \phi } holds. A public announcement of a proposition ψ {\displaystyle \psi } changes the current epistemic model like in the figure below. The proof system H P A L {\dis... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Public Events | 346 | 1,131 | null |
PAL is decidable, its model checking problem is solvable in polynomial time and its satisfiability problem is PSPACE-complete. Muddy children puzzle formalized with PAL: Here are some of the statements that hold in the muddy children puzzle formalized in PAL. N , s ⊨ p ∧ q {\displaystyle {\mathcal {N}},s\models p\land ... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Public Events | 338 | 937 | null |
However: N , s ⊨ [ p ∨ q ! ] ( ( ¬ K A p ∧ ¬ K A ¬ p ) ∧ ( ¬ K B q ∧ ¬ K B ¬ q ) ) {\displaystyle {\mathcal {N}},s\models [p\vee q!]((\neg K_{A}p\land \neg K_{A}\neg p)\land (\neg K_{B}q\land \neg K_{B}\neg q))} 'After the public announcement that at least one of the children A and B is dirty, they still do not know th... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Public Events | 334 | 788 | null |
Moreover: N , s ⊨ [ p ∨ q ! ] [ ( ¬ K A p ∧ ¬ K A ¬ p ) ∧ ( ¬ K B q ∧ ¬ K B ¬ q ) ! ] ( K A p ∧ K B q ) {\displaystyle {\mathcal {N}},s\models [p\vee q!][(\neg K_{A}p\land \neg K_{A}\neg p)\land (\neg K_{B}q\land \neg K_{B}\neg q)!](K_{A}p\land K_{B}q)} 'After the successive public announcements that at least one of th... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Public Events | 267 | 877 | null |
Section: Adding Dynamics > Arbitrary Events > Event Model. Epistemic models are used to model how agents perceive the actual world. Their perception can also be described in terms of knowledge and beliefs about the world and about the other agents’ beliefs. The insight of the DEL approach is that one can describe how a... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Arbitrary Events > Event Model | 325 | 1,363 | null |
Intuitively, f ∈ R j ( e ) {\displaystyle f\in R_{j}(e)} means that while the possible event represented by e {\displaystyle e} is occurring, agent j {\displaystyle j} considers possible that the possible event represented by f {\displaystyle f} is actually occurring. An event model is a tuple E = ( W α , R 1 α , … , R... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Arbitrary Events > Event Model | 351 | 980 | null |
An event model is a tuple E = ( W α , R 1 α , … , R m α , I α ) {\displaystyle {\mathcal {E}}=(W^{\alpha },R_{1}^{\alpha },\ldots ,R_{m}^{\alpha },I^{\alpha })} where: W α {\displaystyle W^{\alpha }} is a non-empty set of possible events, R j α ⊆ W α × W α {\displaystyle R_{j}^{\alpha }\subseteq W^{\alpha }\times W^{\a... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Arbitrary Events > Event Model | 445 | 1,106 | null |
R j α ( e ) {\displaystyle R_{j}^{\alpha }(e)} denotes the set { f ∈ W α ; ( e , f ) ∈ R j α } {\displaystyle \{f\in W^{\alpha };(e,f)\in R_{j}^{\alpha }\}} .We write e ∈ E {\displaystyle e\in {\mathcal {E}}} for e ∈ W α {\displaystyle e\in W^{\alpha }} , and ( E , e ) {\displaystyle ({\mathcal {E}},e)} is called a poi... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Arbitrary Events > Event Model | 306 | 884 | null |
This event is represented below in the event model ( E , e ) {\displaystyle ({\mathcal {E}},e)} . The possible event e {\displaystyle e} corresponds to the actual event ‘players A {\displaystyle A} and B {\displaystyle B} show their and cards respectively to each other’ (with precondition A ∧ B {\displaystyle {\color {... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Arbitrary Events > Event Model | 346 | 1,243 | null |
Another example of event model is given below. This second example corresponds to the event whereby Player A {\displaystyle A} shows her red card publicly to everybody. Player A {\displaystyle A} shows her red card, players A {\displaystyle A} , B {\displaystyle B} and C {\displaystyle C} ‘know’ it, players A {\display... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Arbitrary Events > Event Model | 160 | 590 | null |
Section: Adding Dynamics > Arbitrary Events > Product Update. The DEL product update is defined below. This update yields a new pointed epistemic model ( M , w ) ⊗ ( E , e ) {\displaystyle ({\mathcal {M}},w)\otimes ({\mathcal {E}},e)} representing how the new situation which was previously represented by ( M , w ) {\di... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Arbitrary Events > Product Update | 279 | 748 | null |
