Powers and limitations of Urquhart-style semantics I: basic substructural logics

This paper addresses three kinds of binary operational semantics, called here Urquhart-style semantics, for basic substructural logics. First, we discuss the most basic substructural logic GL introduced by Galatos and Ono and its expansions with structural axioms and their algebraic semantics. Next,...

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Bibliographic Details
Published inReports on mathematical logic Vol. 59; no. 59; pp. 49 - 78
Main Author Yang, Eunsuk
Format Journal Article
LanguageEnglish
Published Kraków Wydawnictwo Uniwersytetu Jagiellońskiego 01.01.2024
Jagiellonian University Press
Jagiellonian University-Jagiellonian University Press
Subjects
Algebra
Axioms
Logic
Semantics
star operations for negations
Urquhartstyle semantics
Operational semantics
substructural logics
algebraic semantics
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Summary:This paper addresses three kinds of binary operational semantics, called here Urquhart-style semantics, for basic substructural logics. First, we discuss the most basic substructural logic GL introduced by Galatos and Ono and its expansions with structural axioms and their algebraic semantics. Next, we provide one kind of Urquhart-style semantics, whose frames form the same structures as algebraic semantics, for those substructural logics and consider powers and limitations of this kind of semantics in substructural logic. We then introduce another kind of Urquhart-style semantics, whose canonical frames are based on prime theories, for DL, the GL with distributivity, and some of its non-associative expansions and extend it to the semantics with star operations for negations. Similarly, we consider powers and limitations of these two kinds of semantics in substructural logic.
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ISSN:0137-2904
2084-2589
DOI:10.4467/20842589RM.24.001.20698