Syllogisms with fractional quantifiers - Johnson, Fred (Frederick A.), author; Kluwer Academic Publishers, publisher (Colorado State University. Libraries, 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.
Keywords: quantifier; model; logic; fraction; syllogism