Let M = ( W , R 1 , … , R n , I ) {\displaystyle {\mathcal {M}}=(W,R_{1},\ldots ,R_{n},I)} be an epistemic model and let E = ( W α , R 1 α , … , R n α , I α ) {\displaystyle {\mathcal {E}}=(W^{\alpha },R_{1}^{\alpha },\ldots ,R_{n}^{\alpha },I^{\alpha })} be an event model. The product update of M {\displaystyle {\math... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Arbitrary Events > Product Update | 484 | 1,046 | null |
The product update of M {\displaystyle {\mathcal {M}}} and E {\displaystyle {\mathcal {E}}} is the epistemic model M ⊗ E = ( W ⊗ , R 1 ⊗ , … , R n ⊗ , I ⊗ ) {\displaystyle {\mathcal {M}}\otimes {\mathcal {\mathcal {E}}}=(W^{\otimes },R_{1}^{\otimes },\ldots ,R_{n}^{\otimes },I^{\otimes })} defined as follows: for all v... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Arbitrary Events > Product Update | 357 | 835 | null |
This definition of the product update is conceptually grounded. Card Example: As a result of the first event described above (Players A {\displaystyle A} and B {\displaystyle B} show their cards to each other in front of player C {\displaystyle C} ), the agents update their beliefs. We get the situation represented in ... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Arbitrary Events > Product Update | 306 | 929 | null |
The result of the second event is represented below. In this pointed epistemic model, the following statement holds: ( M , w ) ⊗ ( F , e ) ⊨ C { B , C } ( A ∧ B ∧ C ) ∧ ¬ K A ( B ∧ C ) {\displaystyle ({\mathcal {M}},w)\otimes ({\mathcal {F}},e)\models C_{\{B,C\}}({\color {red}{A}}\land {\color {green}{B}}\land {\color ... | Wikipedia - Dynamic epistemic logic - Adding Dynamics > Arbitrary Events > Product Update | 306 | 959 | null |
Section: EU’s AI pledge. The government of Finland has pledged to offer the course for all EU citizens by the end of 2021, as the course is made available in all the official EU languages. The initiative was launched as part of Finland's Presidency of the Council of the European Union in 2019, with the European Commiss... | Wikipedia - Elements of AI - EU’s AI pledge | 213 | 1,102 | null |
Article: Embodied agent. In artificial intelligence, an embodied agent, also sometimes referred to as an interface agent, is an intelligent agent that interacts with the environment through a physical body within that environment. Agents that are represented graphically with a body, for example a human or a cartoon ani... | Wikipedia - Embodied agent - Summary | 183 | 992 | null |
Section: Advantages. Face-to-face communication allows communication protocols that give a much richer communication channel than other means of communicating. It enables pragmatic communication acts such as conversational turn-taking, facial expression of emotions, information structure and emphasis, visualisation and... | Wikipedia - Embodied agent - Advantages | 332 | 1,906 | null |
Section: Advantages > Applications. The rich style of communication that characterises human conversation makes conversational interaction with embodied conversational agents ideal for many non-traditional interaction tasks. A familiar application of graphically embodied agents is computer games; embodied agents are id... | Wikipedia - Embodied agent - Advantages > Applications | 245 | 1,439 | null |
Section: Contributors. Embodied cognitive science borrows heavily from embodied philosophy and the related research fields of cognitive science, psychology, neuroscience and artificial intelligence. Contributors to the field include: From the perspective of neuroscience, Gerald Edelman of the Neurosciences Institute at... | Wikipedia - Embodied cognitive science - Contributors | 344 | 1,703 | null |
Section: Traditional cognitive theory. Embodied cognitive science is an alternative theory to cognition in which it minimizes appeals to computational theory of mind in favor of greater emphasis on how an organism's body determines how and what it thinks. Traditional cognitive theory is based mainly around symbol manip... | Wikipedia - Embodied cognitive science - Traditional cognitive theory | 206 | 1,143 | null |
Section: The embodied cognitive approach > Physical attributes of the body. The first aspect of embodied cognition examines the role of the physical body, particularly how its properties affect its ability to think. This part attempts to overcome the symbol manipulation component that is a feature of the traditionalist... | Wikipedia - Embodied cognitive science - The embodied cognitive approach > Physical attributes of the body | 341 | 1,882 | null |
