AN ALGEBRAIC APPROACH TO INQUISITIVE AND DNA-LOGICS

Bezhanishvili, Nick; Grilletti, Gianluca and Quadrellaro, Davide Emilio (2021): AN ALGEBRAIC APPROACH TO INQUISITIVE AND DNA-LOGICS. In: Review of Symbolic Logic, Vol. 15, No. 4: pp. 950-990

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 Birkhoff's classic variety theorems. We also introduce locally 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 omega + 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 [9].(1)

• Item Type: Journal article
• Faculties: Philosophy, Philosophy of Science and Religious Science
• Subjects: 100 Philosophy and Psychology > 100 Philosophy
• ISSN: 1755-0203
• Language: English