Understanding infinitary logics via their symmetrizations

Authors: Marta Bílková, Petr Cintula
Publication year: 2018
Publication type: Abstrakt
Periodical: SYSMICS 2018. Duality in Algebra and Logic. Abstracts
Bibliographic citation: BÍLKOVÁ, Marta, CINTULA, Petr. Understanding infinitary logics via their symmetrizations. In: SYSMICS 2018. Duality in Algebra and Logic. Abstracts. Orange: Chapman University, 2018, S. 1-1. Dostupné z: http://math.chapman.edu/~jipsen/sysmics/SYSMICS4abstracts.pdf
ID: 508282

Abstract

Considering a logic I- cast as a Tarskian consequence relation between sets of formulas and formulas, there are several ways how to construct its symmetric version II- with a disjuncture flavour on the right-hand side. The situation becomes even more complex if the logic in question is infinitary. Dunn and Hardegree showed that the proper Cut rule for such symmetric logic is equivalent to Pair Extension Property which plays a crucial rule in the completeness proofs for many modal logics.