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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Abstract
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 Mathematics |
| 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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