Unification of stratified second-order terms

  • We consider the problem of unifying a set of equations between second-order terms. Terms are constructed from function symbols, constant symbols and variables, and furthermore using monadic second-order variables that may stand for a term with one hole, and parametric terms. We consider stratified systems, where for every first-order and second-order variable, the string of second-order variables on the path from the root of a term to every occurrence of this variable is always the same. It is shown that unification of stratified second-order terms is decidable by describing a nondeterministic decision algorithm that eventually uses Makanin's algorithm for deciding the unifiability of word equations. As a generalization, we show that the method can be used as a unification procedure for non-stratified second-order systems, and describe conditions for termination in the general case.

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Author:Manfred Schmidt-SchaußORCiDGND
Parent Title (English):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik ; 1
Parent Title (German):Universität Frankfurt am Main. Fachbereich Informatik: Interner Bericht ; 94,12
Series (Serial Number):Interner Bericht / Fachbereich Informatik, Johann Wolfgang Goethe-Universität Frankfurt a.M. (94,12)
Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik (1)
Publisher:Johann Wolfgang Goethe-Univ., Fachbereich Informatik und Mathematik, Inst. für Informatik, Research group for Artificial Intelligence and Software Technology
Place of publication:Frankfurt [am Main]
Document Type:Working Paper
Year of Completion:1994
Year of first Publication:1994
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/05/12
Page Number:39
First Page:1
Last Page:39
Source:Internal report 12/94
Institutes:Informatik und Mathematik / Informatik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):License LogoDeutsches Urheberrecht