A Reinterpretation of the Semilattice Semantics with Applications

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

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Yale Weiss
CUNY Graduate Center

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References found in this work

Truthmaker Semantics.Kit Fine - 2017 - In Bob Hale, Crispin Wright & Alexander Miller (eds.), A Companion to the Philosophy of Language. Chichester, UK: Wiley. pp. 556–577.
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.

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