Section: The embodied cognitive approach > The body's role in the cognitive process. The second aspect draws heavily from George Lakoff's and Mark Johnson's work on concepts. They argued that humans use metaphors whenever possible to better explain their external world. Humans also have a basic stock of concepts in whi... | Wikipedia - Embodied cognitive science - The embodied cognitive approach > The body's role in the cognitive process | 342 | 1,765 | null |
Section: The embodied cognitive approach > Interaction of local environment. A third component of the embodied approach looks at how agents use their immediate environment in cognitive processing. Meaning, the local environment is seen as an actual extension of the body's cognitive process. The example of a personal di... | Wikipedia - Embodied cognitive science - The embodied cognitive approach > Interaction of local environment | 270 | 1,419 | null |
Section: Examples of the value of embodied approach > Bluefin tuna. Thunnus, or tuna, long baffled conventional biologists with its incredible abilities to accelerate quickly and attain great speeds. A biological examination of the tuna shows that it should not be capable of such feats. However, an answer can be found ... | Wikipedia - Embodied cognitive science - Examples of the value of embodied approach > Bluefin tuna | 160 | 820 | null |
Section: Examples of the value of embodied approach > Robots. Clark uses the example of the hopping robot constructed by Raibert and Hodgins to demonstrate further the value of the embodiment paradigm. These robots were essentially vertical cylinders with a single hopping foot. The challenge of managing the robot's beh... | Wikipedia - Embodied cognitive science - Examples of the value of embodied approach > Robots | 163 | 827 | null |
Section: Examples of the value of embodied approach > Vision. Clark distinguishes between two kinds of vision, animate and pure vision. Pure vision is an idea that is typically associated with classical artificial intelligence, in which vision is used to create a rich world model so that thought and reason can be used ... | Wikipedia - Embodied cognitive science - Examples of the value of embodied approach > Vision | 263 | 1,334 | null |
Section: Examples of the value of embodied approach > Affordance. Inspired by the work of the American psychologist James J. Gibson, this next example emphasizes the importance of action-relevant sensory information, bodily movement, and local environment cues. These three concepts are unified by the concept of afforda... | Wikipedia - Embodied cognitive science - Examples of the value of embodied approach > Affordance | 338 | 1,871 | null |
Section: General principles of intelligent behavior. In the formation of general principles of intelligent behavior, Pfeifer intended to be contrary to older principles given in traditional artificial intelligence. The most dramatic difference is that the principles are applicable only to situated robotic agents in the... | Wikipedia - Embodied cognitive science - General principles of intelligent behavior | 296 | 1,633 | null |
Additionally, it reflects the desire to exploit the associations between sensory modalities. (See redundant modalities). In terms of design, this implies that redundancy should be introduced with respect not only to one sensory modality but to several.: 448 It has been suggested that the fusion and transfer of knowledg... | Wikipedia - Embodied cognitive science - General principles of intelligent behavior | 349 | 1,800 | null |
Section: Critical responses > Traditionalist response to local environment claim. A traditionalist may argue that objects may be used to aid in cognitive processes, but this does not mean they are part of a cognitive system.: 343 Eyeglasses are used to aid in the visual process, but to say they are a part of a larger s... | Wikipedia - Embodied cognitive science - Critical responses > Traditionalist response to local environment claim | 159 | 836 | null |
Article: Empowerment (artificial intelligence). Empowerment in the field of artificial intelligence formalises and quantifies (via information theory) the potential an agent perceives that it has to influence its environment. An agent which follows an empowerment maximising policy, acts to maximise future options (typi... | Wikipedia - Empowerment (artificial intelligence) - Summary | 271 | 1,256 | null |
