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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References
Aristotle, Topica. Any edition may be used as the Bekker numbering has been cited.
F. Brentano, Die Lehre vom richtigen Urteil, edited by F. Mayer-Hillebrand, Francke, Bern, 1956.
L. Carroll (= Dodgson, Charles L.), Lewis Carroll's Symbolic Logic, edited by W. W. Bartley III, Harvester Press, Hassocks, 1977.
W. Hodges, Logic, Penguin, Harmondsworth, 1977.
R. Jeffrey, Formal Logic: Its Scope and Limits, McGraw-Hill, New York, 2nd ed., 1981.
W. S. Jevons, The Substitution of Similars, the true Principle of Reasoning, derived from a modification of Aristotle's Dictum, Macmillan, London, 1869.
W. Mays and D. P. Henry, Jevons and Logic, Mind 62 (1953), pp. 484–505.
P. M. Simons, Brentano's Reform of Logic, Topoi 6 (1987), pp. 25–38.
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To the memory of Jerzy Słupecki
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Simons, P.M. Tree proofs for syllogistic. Studia Logica 48, 539–554 (1989). https://doi.org/10.1007/BF00370206
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DOI: https://doi.org/10.1007/BF00370206