Three-Valued Semantics for the Disjunction-Free Fragment of Jaskowski's Discussive Logic D2
Jaskowski's discussive (discursive) logic D2 is an early paraconsistent logic defined through a modal translation, distinguishing a merely contradictory theory from a trivial one. This result shows that the fragment of D2 without disjunction, written in the classical language, is sound and complete with respect to a three-valued (and four-valued) truth-table semantics derived as a two-world special case of its Kripke semantics, and derives from this a simple finite axiomatization of the fragment.
2501.00501
Jaskowski's discussive (discursive) logic D2 is an early paraconsistent logic — Jaskowski distinguished a merely contradictory theory from a trivial one — and D2 is known to have no finitely many-val…