Please use this identifier to cite or link to this item: doi:10.22028/D291-40200
Title: On Solving Equations and Disequations
Author(s): Buntine, Wray L.
Bürckert, Hans-Jürgen
Language: English
Year of Publication: 1989
Place of publication: Kaiserslautern
Free key words: equational theory
definite clause
logic programming
solving equations and disequations
DDC notations: 004 Computer science, internet
Publikation type: Report
Abstract: We are interested in the problem of solving a system 〈s_i= t_i: 1≤i≤n,p_j≠q_j:1≤j≤m〉 of equations and disequations, also known as disunification. Solutions to disunification problems are substitutions for the variables of the problem that make the two terms of each equation equal, but leave those of the disequations different. We investigate this in both algebraic and logical contexts where equality is defined by an equational theory and more generally by a definite clause equality theory E. We show how E-disunification can be reduced to E-unification, that is solving equations only, and give a disunification algorithm for theories given a unification algorithm. In fact this result shows that for theories where the solutions of all unification problems can be represented by finitely many substitutions, the solutions of all disunifieation problems can also be represented finitely. We apply disunifieation to handle negation in logic programming with equality in a similar style to Colmerauer‘s logic programming with rational trees, and to represent many solutions to AC-unification problems by a few solutions to AC1-disunification problems.
Link to this record: urn:nbn:de:bsz:291--ds-402005
Series name: SEKI-Report / Deutsches Forschungszentrum für Künstliche Intelligenz, DFKI [ISSN 1437-4447]
Series volume: 89,3
Date of registration: 11-Aug-2023
Faculty: SE - Sonstige Einrichtungen
Department: SE - DFKI Deutsches Forschungszentrum für Künstliche Intelligenz
Professorship: SE - Sonstige
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