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SUBSTRUCTURAL INQUISITIVE LOGICS

Published online by Cambridge University Press:  01 February 2019

VÍT PUNČOCHÁŘ*
Affiliation:
Institute of Philosophy, Czech Academy of Sciences
*
*INSTITUTE OF PHILOSOPHY CZECH ACADEMY OF SCIENCES JILSKÁ 1, 110 00 PRAGUE, CZECH REPUBLIC E-mail: vit.puncochar@centrum.cz

Abstract

This paper shows that any propositional logic that extends a basic substructural logic BSL (a weak, nondistributive, nonassociative, and noncommutative version of Full Lambek logic with a paraconsistent negation) can be enriched with questions in the style of inquisitive semantics and logic. We introduce a relational semantic framework for substructural logics that enables us to define the notion of an inquisitive extension of λ, denoted as ${\lambda ^?}$, for any logic λ that is at least as strong as BSL. A general theory of these “inquisitive extensions” is worked out. In particular, it is shown how to axiomatize ${\lambda ^?}$, given the axiomatization of λ. Furthermore, the general theory is applied to some prominent logical systems in the class: classical logic Cl, intuitionistic logic Int, and t-norm based fuzzy logics, including for example Łukasiewicz fuzzy logic Ł. For the inquisitive extensions of these logics, axiomatization is provided and a suitable semantics found.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2019 

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