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Browsing Faculty Publications by Author "Kluwer Academic Publishers, publisher"

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    Extended Gergonne syllogisms
    (Colorado State University. Libraries, 1997) Johnson, Fred (Frederick A.), author; Kluwer Academic Publishers, publisher
    Syllogisms with or without negative terms are studied by using Gergonne's ideas. Soundness, completeness, and decidability results are given.
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    Syllogisms with fractional quantifiers
    (Colorado State University. Libraries, 1994) Johnson, Fred (Frederick A.), author; Kluwer Academic Publishers, publisher
    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.