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Abstract

Aristotle's syllogistic is extended to include denumerably many quantifiers such as ‘more than 2/3’ and ‘exactly 2/3.’ Syntactic and semantic decision procedures determine the validity, or invalidity, of syllogisms with any finite number of premises. One of the syntactic procedures uses a natural deduction account of deducibility, which is sound and complete. The semantics for the system is non-classical since sentences may be assigned a value other than true or false. Results about symmetric systems are given. And reasons are given for claiming that syllogistic validity is relevant validity.

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Johnson, F. Syllogisms with fractional quantifiers. J Philos Logic 23, 401–422 (1994). https://doi.org/10.1007/BF01048688

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  • DOI: https://doi.org/10.1007/BF01048688

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