
53Suppositional reasoningIn Frans H. Van Eemeren (ed.), Proceedings of the Second International Conference on Argumentation 1990, . pp. 281287. 1991.

199A threevalued interpretation for a relevance logicThe Relevance Logic Newsletter 1 (3): 123128. 1976.

142Copi's method of deductionNotre Dame Journal of Formal Logic 20 (2): 295300. 1979.Copi's method of deduction is formalized and shown to be complete

261Categorical consequence for paraconsistent logicIn Walter Carnielli (ed.), Paraconsistency:the logical way to the inconsistent, . pp. 141150. 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.

94Counting functionsNotre Dame Journal of Formal Logic 33 (4): 567568. 1992.Counting functions are shown to be complete by using a simpler argument than that used by Pelletier and Martin.

136Threemembered domains for Aristotle's syllogisticStudia Logica 50 (2). 1991.The 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 nonempty, nonuniversal subsets of the domain to terms such that the model invalidates the polysyllogism.

137Extended Gergonne SyllogismsJournal of Philosophical Logic 26 (5): 553567. 1997.Syllogisms with or without negative terms are studied by using Gergonne's ideas. Soundness, completeness, and decidability results are given

212Models for modal syllogismsNotre Dame Journal of Formal Logic 30 (2): 271284. 1989.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.

263Trees for a 3valued logicAnalysis 44 (1): 436. 1984.Fred shows how problems with Slater's restriction of the classical propositional logic can be solved.

1Review or Open Minds and Everyday Reasoning by Zachary Seech (review)Philosophy in Review 14 (3): 211212. 1994.

155Modal EcthesisHistory and Philosophy of Logic 14 (2): 171182. 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 BarocoXLL and BocardoLXL, 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 LXM are derivable. Formal proofs are shown to be sound.

105Parry SyllogismsNotre Dame Journal of Formal Logic 40 (3): 414419. 1999.Parry 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

213Aristotle's modal syllogismsIn Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the History of Logic, Elsevier. pp. 1247. 2004.McCall's system for contingent syllogisms is modified. A semantics for the resulting system is provided.

178Apodeictic syllogisms: Deductions and decision proceduresHistory and Philosophy of Logic 16 (1): 118. 1995.One semantic and two syntactic decision procedures are given for determining the validity of Aristotelian assertoric and apodeictic syllogisms. Results are obtained by using the Aristotelian deductions that necessarily have an even number of premises.

173Syllogisms with fractional quantifiersJournal of Philosophical Logic 23 (4). 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 nonclassical since sentences may be assigned a value other than true or false. Results about symmetric sy…Read more

158Rejection and TruthValue GapsNotre Dame Journal of Formal Logic 40 (4): 574577. 1999.A theorem due to Shoesmith and Smiley that axiomatizes twovalued multipleconclusion logics is extended to partial logics
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Areas of Specialization
Logic and Philosophy of Logic 
Areas of Interest
Logic and Philosophy of Logic 