Revisiting Semilattice Semantics

In Ivo Düntsch & Edwin Mares, Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs. Cham: Springer Verlag. pp. 243-259 (2021)
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Abstract

The operational semantics of Urquhart is a deep and important part of the development of relevant logics. In this paper, I present an overview of work on Urquhart’s operational semantics. I then present the basics of collection frames. Finally, I show how one kind of collection frame, namely, functional set frames, is equivalent to Urquhart’s semilattice semantics.

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9783030714291

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10.1007/978-3-030-71430-7_7

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Shawn Standefer
Tohoku University

Citations of this work

What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.
The relevance logic of Boolean groups.Yale Weiss - 2023 - Logic Journal of the IGPL 31 (1):96-114.
Multiset-Multiset Frames.Takuro Onishi - 2024 - Journal of Philosophical Logic 53 (5):1241-1264.

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References found in this work

Entailment: The Logic of Relevance and Necessity. - 1975 - Studia Logica 54 (2):261-266.
The non-triviality of dialectical set theory.Ross T. Brady - 1989 - In Graham Priest, Richard Routley & Jean Norman, Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. pp. 437--470.
Universal Logic.Ross Brady - 2007 - Studia Logica 87 (2-3):359-362.

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