Syllogisms with fractional quantifiers
Journal of Philosophical Logic 23 (4):401 - 422 (1994)
| 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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