Substructural inquisitive logics

0505202 - FLÚ 2020 RIV GB eng J - Journal Article
Punčochář, Vít
Substructural inquisitive logics.
Review of Symbolic Logic. Roč. 12, č. 2 (2019), s. 296-330. ISSN 1755-0203. E-ISSN 1755-0211
R&D Projects: GA ČR(CZ) GC16-07954J
Institutional support: RVO:67985955
Keywords : inquisitive semantics * logic of questions * substructural logic * classical logic * intuitionistic logic * fuzzy logic
OECD category: Philosophy, History and Philosophy of science and technology
Impact factor: 0.750, year: 2019
Method of publishing: Limited access
https://www.cambridge.org/core/journals/review-of-symbolic-logic/article/substructural-inquisitive-logics/81285524FFC11723B452B2D8434FEF79

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 λ?, 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  λ?, 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.
Permanent Link: http://hdl.handle.net/11104/0296698