Relevant Consequence Relations: An Invitation

0574131 - ÚI 2025 GB eng J - Journal Article
Badia, G. - Běhounek, L. - Cintula, Petr - Tedder, A.
Relevant Consequence Relations: An Invitation.
Review of Symbolic Logic. Online 30 June 2023 (2024). ISSN 1755-0203. E-ISSN 1755-0211
R&D Projects: GA ČR(CZ) GA22-01137S; GA ČR(CZ) GA18-00113S
Institutional support: RVO:67985807
Keywords : relevant entailment * substructural logics * multiset consequence relations * multiple conclusions
Impact factor: 0.6, year: 2022
Method of publishing: Limited access

We generalize the notion of consequence relation standard in abstract treatments of logic to accommodate intuitions of relevance. The guiding idea follows the use criterion, according to which in order for some premises to have some conclusion(s) as consequence(s), the premises must each be used in some way to obtain the conclusion(s). This relevance intuition turns out to require not just a failure of monotonicity, but also a move to considering consequence relations as obtaining between multisets. We motivate and state basic definitions of relevant consequence relations, both in single conclusion (asymmetric) and multiple conclusion (symmetric) settings, as well as derivations and theories, guided by the use intuitions, and prove a number of results indicating that the definitions capture the desired results (at least in many cases).
Permanent Link: https://hdl.handle.net/11104/0344479