Syllogisms with fractional quantifiers

Journal of Philosophical Logic 23 (4):401 - 422 (1994)
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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DOI 10.1007/BF01048688
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References found in this work BETA
T. J. Smiley (1973). What is a Syllogism? Journal of Philosophical Logic 2 (1):136 - 154.
Alan Ross Anderson & Nuel D. Belnap (1977). Entailment. Vol. 1. Canadian Journal of Philosophy 7 (2):405-411.

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Philip L. Peterson (1995). Distribution and Proportion. Journal of Philosophical Logic 24 (2):193 - 225.

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