Directional Deduction

Roderick Batchelor

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arXiv · 2208.03925

Directional Deduction

Roderick Batchelor

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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.

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BibTeX RIS

Roderick Batchelor. 2022-08-08. Directional Deduction. https://arxiv.org/abs/2208.03925

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