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General domain circumscription and its first-order reduction

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Practical Reasoning (FAPR 1996)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1085))

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Abstract

We first define general domain circumscription (GDC) and provide it with a semantics. GDC subsumes existing domain circumscription proposals in that it allows varying of arbitrary predicates, functions, or constants, to maximize the minimization of the domain of a theory. We then show that for the class of semi-universal theories without function symbols, that the domain circumscription of such theories can be constructively reduced to logically equivalent first-order theories by using an extension of the DLS algorithm, previously proposed by the authors for reducing second-order formulas. We also isolate a class of domain circumscribed theories, such that any arbitrary second-order circumscription policy applied to these theories is guaranteed to be reducible to a logically equivalent first-order theory. In the case of semi-universal theories with functions and arbitrary theories which are not separated, we provide additional results, which although not guaranteed to provide reductions in all cases, do provide reductions in some cases. These results are based on the use of fixpoint reductions.

Supported in part by the Swedish Council for Engineering Sciences (TFR).

Supported in part by KBN grant 3 P406 019 06.

Supported in part by KBN grant 3 P406 019 06.

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Author information

Authors and Affiliations

  1. Department of Computer and Information Science, Linköping University, S-581 83, Linköping, Sweden

    Patrick Doherty

  2. Institute of Informatics, Warsaw University, ul. Banacha 2, 02-097, Warsaw, Poland

    Witold Łukaszewicz & Andrzej Szałas

Authors
  1. Patrick Doherty
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  2. Witold Łukaszewicz
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  3. Andrzej Szałas
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Editor information

Dov M. Gabbay Hans Jürgen Ohlbach

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© 1996 Springer-Verlag Berlin Heidelberg

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Doherty, P., Łukaszewicz, W., Szałas, A. (1996). General domain circumscription and its first-order reduction. In: Gabbay, D.M., Ohlbach, H.J. (eds) Practical Reasoning. FAPR 1996. Lecture Notes in Computer Science, vol 1085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61313-7_65

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  • DOI: https://doi.org/10.1007/3-540-61313-7_65

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61313-8

  • Online ISBN: 978-3-540-68454-1

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