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The Well-Founded Semantics Is the Principle of Inductive Definition

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Logics in Artificial Intelligence (JELIA 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1489))

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Abstract

Existing formalisations of (transfinite) inductive definitions in constructive mathematics are reviewed and strong correspondences with LP under least model and perfect model semantics become apparent. I point to fundamental restrictions of these existing formalisations and argue that the well-founded semantics (wfs) overcomes these problems and hence, provides a superior formalisation of the principle of inductive definition. The contribution of this study for LP is that it (re-) introduces the knowledge theoretic interpretation of LP as a logic for representing definitional knowledge. I point to fundamental differences between this knowledge theoretic interpretation of LP and the more commonly known interpretations of LP as default theories or auto-epistemic theories. The relevance is that differences in knowledge theoretic interpretation have strong impact on knowledge representation methodology and on extensions of the LP formalism, for example for representing uncertainty.

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Author information

Authors and Affiliations

  1. Department of Computer Science, K.U.Leuven, Belgium

    Marc Denecker

Authors
  1. Marc Denecker
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Maryland, College Park, Maryland, 20742, USA

    Jürgen Dix

  2. I.R.I.T. Université Paul Sabatier, 118 route de Narbonne, F-31062, Toulouse Cedex, France

    Luís Fariñas del Cerro

  3. Fachbereich 4: Informatik, Universität Koblenz, Rheinau 1, D-56075, Koblenz, Germany

    Ulrich Furbach

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© 1998 Springer-Verlag Berlin Heidelberg

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Denecker, M. (1998). The Well-Founded Semantics Is the Principle of Inductive Definition. In: Dix, J., del Cerro, L.F., Furbach, U. (eds) Logics in Artificial Intelligence. JELIA 1998. Lecture Notes in Computer Science(), vol 1489. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49545-2_1

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  • DOI: https://doi.org/10.1007/3-540-49545-2_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65141-3

  • Online ISBN: 978-3-540-49545-1

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