Algebraic and Topological Semantics for Inquisitive Logic via Choice-Free Duality
| Autor: | Bezhanishvili, N., Grilletti, G., Holliday, W.H., Iemhoff, R., Moortgat, M., de Queiroz, R. |
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| Přispěvatelé: | ILLC (FNWI), Logic and Language (ILLC, FNWI/FGw), Logic and Computation (ILLC, FNWI/FGw) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
010102 general mathematics 05 social sciences Duality (mathematics) Extension (predicate logic) Characterization (mathematics) 16. Peace & justice Space (mathematics) 01 natural sciences 050105 experimental psychology Boolean algebra symbols.namesake Algebraic semantics Computer Science::Logic in Computer Science symbols 0501 psychology and cognitive sciences 0101 mathematics Algebraic number Connection (algebraic framework) Mathematics |
| Zdroj: | Logic, Language, Information, and Computation: 26th International Workshop, WoLLIC 2019, Utrecht, The Netherlands, July 2-5, 2019 : proceedings, 35-52 STARTPAGE=35;ENDPAGE=52;TITLE=Logic, Language, Information, and Computation Logic, Language, Information, and Computation-26th International Workshop, WoLLIC 2019, Utrecht, The Netherlands, July 2-5, 2019, Proceedings Logic, Language, Information, and Computation ISBN: 9783662595329 WoLLIC Lecture Notes in Computer Science Lecture Notes in Computer Science-Logic, Language, Information, and Computation |
| ISSN: | 0302-9743 1611-3349 |
| DOI: | 10.1007/978-3-662-59533-6_3 |
| Popis: | We introduce new algebraic and topological semantics for inquisitive logic. The algebraic semantics is based on special Heyting algebras, which we call inquisitive algebras, with propositional valuations ranging over only the ¬¬-fixpoints of the algebra. We show how inquisitive algebras arise from Boolean algebras: for a given Boolean algebra B, we define its inquisitive extension H(B) and prove that H(B) is the unique inquisitive algebra having B as its algebra of ¬¬-fixpoints. We also show that inquisitive algebras determine Medvedev’s logic of finite problems. In addition to the algebraic characterization of H(B), we give a topological characterization of H(B) in terms of the recently introduced choice-free duality for Boolean algebras using so-called upper Vietoris spaces (UV-spaces). In particular, while a Boolean algebra B is realized as the Boolean algebra of compact regular open elements of a UV-space dual to B, we show that H(B) is realized as the algebra of compact open elements of this space. This connection yields a new topological semantics for inquisitive logic. |
| Databáze: | OpenAIRE |
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