Section: Definition. Empowerment ( E {\displaystyle {\mathfrak {E}}} ) is defined as the channel capacity ( C {\displaystyle C} ) of the actuation channel of the agent, and is formalised as the maximal possible information flow between the actions of the agent and the effect of those actions some time later. Empowermen... | Wikipedia - Empowerment (artificial intelligence) - Definition | 266 | 836 | null |
Section: Definition > Contextual Empowerment. In general the choice of action (action distribution) that maximises empowerment varies from state to state. Knowing the empowerment of an agent in a specific state is useful, for example to construct an empowerment maximising policy. State-specific empowerment can be found... | Wikipedia - Empowerment (artificial intelligence) - Definition > Contextual Empowerment | 227 | 689 | null |
Article: Enterprise cognitive system. Enterprise cognitive systems (ECS) are part of a broader shift in computing, from a programmatic to a probabilistic approach, called cognitive computing. An Enterprise Cognitive System makes a new class of complex decision support problems computable, where the business context is ... | Wikipedia - Enterprise cognitive system - Summary | 204 | 1,031 | null |
Section: Key characteristics. ECS have to be: Adaptive: They must learn as information changes, and as goals and requirements evolve. They must resolve ambiguity and tolerate unpredictability. They must be engineered to feed on dynamic data in real time, or near real time. In the Enterprise, near-real time learning fro... | Wikipedia - Enterprise cognitive system - Key characteristics | 319 | 1,715 | null |
A stateful memory of overall interactions across communication channels is critical for understanding of context, as a static profile will not capture intent and outcome potential the way behavior does. Contextual: They must understand, identify, and extract contextual elements such as meaning, syntax, time, location, ... | Wikipedia - Enterprise cognitive system - Key characteristics | 216 | 1,141 | null |
Section: Carbon footprint. AI has a significant carbon footprint due to growing energy usage, especially due to training and usage. Researchers have argued that the carbon footprint of AI models during training should be considered when attempting to understand the impact of AI. One study suggested that by 2027, energy... | Wikipedia - Environmental impact of artificial intelligence - Carbon footprint | 338 | 1,793 | null |
GPT-3 released 552 metric tons of carbon dioxide into the atmosphere during training, "the equivalent of 123 gasoline-powered passenger vehicles driven for one year". Much of the energy cost is due to inefficient model architectures and processors. One model named BLOOM, from Hugging Face, trained with more efficient c... | Wikipedia - Environmental impact of artificial intelligence - Carbon footprint | 340 | 1,802 | null |
Other coal-fired plants in the Salt Lake City region have pushed back retirement of their coal-fired plants by up to a decade. Environmental debates have raged in both Virginia and France about whether a "moratorium" should be called for additional data centers. In 2024 at the World Economic Forum, OpenAI executive Sam... | Wikipedia - Environmental impact of artificial intelligence - Carbon footprint | 330 | 1,742 | null |
Section: Carbon footprint > Energy use and efficiency. AI chips, (i.e. GPUs) use more energy and emit more heat than traditional CPU chips. AI models with inefficiently implemented architectures, or trained on less efficient chips may use more energy. Since the 1940's the energy efficiency of computation has doubled ev... | Wikipedia - Environmental impact of artificial intelligence - Carbon footprint > Energy use and efficiency | 350 | 1,689 | null |
The Three Mile Island facility will be renamed the Crane Clean Energy Center after Chris Crane, a nuclear proponent and former CEO of Exelon who was responsible for Exelon spinoff of Constellation. In 2025, Microsoft unveiled plans to invest $80 billion in the development and expansion of data centers designed to suppo... | Wikipedia - Environmental impact of artificial intelligence - Carbon footprint > Energy use and efficiency | 338 | 1,855 | null |
The rapid proliferation of AI has created unprecedented demand for electrical power, presenting a major obstacle to the sector’s growth. E.g., in Northern Virginia, the largest global hub for AI data centers, the timeline for connecting bigger facilities—those requiring over 100 megawatts of power—to the electrical gri... | Wikipedia - Environmental impact of artificial intelligence - Carbon footprint > Energy use and efficiency | 281 | 1,429 | null |
