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LOGICS FOR THE RELATIONAL SYLLOGISTIC

  • IAN PRATT-HARTMANN (a1) and LAWRENCE S. MOSS (a2)
  • DOI: http://dx.doi.org/10.1017/S1755020309990086
  • Published online: 01 December 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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Corresponding author
*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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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

J. N Martin . (1997). Aristotle’s natural deduction revisited. History and Philosophy of Logic, 18(1), 115.

D. A. McAllester , & R Givan . (1992). Natural language syntax and first-order inference. Artificial Intelligence, 56, 120.

D. D Merrill . (1990). Augustus De Morgan and the Logic of Relations. Dordrecht, The Netherlands: Kluwer Academic Publishers.

I Pratt-Hartmann . (2004). Fragments of language. Journal of Logic, Language and Information, 13, 207223.

T. J Smiley . (1973). What is a syllogism? Journal of Philosophical Logic, 2, 135154.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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