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O IS NOT ENOUGH

  • J. B. PARIS (a1) and R. SIMMONDS (a1)
  • DOI: http://dx.doi.org/10.1017/S1755020309090236
  • Published online: 01 June 2009
Abstract

We examine the closure conditions of the probabilistic consequence relation of Hawthorne and Makinson, specifically the outstanding question of completeness in terms of Horn rules, of their proposed (finite) set of rules O. We show that on the contrary no such finite set of Horn rules exists, though we are able to specify an infinite set which is complete.

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*SCHOOL OF MATHEMATICS, UNIVERSITY OF MANCHESTER, MANCHESTER M13 9PL, UK. E-mail:jeff.paris@manchester.ac.uk
SCHOOL OF MATHEMATICS, UNIVERSITY OF MANCHESTER, MANCHESTER M13 9PL, UK. E-mail:richard.simmonds@gmail.com
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J Hawthorne . (1996). On the logic on non-monotonic conditionals and conditional probabilies. Journal of Philosophical Logic, 25, 185218.

J Hawthorne . (2007). Nonmonotonic conditionals that behave like conditional probabilities above a threshold. Journal of Applied Logic, 5, 625637.

J. Hawthorne , & D Makinson . (2007). The qualitative/quantitative watershed for rules of uncertain inference. Studia Logica, 86, 247297.

S. Krauss , D. Lehmann , & M Magidor . (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44, 167207.

D. Lehmann , & M Magidor . (1992). What does a conditional knowledge base entail? Artificial Intelligence, 55, 160.

A Pillay . (1981). Models of Peano Arithmetic, In editors Berline, McAloon, and Ressayre, editors. Model Theory and Arithmetic, Lecture Notes in Mathematics, Vol. 890. Berlin: Springer-Verlag, pp. 112.

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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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