Non-involutive twist-structures

Umberto Rivieccio; Paulo Maia; Achim Jung

doi:10.1093/jigpal/jzy070

Non-involutive twist-structures

Umberto Rivieccio, Paulo Maia, Achim Jung

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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.

Original language	English
Article number	jzy070
Number of pages	27
Journal	Interest Group in Pure and Applied Logics. Logic Journal
Early online date	29 Nov 2018
DOIs	https://doi.org/10.1093/jigpal/jzy070
Publication status	E-pub ahead of print - 29 Nov 2018

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Rivieccio_et_al_Non-involutive_twist-structures_Logic_Journal_2018
Checked for eligibility 04/01/2019 This is a pre-copyedited, author-produced version of an article accepted for publication in [insert journal title] following peer review. The version of record; Rivieccio et al. Logic Journal of the IGPL, jzy070 is available online at: https://doi.org/10.1093/jigpal/jzy070
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Non-involutive twist-structures

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