PP-2020-10: An Algebraic Approach to Inquisitive and DNA-Logics

PP-2020-10: Bezhanishvili, Nick and Grilletti, Gianluca and Quadrellaro, Davide Emilio (2020) An Algebraic Approach to Inquisitive and DNA-Logics. [Pre-print] (Submitted)

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This article provides an algebraic study of the propositional system InqB of inquisitive logic. We also investigate the wider class of DNA-logics, which are negative variants of intermediate logics, and the corresponding algebraic structures, DNA-varieties. We prove that the lattice of DNA-logics is dually isomorphic to the lattice of DNA-varieties. We characterise maximal and minimal intermediate logics with the same negative variant, and we prove a suitable version of Tarski’s and Birkhoff’s classic variety theorems. We also introduce finite DNA-varieties and show that these varieties are axiomatised by the analogues of Jankov formulas. Finally, we prove that the lattice of extensions of InqB is dually isomorphic to the ordinal ω + 1 and give an axiomatisation of these logics via Jankov DNA-formulas. This shows that these extensions coincide with the so-called inquisitive hierarchy of Ciardelli (2009).

Item Type: Pre-print
Report Nr: PP-2020-10
Series Name: Prepublication (PP) Series
Year: 2020
Uncontrolled Keywords: inquisitive logic intermediate logics algebraic semantics universal algebra
Subjects: Logic
Depositing User: Drs Gianluca Grilletti
Date Deposited: 01 May 2020 14:07
Last Modified: 01 May 2020 14:07
URI: https://eprints.illc.uva.nl/id/eprint/1739

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