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Relevance logic and the calculus of relations
Review of Symbolic Logic 3 (1):41-70 (2010)
Abstract
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 relationsMy notes
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Citations of this work
Relevance logic and the calculus of relations.Roger D. Maddux - 2010 - Review of Symbolic Logic 3 (1):41-70.
On representable ordered residuated semigroups.Szabolcs Mikulás - 2011 - Logic Journal of the IGPL 19 (1):233-240.
Positive fragments of relevance logic and algebras of binary relations.Robin Hirsch & Szabolcs Mikulás - 2011 - Review of Symbolic Logic 4 (1):81-105.
Lower Semilattice-Ordered Residuated Semigroups and Substructural Logics.Szabolcs Mikulás - 2015 - Studia Logica 103 (3):453-478.
Structural Features in Ernst Schröder's Work. Part I.Davide Bondoni - 2011 - Logic and Logical Philosophy 20 (4):327-359.
References found in this work
Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
Entailment: The Logic of Relevance and Necessity, Vol. II.Alan Ross Anderson, Nuel D. Belnap & J. Michael Dunn - 1992 - Princeton University Press.
The Semantics of Entailment.Richard Routley & Robert K. Meyer - 1973 - In Hugues Leblanc (ed.), Truth, Syntax, and Modality: Proceedings Of The Temple University Conference On Alternative Semantlcs. Amsterdam and London: North-Holland Publishing Company. pp. 199-243.
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