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Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation

Volume 9060 of the series Lecture Notes in Computer Science pp 81-95

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

  • Gabriele Kern-IsbernerAffiliated withDepartment of Computer Science, TU Dortmund
  • , Christoph BeierleAffiliated withDepartment of Computer Science, University of Hagen

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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.