Restricted Higher-Order Anti-Unification for Analogy Making

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...

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Bibliographic Details
Published inAI 2007: Advances in Artificial Intelligence Vol. 4830; pp. 273 - 282
Main Authors Krumnack, Ulf, Schwering, Angela, Gust, Helmar, Kühnberger, Kai-Uwe
Format Book Chapter
LanguageEnglish
Published Germany Springer Berlin / Heidelberg 2007
Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Artificial intelligence
Basic Substitution
Complexity Measure
Data mining
Function Symbol
General Generalization
Mathematical theory of computation
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ISBN9783540769262
3540769269
ISSN0302-9743
1611-3349
DOI10.1007/978-3-540-76928-6_29

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Summary: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.
ISBN:9783540769262
3540769269
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-540-76928-6_29