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20 relations: Abductive reasoning, Autoepistemic logic, Belief revision, Binary relation, Circumscription (logic), Closed-world assumption, Completeness (logic), Default logic, Defeasible reasoning, Logic programming, Logical consequence, Mathematical logic, Monotonicity of entailment, Negation as failure, Paraconsistent logic, Rational consequence relation, Rule of inference, Semantics, Soundness, Stable model semantics.
Abductive reasoning
Abductive reasoning (also called abduction,For example: abductive inference, or retroduction) is a form of logical inference which starts with an observation or set of observations then seeks to find the simplest and most likely explanation.
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Autoepistemic logic
The autoepistemic logic is a formal logic for the representation and reasoning of knowledge about knowledge.
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Belief revision
Belief revision is the process of changing beliefs to take into account a new piece of information.
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Binary relation
In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.
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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.
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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.
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Completeness (logic)
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete.
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Default logic
Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions.
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Defeasible reasoning
In logic, defeasible reasoning is a kind of reasoning that is rationally compelling, though not deductively valid.
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Logic programming
Logic programming is a type of programming paradigm which is largely based on formal logic.
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Logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Monotonicity of entailment
Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended with additional assumptions.
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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.
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Paraconsistent logic
A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way.
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Rational consequence relation
In logic, a rational consequence relation is a non-monotonic consequence relation satisfying certain properties listed below.
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Rule of inference
In logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).
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Semantics
Semantics (from σημαντικός sēmantikós, "significant") is the linguistic and philosophical study of meaning, in language, programming languages, formal logics, and semiotics.
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Soundness
In mathematical logic, a logical system has the soundness property if and only if every formula that can be proved in the system is logically valid with respect to the semantics of the system.
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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.
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