Bergen Logic Seminar: Logic of sentential predicates

Logic of sentential predicates

Abstract: Sentential predicates, applicable to sentences and not their names, with truth and modal operators as special cases, extend FOL with a single layered meta-language. An example is a language with sentential predicate satisfying convention (T), capable of self-reference and free from paradoxes. Arbitrary sentential predicates can cause paradoxes, which can be diagnosed using a complete reasoning system LSP, extending LK with two rules. Paraconsistent semantics allows meta-level paradoxes to coexist with meaningful parts, without affecting truth at the object-level. Adding (cut) to LSP gives a complete reasoning for explosive semantics.