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2005
Summary: The classical analytic tableau method has been extended successfully to modal logics and also to relevant and paraconsistent logics. The classical connection method has been extended to modal and intuitionistic logics, and the purpose of this paper is to investigate whether a similar adaptation to relevant logic is possible. A hybrid method is
Gochet, Paul +2 more
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Summary: The classical analytic tableau method has been extended successfully to modal logics and also to relevant and paraconsistent logics. The classical connection method has been extended to modal and intuitionistic logics, and the purpose of this paper is to investigate whether a similar adaptation to relevant logic is possible. A hybrid method is
Gochet, Paul +2 more
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QUANTIFIED MODAL RELEVANT LOGICS
The Review of Symbolic Logic, 2021AbstractHere, I combine the semantics of Mares and Goldblatt [20] and Seki [29, 30] to develop a semantics for quantified modal relevant logics extending ${\bf B}$ . The combination requires demonstrating that the Mares–Goldblatt approach is apt for quantified extensions of ${\bf B}$ and other relevant logics, but no significant bridging principles ...
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The Relevance of Relevance to Relevance Logic
2015I explore the question of whether the concept of relevance is relevant to the study of what Anderson and Belnap call “relevance logic.” The answer should be “Of course!” But there are some twists and turns, as is shown by the fact that it has taken over 50 years to get here. Despite protests by R. K.
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Symmetry and Completeness in Relevant Epistemic Logic
Journal of Philosophical LogicIn this paper, we provide an axiom system for the relevant logic of equivalence relation frames and prove completeness for it. This provides a partial answer to the longstanding open problem of axiomatizing frames for relevant modal logics where the ...
Shawn Standefer, Edwin David Mares
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RELEVANCE LOGICS AND RELATION ALGEBRAS
The Review of Symbolic Logic, 2009Relevance logicsare known to be sound and complete for relational semantics with a ternary accessibility relation. This paper investigates the problem of adequacy with respect to special kinds ofdynamic semantics(i.e., proper relation algebras and relevant families of relations). We prove severalsoundnessresults here.
Katalin Bimbó +2 more
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Journal of Symbolic Logic, 1972
In what follows there is presented a unified semantic treatment of certain “paradox-free” systems of entailment, including Church's weak theory of implication (Church [7]) and logics akin to the systems E and R of Anderson and Belnap (Anderson [3], Belnap [6]).
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In what follows there is presented a unified semantic treatment of certain “paradox-free” systems of entailment, including Church's weak theory of implication (Church [7]) and logics akin to the systems E and R of Anderson and Belnap (Anderson [3], Belnap [6]).
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Journal of Philosophical Logic, 1992
Novel conditions of relevance are defined for conditionals in order to weed out some of the deontic paradoxes, such as Ross's paradox. Semantically, first-degree positive relevant entailment is defined in terms of fulfilment conditions, which are sets of sets of literals (atomic sentences or their negations).
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Novel conditions of relevance are defined for conditionals in order to weed out some of the deontic paradoxes, such as Ross's paradox. Semantically, first-degree positive relevant entailment is defined in terms of fulfilment conditions, which are sets of sets of literals (atomic sentences or their negations).
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Journal of Automated Reasoning, 1991
Several authors suggested extension of Horn clause programming using bottom-up proof search in Gentzen-type systems for intuitionistic logic with suitable restriction of the language. The author describes a similar program based on the relevance logic LR\(^ +\) without negation and distributivity axiom.
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Several authors suggested extension of Horn clause programming using bottom-up proof search in Gentzen-type systems for intuitionistic logic with suitable restriction of the language. The author describes a similar program based on the relevance logic LR\(^ +\) without negation and distributivity axiom.
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RELEVANCE LOGIC AND THE CALCULUS OF RELATIONS
The Review of Symbolic Logic, 2010Sound 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 ...
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An Incomplete Relevant Modal Logic
Journal of Philosophical Logic, 2000The propositional modal logic \(G\) considered in this paper is an extension of the Anderson-Belnap system \(R\), which is incomplete in Routley-Meyer semantics for relevant modal logics.
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