Positive Fragments of Relevance Logic and Algebras of Binary Relations
نویسندگان
چکیده
We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a non-finitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.
منابع مشابه
Residuated Algebras of Binary Relations and Positive Fragments of Relevance Logic
The aim of this paper is to apply some results obtained jointly with Hajnal Andréka and István Németi about finite axiomatizability of Tarski’s representable relation algebras in the context of completeness of fragments of relevance logic.
متن کاملPositive Reducts of Relevance Logic and Algebras of Binary Relations
We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a non-finitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.
متن کاملAxiomatizability of positive algebras of binary relations
We consider all positive fragments of Tarski’s representable relation algebras and determine whether the equational and quasiequational theories of these fragments are finitely axiomatizable in first-order logic. We also look at extending the signature with reflexive, transitive closure and the residuals of composition.
متن کاملAlgebras of Relations and Relevance Logic
We prove that algebras of binary relations whose similarity type includes intersection, composition, converse negation and the identity constant form a non-finitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of relevant logic with respect to binary relations.
متن کاملRelevance Logic and the Calculus of Relations
Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.
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ورودعنوان ژورنال:
- Rew. Symb. Logic
دوره 4 شماره
صفحات -
تاریخ انتشار 2011