Logica Universalis 15 (2):171-191 (2021)

Authors
Yale Weiss
CUNY Graduate Center
Abstract
In the early 1970s, Alasdair Urquhart proposed a semilattice semantics for relevance logic which he provided with an influential informational interpretation. In this article, I propose a BHK-inspired reinterpretation of the semantics which is related to Kit Fine’s truthmaker semantics. I discuss and compare Urquhart’s and Fine’s semantics and show how simple modifications of Urquhart’s semantics can be used to characterize both full propositional intuitionistic logic and Jankov’s logic. I then present (quasi-)relevant companions for both of these systems. Finally, I provide sound and complete labelled sequent calculi for all of the systems discussed.
Keywords Semilattice semantics  Truthmaker semantics  Relevance logic  Intuitionistic logic  Constructive logic  BHK semantics
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DOI 10.1007/s11787-021-00273-6
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References found in this work BETA

Truth-Maker Semantics for Intuitionistic Logic.Kit Fine - 2014 - Journal of Philosophical Logic 43 (2-3):549-577.
Truthmaker Semantics for Relevant Logic.Mark Jago - 2020 - Journal of Philosophical Logic 49 (4):681-702.
Explicit Provability and Constructive Semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
Facts and Tautological Entailments.Bas C. Van Fraassen - 1969 - Journal of Philosophy 66 (15):477-487.
Models for Entailment.Kit Fine - 1974 - Journal of Philosophical Logic 3 (4):347 - 372.

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