An Abstract Approach to Consequence Relations

0501907 - ÚI 2020 RIV GB eng J - Journal Article
Cintula, Petr - Gil-Férez, J. - Moraschini, Tommaso - Paoli, F.
An Abstract Approach to Consequence Relations.
Review of Symbolic Logic. Roč. 12, č. 2 (2019), s. 331-371. ISSN 1755-0203. E-ISSN 1755-0211
R&D Projects: GA ČR GBP202/12/G061
EU Projects: European Commission(XE) 689176 - SYSMICS
Institutional support: RVO:67985807
Keywords : structural consequence relation * multisets * deductive relations * Hilbert systems * abstract algebraic logic * category theory * non-contraction
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impact factor: 0.750, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1017/S175502031900008X

We generalise the Blok–Jónsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and Jonsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents or equations), these objects are invariably aggregated via set-theoretical union. Our approach is more general in that non-idempotent forms of premiss and conclusion aggregation, including multiset sum and fuzzy set union, are considered. In their abstract form, thus, deductive relations are defined as additional compatible preorderings over certain partially ordered monoids. We investigate these relations using categorical methods and provide analogues of the main results obtained in the general theory of consequence relations. Then we focus on the driving example of multiset deductive relations, providing variations of the methods of matrix semantics and Hilbert systems in Abstract Algebraic Logic.
Permanent Link: http://hdl.handle.net/11104/0293884