Logics for the Relational Syllogistic

Details Logics for the Relational Syllogistic Logics for the Relational Syllogistic

2008-08-04

arxiv.org/abs/0808.0521v1

Computer Science

Logic in Computer Science

Scientific paper

The Aristotelian syllogistic cannot account for the validity of many 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 non-existence) of syllogistic proof systems for relational fragments. We also determine the computational complexity of all our fragments.

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