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Published in:
2020 | OriginalPaper | Chapter
11. Sticking to the Point: Relevance in Logic
Author : David Makinson
Published in: Sets, Logic and Maths for Computing
Publisher: Springer International Publishing
Abstract
When presenting classical propositional logic in Chap. 8, we observed that the connective of material implication, defined by its truth-table, makes no claim of any kind of ‘relevance’ between antecedent and consequent; nor does the relation of tautological implication require that premises and conclusion share any content. This leads to some rather surprising results, notably the so-called principles of ‘explosion’. In this chapter, we explore a way of excluding such runaway principles while retaining a logic that is smoothly behaved and easily applied. The basic idea is to adapt the method of truth-trees, from Chap. 8 Sect. 8.5, by imposing syntactic constraints of ‘actual use’ of antecedents and consequents in the production of crash-pairs.
