MoL-2019-25: Lattices of DNA-Logics and Algebraic Semantics of Inquisitive Logic

MoL-2019-25: Quadrellaro, Davide Emilio (2019) Lattices of DNA-Logics and Algebraic Semantics of Inquisitive Logic. [Report]

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This thesis studies algebraic semantics for the inquisitive logic InqB and for the related class of DNA-logics. DNA-logics were previously known in literature as negative variants of intermediate logics and have been studied only in syntactic terms. In this thesis, we show that there is a dual isomorphism between the lattice of DNA-logics and the lattice of suitable classes of Heyting algebras that we call DNA-varieties. We study several properties of DNA-logics and DNA-varieties and we prove a version of Tarski and Birkhoff Theorems for DNA-varieties. A special attention is then paid to introduce a notion of locally finiteness for this setting and to prove two key results concerning this property, i.e. that the DNA-variety of all Heyting algebras is not locally finite and that locally finite DNA-logics can be axiomatised by a version of Jankov formulas. Finally, we apply the general theory of DNA-logics to the case of inquisitive logic. We show that InqB is a DNA-logic and we use the method of Jankov formulas to prove that the sublattice Λ(InqB) of the extensions of InqB is dually isomorphic to ω + 1.

Item Type: Report
Report Nr: MoL-2019-25
Series Name: Master of Logic Thesis (MoL) Series
Year: 2019
Subjects: Logic
Depositing User: Dr Marco Vervoort
Date Deposited: 14 Nov 2019 16:22
Last Modified: 14 Nov 2019 16:22

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