Structural Completeness and Superintuitionistic Inquisitive Logics

0575743 - FLÚ 2024 RIV CH eng C - Konferenční příspěvek (zahraniční konf.)
Ferguson, Thomas - Punčochář, Vít
Structural Completeness and Superintuitionistic Inquisitive Logics.
Logic, Language, Information, and Computation. Cham: Springer, 2023 - (Hansen, H.; Scedrov, A.; de Queiroz, R.), s. 194-210. Lecture Notes in Computer Science, 13923. ISBN 978-3-031-39783-7.
[WoLLIC 2023: Workshop on Logic, Language, Information and Computation /29./. Halifax (CA), 11.07.2023-14.07.2023]
Grant CEP: GA ČR(CZ) GM21-23610M
Institucionální podpora: RVO:67985955
Klíčová slova: structural completeness * inquisitive logic * superintuitionistic logics * substitution
Obor OECD: Philosophy, History and Philosophy of science and technology
https://doi.org/10.1007/978-3-031-39784-4_12

In this paper, the notion of structural completeness is explored in the context of a generalized class of superintuitionistic logics involving also systems that are not closed under uniform substitution. We just require that each logic must be closed under D-substitutions assigning to atomic formulas only disjunction-free formulas. For these systems we introduce four different notions of structural completeness and study how they are related. We focus on superintuitionistic inquisitive logics that validate a schema called Split and have the disjunction property. In these logics disjunction can be interpreted in the sense of inquisitive semantics as a question forming operator. It is shown that a logic is structurally complete with respect to D-substitutions if and only if it includes the weakest superintuitionistic inquisitive logic. Various consequences of this result are explored. For example, it is shown that every superintuitionistic inquisitive logic can be characterized by a Kripke model built up from D-substitutions. Additionally, we resolve a conjecture concerning superintuitionistic inquisitive logics due to Miglioli et al..
Trvalý link: https://hdl.handle.net/11104/0346056