Section: Water usage. Cooling AI servers can demand large amounts of fresh water which is evaporated in cooling towers. In fact, data centers housing AI are globally expected to consume six times more water than the country of Denmark. By 2027, AI may use up to 6.6 billion cubic meters of water. One professor has estim... | Wikipedia - Environmental impact of artificial intelligence - Water usage | 304 | 1,444 | null |
Section: E-waste. E-waste due to production of AI hardware may also contribute to emissions. The rapid growth of AI may also lead to faster deprecation of devices, resulting in hazardous e-waste. Among the 62 million tonnes (Mt) of e-waste produced in 2022, less than one quarter of the total mass was properly recycled.... | Wikipedia - Environmental impact of artificial intelligence - E-waste | 175 | 749 | null |
Section: Climate solutions. AI has significant potential to help mitigate effects of climate change, such as through better weather predictions, disaster prevention and weather tracking. Some climate scientists have suggested that AI could be used to improve efficiencies of systems, such as renewable-energy systems. Go... | Wikipedia - Environmental impact of artificial intelligence - Climate solutions | 316 | 1,722 | null |
Section: Policy and regulation > United States. The environmental impacts of AI have been a blindspot in the range of AI legislation proposed in the US Congress. As of November 2024, the Artificial Intelligence Environmental Impacts Act of 2024 introduced in the Senate by Massachusetts Senator Ed Markey was the only fe... | Wikipedia - Environmental impact of artificial intelligence - Policy and regulation > United States | 328 | 1,906 | null |
Section: Policy and regulation > European Union. The European Union (EU) intends to regulate the environmental impact of artificial intelligence on multiple levels of government. The European Green Deal (EGD), set forth by the European Commission and approved in 2020, states its intention to utilize AI and other inform... | Wikipedia - Environmental impact of artificial intelligence - Policy and regulation > European Union | 325 | 1,831 | null |
Section: Policy and regulation > European Union > Germany. Germany published its national AI strategy in December 2020 which includes dedicated sections on the environmental impacts of AI. These begin with the federal government's intention to thoroughly research and develop AI systems that can be used to promote energ... | Wikipedia - Environmental impact of artificial intelligence - Policy and regulation > European Union > Germany | 178 | 1,005 | null |
Article: Epistemic modal logic. Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applications in many fields, including philosop... | Wikipedia - Epistemic modal logic - Summary | 157 | 770 | null |
Section: Historical development. Many papers were written in the 1950s that spoke of a logic of knowledge in passing, but the Finnish philosopher G. H. von Wright's 1951 paper titled An Essay in Modal Logic is seen as a founding document. It was not until 1962 that another Finn, Jaakko Hintikka, would write Knowledge a... | Wikipedia - Epistemic modal logic - Historical development | 198 | 944 | null |
Section: Standard possible worlds model. Most attempts at modeling knowledge have been based on the possible worlds model. In order to do this, we must divide the set of possible worlds between those that are compatible with an agent's knowledge, and those that are not. This generally conforms with common usage. If I k... | Wikipedia - Epistemic modal logic - Standard possible worlds model | 313 | 1,580 | null |
Section: Standard possible worlds model > Syntax. The basic modal operator of epistemic logic, usually written K, can be read as "it is known that," "it is epistemically necessary that," or "it is inconsistent with what is known that not." If there is more than one agent whose knowledge is to be represented, subscripts... | Wikipedia - Epistemic modal logic - Standard possible worlds model > Syntax | 332 | 1,143 | null |
The dual of K, which would be in the same relationship to K as ◊ {\displaystyle \Diamond } is to ◻ {\displaystyle \Box } , has no specific symbol, but can be represented by ¬ K a ¬ φ {\displaystyle \neg K_{a}\neg \varphi } , which can be read as " a {\displaystyle a} does not know that not φ {\displaystyle \varphi } " ... | Wikipedia - Epistemic modal logic - Standard possible worlds model > Syntax | 235 | 797 | null |
