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AGM Postulates
Belief revision is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents. What makes belief revision non-trivial is that several different ways for performing this operation may be possible. For example, if the current knowledge includes the three facts " A displaystyle A is true", " B displaystyle B is true" and "if A displaystyle A and B displaystyle B are true then C displaystyle C is true", the introduction of the new information " C displaystyle C is false" can be done preserving consistency only by removing at least one of the three facts. In this case, there are at least three different ways for performing revision
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Formal Logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science.[1] The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems. Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see Logic
Logic
in computer science for those. Since its inception, mathematical logic has both contributed to, and has been motivated by, the study of foundations of mathematics
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Defeasible Reasoning
In logic, defeasible reasoning is a kind of reasoning that is rationally compelling, though not deductively valid.[1]Contents1 Overview 2 History 3 Political and judicial use 4 Specificity 5 Nature of defeasibility 6 See also 7 References 8 Further reading 9 External linksOverview[edit] Defeasible reasoning is a particular kind of non-demonstrative reasoning, where the reasoning does not produce a full, complete, or final demonstration of a claim, i.e., where fallibility and corrigibility of a conclusion are acknowledged. In other words, defeasible reasoning produces a contingent statement or claim. Other kinds of non-demonstrative reasoning are probabilistic reasoning, inductive reasoning, statistical reasoning, abductive reasoning, and paraconsistent reasoning
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Polynomial Hierarchy
In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes P, NP and co-NP to oracle machines
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Cyc
Cyc (/ˈsaɪk/) is the world's longest-lived artificial intelligence project, attempting to assemble a comprehensive ontology and knowledge base that spans the basic concepts and "rules of thumb" about how the world works (think common sense knowledge but focusing more on things that rarely get written down or said, in contrast with facts one might find somewhere on the internet or retrieve via Google or), with the goal of enabling AI applications to perform human-like reasoning and be less "brittle" when confronted with novel situations that were not preconceived. Douglas Lenat
Douglas Lenat
began the project in July, 1984 at MCC, where he was Principal Scientist 1984-1994, and then, since January 1995, has been under active development by the Cycorp company, where he was CEO until early 2017
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Bayesian Inference
Bayesian inference
Bayesian inference
is a method of statistical inference in which Bayes' theorem
Bayes' theorem
is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference
Bayesian inference
is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference
Bayesian inference
has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law
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Artificial Intelligence
Artificial intelligence
Artificial intelligence
(AI, also machine intelligence, MI) is intelligence demonstrated by machines, in contrast to the natural intelligence (NI) displayed by humans and other animals
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Inquiry
An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem
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Knowledge Representation
Knowledge representation and reasoning (KR) is the field of artificial intelligence (AI) dedicated to representing information about the world in a form that a computer system can utilize to solve complex tasks such as diagnosing a medical condition or having a dialog in a natural language. Knowledge representation incorporates findings from psychology[citation needed] about how humans solve problems and represent knowledge in order to design formalisms that will make complex systems easier to design and build. Knowledge representation and reasoning also incorporates findings from logic to automate various kinds of reasoning, such as the application of rules or the relations of sets and subsets. Examples of knowledge representation formalisms include semantic nets, systems architecture, frames, rules, and ontologies
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Belief Propagation
Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks
Bayesian networks
and Markov random fields. It calculates the marginal distribution for each unobserved node, conditional on any observed nodes
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Reason Maintenance
Reason maintenance[1][2] is a knowledge representation approach to efficient handling of inferred information that is explicitly stored. Reason maintenance distinguishes between base facts, which can be defeated, and derived facts. As such it differs from belief revision which, in its basic form, assumes that all facts are equally important. Reason maintenance was originally developed as a technique for implementing problem solvers.[2] It encompasses a variety of techniques that share a common architecture:[3] two components—a reasoner and a reason maintenance system—communicate with each other via an interface. The reasoner uses the reason maintenance system to record its inferences and justifications of ("reasons" for) the inferences. The reasoner also informs the reason maintenance system which are the currently valid base facts (assumptions)
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Epistemic Closure
Epistemic closure[1] is a property of some belief systems. It is the principle that if a subject S displaystyle S knows p displaystyle p , and S displaystyle S knows that p displaystyle p entails q displaystyle q , then S displaystyle S can thereby come to know q displaystyle q . Most epistemological theories involve a closure principle and many skeptical arguments assume a closure principle. On the other hand, some epistemologists, including Robert Nozick, have denied closure principles on the basis of reliabilist accounts of knowledge. Nozick, in Philosophical Explanations, advocated that, when considering the Gettier problem, the least counter-intuitive assumption we give up should be epistemic closure
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Non-monotonic Logic
A non-monotonic logic is a formal logic whose consequence relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences (cf. defeasible reasoning), i.e., a kind of inference in which reasoners draw tentative conclusions, enabling reasoners to retract their conclusion(s) based on further evidence.[1] Most studied formal logics have a monotonic consequence relation, meaning that adding a formula to a theory never produces a reduction of its set of consequences. Intuitively, monotonicity indicates that learning a new piece of knowledge cannot reduce the set of what is known
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Reasoning
Reason
Reason
is the capacity for consciously making sense of things, establishing and verifying facts, applying logic, and changing or justifying practices, institutions, and beliefs based on new or existing information.[1] It is closely associated with such characteristically human activities as philosophy, science, language, mathematics, and art and is normally considered to be a distinguishing ability possessed by humans.[2] Reason, or an aspect of it, is sometimes referred to as rationality. Reasoning is associated with thinking, cognition, and intellect. The philosophical field of logic studies ways in which humans reason formally through argument.[3] Reasoning may be subdivided into forms of logical reasoning (forms associated with the strict sense): deductive reasoning, inductive reasoning, abductive reasoning; and other modes of reasoning considered more informal, such as intuitive reasoning and verbal reasoning
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Social Choice Theory
Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a collective decision or social welfare in some sense.[1] A non-theoretical example of a collective decision is enacting a law or set of laws under a constitution
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Philosophy Of Science
Philosophy
Philosophy
of science is a sub-field of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ultimate purpose of science. This discipline overlaps with metaphysics, ontology, and epistemology, for example, when it explores the relationship between science and truth. There is no consensus among philosophers about many of the central problems concerned with the philosophy of science, including whether science can reveal the truth about unobservable things and whether scientific reasoning can be justified at all. In addition to these general questions about science as a whole, philosophers of science consider problems that apply to particular sciences (such as biology or physics)
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