Directional Deduction (2208.03925v1)

Abstract: We present some new methods for logical deduction, based on ideas from ground theory. Roughly speaking, in our calculi a typical deduction will proceed as follows: we first analyse the premiss down to its ultimate grounds; then we discard information irrelevant to the conclusion; and then we synthesize the conclusion up from its ultimate grounds. We give a series of calculi for: classical propositional logic (Chapter 1); classical predicate logic (Chapter 2); modal propositional logic and modal predicate logic (Chapter 3); and some relevantistic fragments of these various systems (Chapters 4 and 5). In connection with these fragments we develop also some new semantic constructions, of 'truthmaker semantics' type.