| Models for modal syllogisms (Notre Dame Journal of Formal Logic, 1989) |
Abstract -- A semantics is presented for Storrs McCall's separate axiomatizations of Aristotle's accepted and rejected polysyllogisms. The polysyllogisms under discussion are made up of either assertoric or apodeictic propositions. The semantics is given by associating a property with a pair of sets: one set consists of things having the property essentially and the other of things having it accidentally. A completeness proof and a semantic decision procedure are given.
| Three-membered domains for Aristotle's syllogistic (Studia Logica, 1991) |
In this paper Fred proves the surprising result that invalid syllogisms with any finite number of premises can be shown to be invalid by using a domain with no more than three members. He takes advantage of important work done by Cambridge's T. J. Smiley.
| Copi's method of deduction (Notre Dame Journal of Formal Logic, 1979) |
Copi's method of deduction is formalized and shown to be complete.
| Counting functions (Notre Dame Journal of Formal Logic, 1992) |
Counting functions are shown to be complete by using a simpler argument than that used by Pelletier and Martin.
| Parry syllogisms (Notre Dame Journal of Formal Logic, 1999) |
Parry's conjectured decision procedure for validity for his extension of the syllogistic is shown to be complete. Fred also axiomatizes Parry's extension of the syllogistic.
| Rejections and truth-value gaps (Notre Dame Journal of Formal Logic, 1999) |
A theorem due to Shoesmith and Smiley that axiomatizes two-valued multiple conclusion logics is extended to partial logics.
| Trees for a 3-valued logic (Analysis, 1984) |
Fred shows how problems with Slater's restriction of the classical propositional logic can be solved.
| Modal ecthesis (History and Philosophy of Logic, 1993) |
Fred's semantics for McCall's syntactic presentation of Aristotle's assertoric and apodeictic syllogistic is altered to free it from Thom's objections that it is unAristotelian. The altered semantics rejects Baroco-XLL and Bocardo-LXL, which Thom says Aristotle should have accepted. Aristotle's proofs that use ecthesis are formalized by using singular sentences. With one exception the (acceptance) axioms for McCall's system L-X-M are derivable. Formal proofs are shown to be sound.
| Syllogisms with fractional quantifiers (Journal of Philosophical Logic, 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.
| Extended Gergonne syllogisms (Journal of Philosophical Logic, 1997) |
Syllogisms with or without negative terms are studied by using Gergonne's ideas. Soundness, completeness and decidability results are given.
| A natural deduction relevance logic (Bulletin of the Section of Logic, 1977) |
| Categorical consequence for paraconsistent logic (_Paraconsistency_), 2002) |
Consequence rleations 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 consequence relations.
| Aristotle's modal syllogisms (Handbook of the History of Logic, vol. 1, 2004) |
McCall's system for contingent syllogisms is modified. A semantics for the resulting system is provided.
| Aristotle's apodeictic syllogisms: deductions and decision procedures (History and Philosophy of Logic, vol. 16, 1995) |
One semantic and two syntactic decision procedures are given for determining the validity of Aristotelian assertoric and apodeictic syllogims. Results are obtained by using the Aristotelian deductions that necessarily have an even number of premises.
| Review of Open Minds and Everyday Reasoning by Zachary Seech (Philosophy in Review, vol 14, no. 3, 1994) |
| Categoricity of partial logics (The Logica yearbook 1998, 1999) |
This paper extends T. J. Smiley's work by solving the categoricity problem for single-conclusion, partial-valuation logics. The paper focuses on judgment logics.
| Suppositional reasoning (Proceedings of the Second International Conference on Argumentation 1990, 1991) |
| Arguings and arguments (Informal Logic, vol. 6, no. 2, 1984) |
| Deductively-inductively (Informal Logic, vol. 3, 1980) |
| Analogical arguings and explainings (Informal Logic, vol. 11, no. 3, 1989) |
| A three-valued interpretation for a relevance logic (The Relevance Logic Newsletter, vol. 1, no. 3, 1976) |
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