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Tree Proofs for Syllogistic

Peter M. Simons
Studia Logica: An International Journal for Symbolic Logic
Vol. 48, No. 4 (1989), pp. 539-554
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015465
Page Count: 16
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Tree Proofs for Syllogistic
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Abstract

This paper presents a tree method for testing the validity of inferences, including syllogisms, in a simple term logic. The method is given in the form of an algorithm and is shown to be sound and complete with respect to the obvious denotational semantics. The primitive logical constants of the system, which is indebted to the logical works of Jevons, Brentano and Lewis Carroll, are term negation, polyadic term conjunction, and functors affirming and denying existence, and use is also made of a metalinguistic concept of formal synonymy. It is indicated briefly how the method may be extended to other systems.

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