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Non-monotonic Reasoning
A non-monotonic logic is a formal logic whose entailment relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences, i.e., a kind of inference in which reasoners draw tentative conclusions, enabling reasoners to retract their conclusion(s) based on further evidence. Most studied formal logics have a monotonic entailment relation, meaning that adding a formula to the hypotheses never produces a pruning of its set of conclusions. Intuitively, monotonicity indicates that learning a new piece of knowledge cannot reduce the set of what is known. Monotonic logics cannot handle various reasoning tasks such as reasoning by default (conclusions may be derived only because of lack of evidence of the contrary), abductive reasoning (conclusions are only deduced as most likely explanations), some important approaches to reasoning about knowledge (the ignorance of a conclusion must be retracted when the conclusion becomes known), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soundness
In logic and deductive reasoning, an argument is sound if it is both Validity (logic), valid in form and has no false premises. Soundness has a related meaning in mathematical logic, wherein a Formal system, formal system of logic is sound if and only if every well-formed formula that can be proven in the system is logically valid with respect to the Semantics of logic, logical semantics of the system. Definition In deductive reasoning, a sound argument is an argument that is Validity (logic), valid and all of its premises are true (and as a consequence its conclusion is true as well). An argument is valid if, assuming its premises are true, the conclusion ''must be'' true. An example of a sound argument is the following well-known syllogism: : ''(premises)'' : All men are mortal. : Socrates is a man. : ''(conclusion)'' : Therefore, Socrates is mortal. Because of the logical necessity of the conclusion, this argument is valid; and because the argument is valid and its premises ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epistemic 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 philosophy, theoretical computer science, artificial intelligence, economics, and linguistics. While philosophers since Aristotle have discussed modal logic, and Medieval philosophers such as Avicenna, Ockham, and Duns Scotus developed many of their observations, it was C. I. Lewis who created the first symbolic and systematic approach to the topic, in 1912. It continued to mature as a field, reaching its modern form in 1963 with the work of Saul Kripke. 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 unti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Logic Programming
The ''Journal of Logical and Algebraic Methods in Programming'' is a peer-reviewed scientific journal established in 1984. It was originally titled ''The Journal of Logic Programming''; in 2001 it was renamed ''The Journal of Logic and Algebraic Programming'', and in 2014 it obtained its current title. The founding editor-in-chief was J. Alan Robinson. From 1984 to 2000 it was the official journal of the Association of Logic Programming. In 2000, the association and the then editorial board started a new journal under the name ''Theory and Practice of Logic Programming'', published by Cambridge University Press. Elsevier continued the journal with a new editorial board under the title ''Journal of Logic and Algebraic Programming''. According to the ''Journal Citation Reports'', the journal has a 2013 impact factor of 0.383. See also * References External links * ''The Journal of Logic and Algebraic Programming'' Academic journals established in 1984 Computer scienc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Computer And System Sciences
The ''Journal of Computer and System Sciences'' (JCSS) is a peer-reviewed scientific journal in the field of computer science. ''JCSS'' is published by Elsevier, and it was started in 1967. Many influential scientific articles have been published in ''JCSS''; these include five papers that have won the Gödel Prize The Gödel Prize is an annual prize for outstanding papers in the area of theoretical computer science, given jointly by the European Association for Theoretical Computer Science (EATCS) and the Association for Computing Machinery Special Inter .... Its managing editor is Michael Segal. Notes References * * External links * Journal homepageScienceDirect accessDBLP information Computer science journals Elsevier academic journals {{compu-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rational Consequence Relation
In logic, a rational consequence relation is a non-monotonic consequence relation satisfying certain properties listed below. A rational consequence relation is a logical framework that refines traditional deductive reasoning to better model real-world scenarios. It incorporates rules like reflexivity, left logical equivalence, right-hand weakening, cautious monotony, disjunction on the left-hand side, logical and on the right-hand side, and rational monotony. These rules enable the relation to handle everyday situations more effectively by allowing for non-monotonic reasoning, where conclusions can be drawn based on usual rather than absolute implications. This approach is particularly useful in cases where adding more information can change the outcome, providing a more nuanced understanding than monotone consequence relations. Properties A rational consequence relation \vdash satisfies: :; REF : Reflexivity \theta \vdash \theta and the so-called Gabbay– Makinson rules: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stable Model Semantics