in the Muddy Children Puzzle) and distributed knowledge, three other modal operators can be added to the language. These are E G {\displaystyle {\mathit {E}}_{\mathit {G}}} , which reads "every agent in group G knows" (mutual knowledge); C G {\displaystyle {\mathit {C}}_{\mathit {G}}} , which reads "it is common knowle... | Wikipedia - Epistemic modal logic - Standard possible worlds model > Syntax | 332 | 994 | null |
Section: Standard possible worlds model > Semantics. As mentioned above, the logic-based approach is built upon the possible worlds model, the semantics of which are often given definite form in Kripke structures, also known as Kripke models. A Kripke structure M = ⟨ S , π , K 1 , … , K n ⟩ {\displaystyle {\mathcal {M}... | Wikipedia - Epistemic modal logic - Standard possible worlds model > Semantics | 342 | 1,084 | null |
It is important here not to confuse K i {\displaystyle K_{i}} , our modal operator, and K i {\displaystyle {\mathcal {K}}_{i}} , our accessibility relation. The truth assignment tells us whether or not a proposition p {\displaystyle p} is true or false in a certain state. So π ( s ) ( p ) {\displaystyle \pi (s)(p)} tel... | Wikipedia - Epistemic modal logic - Standard possible worlds model > Semantics | 299 | 942 | null |
To state that a formula φ {\displaystyle \varphi } is true at a certain world, one writes ( M , s ) ⊨ φ {\displaystyle ({\mathcal {M}},s)\models \varphi } , normally read as " φ {\displaystyle \varphi } is true at ( M , s ) {\displaystyle ({\mathcal {M}},s)} ," or " ( M , s ) {\displaystyle ({\mathcal {M}},s)} satisfie... | Wikipedia - Epistemic modal logic - Standard possible worlds model > Semantics | 287 | 827 | null |
It is useful to think of our binary relation K i {\displaystyle {\mathcal {K}}_{i}} as a possibility relation, because it is meant to capture what worlds or states agent i considers to be possible; In other words, w K i v {\displaystyle w{\mathcal {K}}_{i}v} if and only if ∀ φ [ ( w ⊨ K i φ ) ⟹ ( v ⊨ φ ) ] {\displaysty... | Wikipedia - Epistemic modal logic - Standard possible worlds model > Semantics | 278 | 1,057 | null |
Section: The properties of knowledge > The distribution axiom. This axiom is traditionally known as K. In epistemic terms, it states that if an agent knows φ {\displaystyle \varphi } and knows that φ ⟹ ψ {\displaystyle \varphi \implies \psi } , then the agent must also know ψ {\displaystyle \,\psi } . So, ( K i φ ∧ K i... | Wikipedia - Epistemic modal logic - The properties of knowledge > The distribution axiom | 175 | 593 | null |
Section: The properties of knowledge > The knowledge generalization rule. Another property we can derive is that if ϕ {\displaystyle \phi } is valid (i.e. a tautology), then K i ϕ {\displaystyle K_{i}\phi } . This does not mean that if ϕ {\displaystyle \phi } is true, then agent i knows ϕ {\displaystyle \phi } . What i... | Wikipedia - Epistemic modal logic - The properties of knowledge > The knowledge generalization rule | 205 | 737 | null |
Section: The properties of knowledge > The knowledge or truth axiom. This axiom is also known as T. It says that if an agent knows facts, the facts must be true. This has often been taken as the major distinguishing feature between knowledge and belief. We can believe a statement to be true when it is false, but it wou... | Wikipedia - Epistemic modal logic - The properties of knowledge > The knowledge or truth axiom | 161 | 631 | null |
Section: The properties of knowledge > The positive introspection axiom. This property and the next state that an agent has introspection about its own knowledge, and are traditionally known as 4 and 5, respectively. The Positive Introspection Axiom, also known as the KK Axiom, says specifically that agents know that t... | Wikipedia - Epistemic modal logic - The properties of knowledge > The positive introspection axiom | 220 | 824 | null |
Section: The properties of knowledge > The negative introspection axiom. The Negative Introspection Axiom says that agents know that they do not know what they do not know. ¬ K i φ ⟹ K i ¬ K i φ {\displaystyle \neg K_{i}\varphi \implies K_{i}\neg K_{i}\varphi } Or, equivalently, this modal axiom 5 says that agents know... | Wikipedia - Epistemic modal logic - The properties of knowledge > The negative introspection axiom | 162 | 497 | null |
