A System Z-like Approach for First-Order Default Reasoning

  • Gabriele Kern-Isberner
  • Christoph Beierle

Abstract

Default rules of the form “If A then (usually, probably) B” can be represented conveniently by conditionals. To every consistent knowledge base \(\mathcal{R}\) with such qualitative conditionals over a propositional language, system Z assigns a unique minimal model that accepts every conditional in \(\mathcal{R}\) and that is therefore a model of \(\mathcal{R}\) inductively completing the explicitly given knowledge. In this paper, we propose a generalization of system Z for a first-order setting. For a first-order conditional knowledge base \(\mathcal{R}\) over unary predicates, we present the definition of a system Z-like ranking function, prove that it yields a model of \(\mathcal{R}\), and illustrate its construction by a detailed example.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Gabriele Kern-Isberner
    • 1
  • Christoph Beierle
    • 2
  1. 1.Department of Computer ScienceTU DortmundGermany
  2. 2.Department of Computer ScienceUniversity of HagenGermany

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