Counterexample Sufficiency in Modifications to Strict-Tolerant Logics

The three-valued strict-tolerant logic 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 Delta are multisets of formulae) is understood as indicating that positions asserting Gamma while denying Delta violate some discursive norm. A modification 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 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 ST and iST, allowing characterizations of which modifications influence the consequence relations of these two systems.