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LOGICS FOR THE RELATIONAL SYLLOGISTIC

Published online by Cambridge University Press:  01 December 2009

IAN PRATT-HARTMANN  and
LAWRENCE S. MOSS
IAN PRATT-HARTMANN*
Affiliation:
School of Computer Science, University of Manchester
LAWRENCE S. MOSS*
Affiliation:
Department of Mathematics, Indiana University
*
*SCHOOL OF COMPUTER SCIENCE, UNIVERSITY OF MANCHESTER, MANCHESTER M13 9PL, UK
†DEPARTMENT OF MATHEMATICS, INDIANA UNIVERSITY, 831 EAST THIRD STREET, BLOOMINGTON, IN 47405-7106, USA
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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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 4 , December 2009 , pp. 647 - 683
Copyright
Copyright © Association for Symbolic Logic 2009

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References

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