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...]]. Specifically, a logic <math>\alpha</math> is said to be as strong as a logic <math>\beta</math> if every [[elementary class]] in <math>\beta</math> is a * [[Abstract logic]] ...

{{Short description|Commonly used rules of replacement in propositional logic}} {{About|the rule of inference|the formula of absolute truth|Tautology (logic)|other uses|Tautology (disambiguation)}} ...

...ut|the Hegelian and Marxist method|the formalisation of dialectic in logic|Logic and dialectic}} ...c]]. The precise nature of the relation between [[dialectic]]al and formal logic was hotly debated within the Soviet Union and China. ...

...e makes it possible to introduce [[Logical conjunction|conjunctions]] to [[formal proof|proofs]]. It is called the law of absorption because the term <math>Q == Formal notation == ...

...]] is the study of parthood relationships. In [[mathematics]] and [[formal logic]], [[wellfoundedness]] prohibits <math>\cdots<x<\cdots<x<\cdots</math> for [[Category:Mathematical logic]] ...

...th/0601147 }}</ref><ref>{{cite book |last1=Preining |first1=Norbert |title=Logic for Programming, Artificial Intelligence, and Reasoning |chapter=Gödel Logi ...]] showed that infinite-valued [[propositional logic|propositional]] Gödel logic can be axiomatised by adding the [[axiom schema]] ...

...ty]] if every [[Well-formed formula|formula]] having the property can be [[formal proof|derived]] using that system, i.e. is one of its [[theorem]]s; otherwi ...on the context, mostly referring to the property of semantical [[Validity (logic)|validity]]. Intuitively, a system is called complete in this particular se ...

...o-variable logic''' is the [[fragment (logics)|fragment]] of [[first-order logic]] where [[formula (logics)|formulae]] can be written using only two differe ...ion Problem for Two-Variable First-Order Logic'', The Bulletin of Symbolic Logic, Vol. ...

{{Short description|Rule of inference in predicate logic}} | field = [[Predicate logic]] ...

{{Short description|Rule of replacement in propositional logic}} ...laced by statements having conditional [[consequent]]s and vice versa in [[formal proof|logical proofs]]. It is the rule that: ...

In [[logic]] and [[model theory]], a '''valuation''' can be: *In [[propositional logic]], an assignment of [[truth value]]s to [[propositional variable]]s, with a ...

'''WSML''' or '''Web Service Modeling Language''' is a [[formal language]] that provides a [[syntax]] and [[semantics]] for the [[WSMO|Web ...Logics|Description Logic]], [[First-order logic|First-order Logic]] and [[Logic Programming]].<ref>J. de Bruijn, H. Lausen, A. Polleres, D. Fensel: The WSM ...

...is a generalization of the usual [[compactness theorem]] for [[first-order logic]] to a certain class of [[infinitary language]]s. It was stated and proved ...issible set]]. Let <math>L</math> be an <math>A</math>-finite relational [[Formal language|language]]. Suppose <math>\Gamma</math> is a set of <math>L_A</mat ...

...ref name="Chierchia2013">{{cite book| first=Gennaro| last=Chierchia| title=Logic in Grammar: Polarity, Free Choice, and Intervention| publisher=Oxford Unive {{Formal semantics}} ...

'''Matching logic''' is a [[formal logic]] mainly used to reason about the correctness of computer programs. Its op ...name="original">{{cite journal |last1=Roșu |first1=Grigore |title=Matching Logic |journal=Logical Methods in Computer Science |date=2017 |url=https://fsl.cs ...

{{Short description|Rule of inference in predicate logic}} | field = [[Predicate logic]] ...

...utation tree logic|computation tree logic (branching time logic)]]([[modal logic]]). So-called ''branching bisimulation'' has to be used.{{Citation needed|d [[Category:Formal methods]] ...

|known_for=Coining the term [[free logic]] ...versity of Salzburg]]. He has written extensively on the subject of [[free logic]], a term which he coined.<ref>{{Cite journal ...

...se they are not [[validity (logic)|valid]] in classical systems of [[modal logic]]. If they were valid, then the semantics of natural language would validat ...erences as [[scalar implicature]]s which arise on the basis of [[classical logic|classical]] lexical entries for disjunction and modality.<ref name = "aloni ...

{{Short description|Principle of classical logic}} ...port-export''' is a name given to the propositional form of [[Exportation (logic)|Exportation]]: ...