Counterexample Sufficiency in Modifications to Strict-Tolerant Logics

• Published in: Proceedings / International Symposium on Multiple-Valued Logic pp. 78 - 84
• Main Authors: Kadlecikova, Jitka, Ferguson, Thomas M.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 28.05.2024
• Subjects: bounds consequence; Logic; non-deterministic matrices; Semantics; sequent calculus; strict-tolerant logic; theory of topic
• ISSN: 2378-2226
• DOI: 10.1109/ISMVL60454.2024.00025

The three-valued strict-tolerant logic \mathsf{ST} that provides a substructural solution to semantic paradoxes appeals to the bounds consequence reading of validity in which provability of a sequent [\Gamma {>\!\!\!-} \Delta] (where \Gamma and \triangle are multisets of formulae) is understood as indicating that positions asserting \Gamma while denying \Delta violate some discursive norm. A modification \textsf{iST} ("intermediate ST") following a broader notion of bounds consequence-including the representation of discursive norms rejecting positions on topical considerations-has been introduced. In \textsf{iST} the third truth value is understood as representing a topical defect (e.g. a sentence's including offensive subject-matter) but further variations on the setting have been proposed. This paper provides a characterization of those modifications that coincide with \textsf{ST} and \textsf{iST} , allowing characterizations of which modifications influence the consequence relations of these two systems.