Restricted higher-order anti-unification for analogy making

  • Authors:
  • Ulf Krumnack;Angela Schwering;Helmar Gust;Kai-Uwe Kühnberger

  • Affiliations:
  • Institute of Cognitive Science, Osnabrück;Institute of Cognitive Science, Osnabrück;Institute of Cognitive Science, Osnabrück;Institute of Cognitive Science, Osnabrück

  • Venue:
  • AI'07 Proceedings of the 20th Australian joint conference on Advances in artificial intelligence
  • Year:
  • 2007

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Abstract

Anti-unification has often be used as a tool for analogy making. But while first-order anti-unification is too simple for many applications, general higher-order anti-unification is too complex and leads into theoretical difficulties. In this paper we present a restricted framework for higher-order substitutions and show that anti-unification is well-defined in this setting. A complexity measure for generalizations can be introduced in a quite natural way, which allows for selecting preferred generalizations. An algorithm for computing such generalizations is presented and the utility of complexity for anti-unifying sets of terms is discussed by an extended example.