Logics for the relational syllogistic

Review of Symbolic Logic 2 (4):647-683 (2009)
Abstract
The Aristotelian syllogistic cannot account for the validity of certain inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subject noun phrase may contain a relative clause. The logics we present are extensions of the classical syllogistic, and we pay special attention to the question of whether reductio ad absurdum is needed. Thus our main goal is to derive results on the existence (or nonexistence) of syllogistic proof systems for relational fragments. We also determine the computational complexity of all our fragments
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References found in this work BETA
John Corcoran (1972). Completeness of an Ancient Logic. Journal of Symbolic Logic 37 (4):696-702.
John M. Martin (1997). Aristotle'S Natural Deduction Reconsidered. History and Philosophy of Logic 18 (1):1-15.
Ian Pratt-Hartmann (2004). Fragments of Language. Journal of Logic, Language and Information 13 (2):207-223.

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Citations of this work BETA
Ian Pratt-Hartmann (2013). The Syllogistic with Unity. Journal of Philosophical Logic 42 (2):391-407.
Lawrence S. Moss (2011). Syllogistic Logic with Comparative Adjectives. Journal of Logic, Language and Information 20 (3):397-417.
Hanoch Ben-Yami (2014). The Quantified Argument Calculus. Review of Symbolic Logic 7 (1):120-146.

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