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Browsing Faculty Publications by Subject "logic"
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Item Unknown A natural deduction relevance logic(Colorado State University. Libraries, 1977) Johnson, Fred (Frederick A.), author; Institute of Philosophy and Sociology, Polish Academy of Sceinces, publisherItem Unknown Analogical arguings and explainings(Colorado State University. Libraries, 1989) Johnson, Fred (Frederick A.), author; University of Windsor, publisherJohnson takes arguings and explainings to be more fundamental than arguments and explanations. The former require agents for their explication. Johnson contends that the texts fail to recognize that many ordinary analogical arguments and explanations have a deductive structure. According to Johnson, analogies are often used to state general principles, which are a part of the structure of analogical arguments and explanations. Johnson compares his analysis of analogies with Levi's analysis of legal reasoning and with Aristotle's analysis of "reasoning by example."Item Open Access Deductively-inductively(Colorado State University. Libraries, 1980) Johnson, Fred (Frederick A.), author; University of Windsor, publisherJohnson separates arguments from acts of arguing and claim that the deductive/inductive distinction belongs with the latter not with the former.Item Open Access Extended Gergonne syllogisms(Colorado State University. Libraries, 1997) Johnson, Fred (Frederick A.), author; Kluwer Academic Publishers, publisherSyllogisms with or without negative terms are studied by using Gergonne's ideas. Soundness, completeness, and decidability results are given.Item Open Access Syllogisms with fractional quantifiers(Colorado State University. Libraries, 1994) Johnson, Fred (Frederick A.), author; Kluwer Academic Publishers, publisherAristotle'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.Item Open Access Three-membered domains for Aristotle's syllogistic(Colorado State University. Libraries, 1991) Johnson, Fred (Frederick A.), author; Ossolineum and Kluwer Academic Publishers, publisherThe paper shows that for any invalid polysyllogism there is a procedure for constructing a model with a domain with exactly three members and an interpretation that assigns non-empty, non-universal subsets of the domain to terms such that the model invalidates the polysyllogism.Item Open Access Trees for a 3-valued logic(Colorado State University. Libraries, 1984) Johnson, Fred (Frederick A.), author; Oxford University Press, publisherJohnson claims that Slater is mistaken in identifying his system, presented by using tree rules, with a natural deduction system that results from modifying a system used by Copi. He then modifies Slater's tree rules and shows that these tree rules can be used to pick out precisely those arguments that are valid in a three-valued logic described by Bochvar.