An Algebraic Approach to Inquisitive and -Logics

Review of Symbolic Logic 15 (4):950-990 (2022)
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This article provides an algebraic study of the propositional system$\mathtt {InqB}$of inquisitive logic. We also investigate the wider class of$\mathtt {DNA}$-logics, which are negative variants of intermediate logics, and the corresponding algebraic structures,$\mathtt {DNA}$-varieties. We prove that the lattice of$\mathtt {DNA}$-logics is dually isomorphic to the lattice of$\mathtt {DNA}$-varieties. We characterise maximal and minimal intermediate logics with the same negative variant, and we prove a suitable version of Birkhoff’s classic variety theorems. We also introduce locally finite$\mathtt {DNA}$-varieties and show that these varieties are axiomatised by the analogues of Jankov formulas. Finally, we prove that the lattice of extensions of$\mathtt {InqB}$is dually isomorphic to the ordinal$\omega +1$and give an axiomatisation of these logics via Jankov$\mathtt {DNA}$-formulas. This shows that these extensions coincide with the so-called inquisitive hierarchy of [9].1.



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Nick Bezhanishvili
University of Amsterdam

Citations of this work

Topological duality for orthomodular lattices.Joseph McDonald & Katalin Bimbó - 2023 - Mathematical Logic Quarterly 69 (2):174-191.

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References found in this work

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Heyting Algebras: Duality Theory.Leo Esakia - 2019 - Cham, Switzerland: Springer Verlag.
Modal Logic.Yde Venema, Alexander Chagrov & Michael Zakharyaschev - 2000 - Philosophical Review 109 (2):286.
Semantic analysis of wh-complements.Jeroen Groenendijk & Martin Stokhof - 1982 - Linguistics and Philosophy 5 (2):175 - 233.
Inquisitive Logic.Ivano Ciardelli & Floris Roelofsen - 2011 - Journal of Philosophical Logic 40 (1):55-94.

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