Directional Deduction

TL;DR

This paper introduces new logical deduction methods inspired by ground theory, analyzing premises to their ultimate grounds, discarding irrelevant info, and synthesizing conclusions, across various logical systems with new semantic models.

Contribution

It develops novel deduction calculi for classical, modal, and relevantistic logics based on ground analysis and introduces new truthmaker semantics.

Findings

Calculi for propositional and predicate logic established

Extensions to modal and relevantistic fragments provided

New semantic constructions of truthmaker semantics introduced

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.