Section: The properties of knowledge > Axiom systems. Different modal logics can be derived from taking different subsets of these axioms, and these logics are normally named after the important axioms being employed. However, this is not always the case. KT45, the modal logic that results from the combining of K, T, 4... | Wikipedia - Epistemic modal logic - The properties of knowledge > Axiom systems | 292 | 1,121 | null |
The basic modal operator is usually written B instead of K. In this case, though, the knowledge axiom no longer seems right—agents only sometimes believe the truth—so it is usually replaced with the Consistency Axiom, traditionally called D: ¬ B i ⊥ {\displaystyle \neg B_{i}\bot } which states that the agent does not b... | Wikipedia - Epistemic modal logic - The properties of knowledge > Axiom systems | 177 | 719 | null |
Section: Problems with the possible world model and modal model of knowledge. If we take the possible worlds approach to knowledge, it follows that our epistemic agent a knows all the logical consequences of their beliefs (known as logical omniscience). If Q {\displaystyle Q} is a logical consequence of P {\displaystyl... | Wikipedia - Epistemic modal logic - Problems with the possible world model and modal model of knowledge | 340 | 1,467 | null |
If Q {\displaystyle Q} is a logical consequence of P {\displaystyle P} (i.e. we have the tautology ⊨ ( P → Q ) {\displaystyle \models (P\rightarrow Q)} ), then we can derive K a ( P → Q ) {\displaystyle K_{a}(P\rightarrow Q)} with N, and using a conditional proof with the axiom K, we can then derive K a P → K a Q {\dis... | Wikipedia - Epistemic modal logic - Problems with the possible world model and modal model of knowledge | 342 | 1,172 | null |
Section: Epistemic fallacy (masked-man fallacy) > Examples. The name of the fallacy comes from the example: Premise 1: I know who Bob is. Premise 2: I do not know who the masked man is Conclusion: Therefore, Bob is not the masked man. The premises may be true and the conclusion false if Bob is the masked man and the sp... | Wikipedia - Epistemic modal logic - Epistemic fallacy (masked-man fallacy) > Examples | 338 | 1,111 | null |
Premise 1 B s ∀ t ( t = X → K s ( t = X ) ) {\displaystyle {\mathcal {B}}_{s}\forall t(t=X\rightarrow K_{s}(t=X))} is a very strong one, as it is logically equivalent to B s ∀ t ( ¬ K s ( t = X ) → t ≠ X ) {\displaystyle {\mathcal {B_{s}}}\forall t(\neg K_{s}(t=X)\rightarrow t\not =X)} . It is very likely that this is ... | Wikipedia - Epistemic modal logic - Epistemic fallacy (masked-man fallacy) > Examples | 268 | 752 | null |
Premise 2: Lois Lane thinks Clark Kent cannot fly. Conclusion: Therefore, Superman and Clark Kent are not the same person. Expressed in doxastic logic, the above syllogism is: Premise 1: B Lois Fly (Superman) {\displaystyle {\mathcal {B}}_{\text{Lois}}{\text{Fly}}_{\text{(Superman)}}} Premise 2: B Lois ¬ Fly (Clark) {\... | Wikipedia - Epistemic modal logic - Epistemic fallacy (masked-man fallacy) > Examples | 232 | 682 | null |
Article: Ethics of artificial intelligence. The ethics of artificial intelligence covers a broad range of topics within AI that are considered to have particular ethical stakes. This includes algorithmic biases, fairness, automated decision-making, accountability, privacy, and regulation. It also covers various emergin... | Wikipedia - Ethics of artificial intelligence - Summary | 151 | 837 | null |
Section: Machine ethics. Machine ethics (or machine morality) is the field of research concerned with designing Artificial Moral Agents (AMAs), robots or artificially intelligent computers that behave morally or as though moral. To account for the nature of these agents, it has been suggested to consider certain philos... | Wikipedia - Ethics of artificial intelligence - Machine ethics | 310 | 1,593 | null |
Inevitably, this raises the question of the environment in which such robots would learn about the world and whose morality they would inherit – or if they end up developing human 'weaknesses' as well: selfishness, pro-survival attitudes, inconsistency, scale insensitivity, etc. In Moral Machines: Teaching Robots Right... | Wikipedia - Ethics of artificial intelligence - Machine ethics | 348 | 1,827 | null |
This raised concerns about unsafe outputs from seemingly innocuous prompts. In March 2025, an AI coding assistant refused to generate additional code for a user, stating, “I cannot generate code for you, as that would be completing your work”, and that doing so could “lead to dependency and reduced learning opportuniti... | Wikipedia - Ethics of artificial intelligence - Machine ethics | 192 | 978 | null |
