Counterexample Sufficiency in Modifications to Strict-Tolerant Logics
Jitka Kadlečíková, Thomas Macaulay Ferguson · 2024
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.