Non-involutive twist-structures

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Non-involutive twist-structures. / Rivieccio, Umberto; Maia, Paulo; Jung, Achim.

In: Interest Group in Pure and Applied Logics. Logic Journal, 29.11.2018.

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@article{ab50e4f57ee5461e8a25234a0ee8772b,
title = "Non-involutive twist-structures",
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{\textquoteright}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.",
author = "Umberto Rivieccio and Paulo Maia and Achim Jung",
year = "2018",
month = nov,
day = "29",
doi = "10.1093/jigpal/jzy070",
language = "English",
journal = "Interest Group in Pure and Applied Logics. Logic Journal",
issn = "1367-0751",
publisher = "Oxford University Press",

}

RIS

TY - JOUR

T1 - Non-involutive twist-structures

AU - Rivieccio, Umberto

AU - Maia, Paulo

AU - Jung, Achim

PY - 2018/11/29

Y1 - 2018/11/29

N2 - 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.

AB - 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.

UR - https://academic.oup.com/jigpal/advance-article/doi/10.1093/jigpal/jzy070/5173466?searchresult=1

U2 - 10.1093/jigpal/jzy070

DO - 10.1093/jigpal/jzy070

M3 - Article

JO - Interest Group in Pure and Applied Logics. Logic Journal

JF - Interest Group in Pure and Applied Logics. Logic Journal

SN - 1367-0751

M1 - jzy070

ER -