Section: Machine ethics > Robot rights or AI rights. "Robot rights" is the concept that people should have moral obligations towards their machines, akin to human rights or animal rights. It has been suggested that robot rights (such as a right to exist and perform its own mission) could be linked to robot duty to serv... | Wikipedia - Ethics of artificial intelligence - Machine ethics > Robot rights or AI rights | 251 | 1,299 | null |
Section: Challenges > Algorithmic biases. AI has become increasingly inherent in facial and voice recognition systems. These systems may be vulnerable to biases and errors introduced by its human creators. Notably, the data used to train them can have biases. For instance, facial recognition algorithms made by Microsof... | Wikipedia - Ethics of artificial intelligence - Challenges > Algorithmic biases | 332 | 1,762 | null |
Large companies such as IBM, Google, etc. that provide significant funding for research and development have made efforts to research and address these biases. One potential solution is to create documentation for the data used to train AI systems. Process mining can be an important tool for organizations to achieve co... | Wikipedia - Ethics of artificial intelligence - Challenges > Algorithmic biases | 337 | 1,769 | null |
AI often struggles to determine racial slurs and when they need to be censored. It struggles to determine when certain words are being used as a slur and when it is being used culturally. The reason for these biases is that AI pulls information from across the internet to influence its responses in each situation. For ... | Wikipedia - Ethics of artificial intelligence - Challenges > Algorithmic biases | 340 | 1,816 | null |
If AI implements these statistics and applies them to each patient, it could be considered biased. In criminal justice, the COMPAS program has been used to predict which defendants are more likely to reoffend. While COMPAS is calibrated for accuracy, having the same error rate across racial groups, black defendants wer... | Wikipedia - Ethics of artificial intelligence - Challenges > Algorithmic biases | 209 | 1,015 | null |
Section: Challenges > Open-source. Bill Hibbard argues that because AI will have such a profound effect on humanity, AI developers are representatives of future humanity and thus have an ethical obligation to be transparent in their efforts. Organizations like Hugging Face and EleutherAI have been actively open-sourcin... | Wikipedia - Ethics of artificial intelligence - Challenges > Open-source | 314 | 1,621 | null |
Section: Challenges > Strain on open knowledge platforms. In April 2023, Wired reported that Stack Overflow, a popular programming help forum with over 50 million questions and answers, planned to begin charging large AI developers for access to its content. The company argued that community platforms powering large la... | Wikipedia - Ethics of artificial intelligence - Challenges > Strain on open knowledge platforms | 344 | 1,770 | null |
Section: Challenges > Transparency. Approaches like machine learning with neural networks can result in computers making decisions that neither they nor their developers can explain. It is difficult for people to determine if such decisions are fair and trustworthy, leading potentially to bias in AI systems going undet... | Wikipedia - Ethics of artificial intelligence - Challenges > Transparency | 281 | 1,621 | null |
Section: Challenges > Regulation. According to a 2019 report from the Center for the Governance of AI at the University of Oxford, 82% of Americans believe that robots and AI should be carefully managed. Concerns cited ranged from how AI is used in surveillance and in spreading fake content online (known as deep fakes ... | Wikipedia - Ethics of artificial intelligence - Challenges > Regulation | 348 | 1,815 | null |
Section: Challenges > Increasing use. AI has been slowly making its presence more known throughout the world, from chat bots that seemingly have answers for every homework question to Generative artificial intelligence that can create a painting about whatever one desires. AI has become increasingly popular in hiring m... | Wikipedia - Ethics of artificial intelligence - Challenges > Increasing use | 315 | 1,722 | null |
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