The Lattice of Super-Belnap Logics

0542368 - ÚI 2024 RIV GB eng J - Článek v odborném periodiku
Přenosil, Adam
The Lattice of Super-Belnap Logics.
Review of Symbolic Logic. Roč. 16, č. 1 (2023), s. 114-163. ISSN 1755-0203. E-ISSN 1755-0211
Grant CEP: GA ČR GBP202/12/G061
Institucionální podpora: RVO:67985807
Klíčová slova: Belnap-Dunn logic * Kleene logic * Logic of Paradox * four-valued logic * paraconsistent logic * abstract algebraic logic
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impakt faktor: 0.6, rok: 2022
Způsob publikování: Omezený přístup
http://dx.doi.org/10.1017/S1755020321000204

We study the lattice of extensions of four-valued Belnap-Dunn logic, called super-Belnap logics by analogy with superintuitionistic logics. We describe the global structure of this lattice by splitting it into several subintervals, and prove some new completeness theorems for super-Belnap logics. The crucial technical tool for this purpose will be the so-called antiaxiomatic (or explosive) part operator. The antiaxiomatic (or explosive) extensions of Belnap-Dunn logic turn out to be of particular interest owing to their connection to graph theory: the lattice of finitary antiaxiomatic extensions of Belnap-Dunn logic is isomorphic to the lattice of upsets in the homomorphism order on finite graphs (with loops allowed). In particular, there is a continuum of finitary super Belnap logics. Moreover, a non-finitary super-Belnap logic can be constructed with the help of this isomorphism. As algebraic corollaries we obtain the existence of a continuum of antivarieties of De Morgan algebras and the existence of a prevariety of De Morgan algebras which is not a quasivariety.
Trvalý link: http://hdl.handle.net/11104/0319795