Syllogisms with fractional quantifiers
Date
1994
Authors
Johnson, Fred (Frederick A.), author
Kluwer Academic Publishers, publisher
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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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Subject
quantifier
model
logic
fraction
syllogism