Non-involutive twist-structures

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

Abstract

A recent paper by Jakl, Jung and Pultr (2016, Electron. Notes Theor. Comput. Sci., 325, 201–219) succeeded for the first time in establishing a very natural link between bilattice logic and the duality theory of d-frames and bitopological spaces. In this paper we further exploit, extend and investigate this link from an algebraic and a logical point of view. In particular, we introduce classes of algebras that extend bilattices, d-frames and N4-lattices (the algebraic counterpart of Nelson’s paraconsistent logic) to a setting in which the negation is not necessarily involutive, and we study corresponding logics. We provide product representation theorems for these algebras, as well as completeness, algebraizability (and some nonalgebraizability) results for the corresponding logics.

Details

Original languageEnglish
Article numberjzy070
Number of pages27
JournalInterest Group in Pure and Applied Logics. Logic Journal
Early online date29 Nov 2018
Publication statusE-pub ahead of print - 29 Nov 2018