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Item Open Access Rejection and truth-value gaps(Colorado State University. Libraries, 1999) Johnson, Fred (Frederick A.), author; Duke University Press, publisherA theorem due to Shoesmith and Smiley that axiomatizes two-valued multiple-conclusion logics is extended to partial logics.Item Open Access Counting functions(Colorado State University. Libraries, 1992) Johnson, Fred (Frederick A.), author; Duke University Press, publisherCounting functions are shown to be closed under composition.Item Open Access Models for modal syllogisms(Colorado State University. Libraries, 1989) Johnson, Fred (Frederick A.), author; Duke University Press, publisherItem Open Access Parry syllogisms(Colorado State University. Libraries, 1999) Johnson, Fred (Frederick A.), author; Duke University Press, publisherParry discusses an extension of Aristotle's syllogistic that uses four nontraditional quantifiers. We show that his conjectured decision procedure for validity for the extended syllogistic is correct even if syllogisms have more than two premises. And we axiomatize this extension of the syllogistic.Item Open Access Copi's method of deduction(Colorado State University. Libraries, 1979-04) Johnson, Fred (Frederick A.), author; Duke University Press, publisherItem Open Access Categoricity of partial logics(Colorado State University. Libraries, 1999) Johnson, Fred (Frederick A.), author; Filosofia, publisherItem Open Access Suppositional reasoning(Colorado State University. Libraries, 1991) Johnson, Fred (Frederick A.), author; SICSAT, publisherThe purpose of this paper is to show how to structure some typical examples of suppositional reasoning. Such reasoning is common, but unfortunately it is typically neglected by writers of logic textbooks, as Fisher points out in [Fisher, p. viii]. Fisher gives a method of diagramming suppositional reasoning and gives credit to Thomas for similar work in [Thomas]. I shall begin by laying out their methods of structuring suppositional reasoning.Item Open Access Categorical consequence for paraconsistent logic(Colorado State University. Libraries, 1999) Woodruff, Peter W., author; Johnson, Fred (Frederick A.), author; Filosofia, publisherConsequence relations over sets of "judgments" are defined by using "overdetermined" as well as "underdetermined" valuations. Some of these relations are shown to be categorical. And generalized soundness and completeness results are given for both multiple and single conclusion categorical consequence relations.Item Open Access Arguings and arguments(Colorado State University. Libraries, 1984) Johnson, Fred (Frederick A.), author; University of Windsor, publisherItem Open Access A three-valued interpretation for a relevance logic(Colorado State University. Libraries, 1976-09) Johnson, Fred (Frederick A.), author; Department of Philosophical Studies, Southern Illinois University at Edwardsville, publisherIn this paper an entailment relation which holds between certain propositions of the propositional calculus will be defined both syntactically and semantically. Some theorems about this relation will show why one could not follow Lewis to prove that a contradiction entails, for the notion of entailment discussed below, every proposition.Item Open Access 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 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 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 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 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 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 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.