Deep ST

Many analyses of notion of metainferences in the non-transitive logic ST have tackled the question of whether ST can be identified with classical logic. In this paper, we argue that the primary analyses are overly restrictive of the notion of metainference. We offer a more elegant and tractable semantics for the strict-tolerant hierarchy based on the three-valued function for the LP material conditional. This semantics can be shown to easily handle the introduction of mixed inferences, i.e., inferences involving objects belonging to more than one inferential level and solves several other limitations of the ST hierarchies introduced by Barrio, Pailos, and Szmuc.