Logics for the Relational Syllogistic

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 th...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Pratt-Hartmann, Ian, Moss, Lawrence S
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 04.08.2008
Subjects:	Fragmentation Fragments
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	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.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.0808.0521