The concept of a stable model, or answer set, is used to define a declarative semantics for logic programs with negation as failure. This is one of several standard approaches to the meaning of negation in logic programming, along with program completion and the well-founded semantics. The stable model semantics is the basis of answer set programming. Motivation Research on the declarative semantics of negation in logic programming was motivated by the fact that the behavior of SLDNF resolution—the generalization of SLD resolution used by Prolog in the presence of negation in the bodies of rules—does not fully match the truth tables familiar from classical propositional logic. Consider, for instance, the program :p :r \leftarrow p, q :s \leftarrow p, \operatorname q. Given this program, the query will succeed, because the program includes as a fact; the query will fail, because it does not occur in the head of any of the rules. The query will fail also, because the only ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negation As Failure
Negation as failure (NAF, for short) is a non-monotonic inference rule in logic programming, used to derive \mathrm~p (i.e. that p is assumed not to hold) from failure to derive p. Note that \mathrm ~p can be different from the statement \neg p of the logical negation of p, depending on the completeness of the inference algorithm and thus also on the formal logic system. Negation as failure has been an important feature of logic programming since the earliest days of both Planner and Prolog. In Prolog, it is usually implemented using Prolog's extralogical constructs. More generally, this kind of negation is known as weak negation, in contrast with the strong (i.e. explicit, provable) negation. Planner semantics In Planner, negation as failure could be implemented as follows: :''if'' (''not'' (''goal'' p)), ''then'' (''assert'' ¬p) which says that if an exhaustive search to prove p fails, then assert ¬p. This states that proposition p shall be assumed as "not true" in any s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic 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. Major logic programming language families include Prolog, Answer Set Programming (ASP) and Datalog. In all of these languages, rules are written in the form of ''clauses'': :A :- B1, ..., Bn. and are read as declarative sentences in logical form: :A if B1 and ... and Bn. A is called the ''head'' of the rule, B1, ..., Bn is called the ''body'', and the Bi are called '' literals'' or conditions. When n = 0, the rule is called a ''fact'' and is written in the simplified form: :A. Queries (or goals) have the same syntax as the bodies of rules and are commonly written in the form: :?- B1, ..., Bn. In the simplest case of Horn clauses (or "definite" clauses), all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed-world Assumption
The closed-world assumption (CWA), in a formal system of logic used for knowledge representation, is the presumption that a statement that is true is also known to be true. Therefore, conversely, what is not currently known to be true, is false. The same name also refers to a logical formalization of this assumption by Raymond Reiter. The opposite of the closed-world assumption is the open-world assumption (OWA), stating that lack of knowledge does not imply falsity. Decisions on CWA vs. OWA determine the understanding of the actual semantics of a conceptual expression with the same notations of concepts. A successful formalization of natural language semantics usually cannot avoid an explicit revelation of whether the implicit logical backgrounds are based on CWA or OWA. Negation as failure is related to the closed-world assumption, as it amounts to believing false every predicate that cannot be proved to be true. Example In the context of knowledge management, the closed-w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circumscription (logic)
Circumscription is a non-monotonic logic created by John McCarthy to formalize the common sense assumption that things are as expected unless otherwise specified. Circumscription was later used by McCarthy in an attempt to solve the frame problem. To implement circumscription in its initial formulation, McCarthy augmented first-order logic to allow the minimization of the extension of some predicates, where the extension of a predicate is the set of tuples of values the predicate is true on. This minimization is similar to the closed-world assumption that what is not known to be true is false. The original problem considered by McCarthy was that of missionaries and cannibals: there are three missionaries and three cannibals on one bank of a river; they have to cross the river using a boat that can only take two, with the additional constraint that cannibals must never outnumber the missionaries on either bank (as otherwise the missionaries would be killed and, presumably, eate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Automated Reasoning
The ''Journal of Automated Reasoning'' was established in 1983 by Larry Wos, who was its editor in chief until 1992. It covers research and advances in automated reasoning, mechanical verification of theorems, and other deductions in classical and non-classical logic. The journal is published by Springer Science+Business Media. As of 2021, the editor-in-chief is Jasmin Blanchette, a professor of theoretical computer science at the Ludwig-Maximilians-Universität München. The journal's 2019 impact factor is 1.431, and it is indexed by several science indexing services, including the Science Citation Index Expanded and Scopus. References External links * {{Official website, 1=https://www.springer.com/computer/theoretical+computer+science/journal/10817 Computer science journals Logic journals English-language journals Academic journals established in 1983 Logic in computer science Formal methods publications Springer Science+Business Media academic journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
