Please use this identifier to cite or link to this item: doi:10.22028/D291-24814
Title: Adding homomorphisms to commutative/monoidal theories or : how algebra can help in equational unification
Author(s): Baader, Franz
Nutt, Werner
Language: English
Year of Publication: 1990
OPUS Source: Kaiserslautern ; Saarbrücken : DFKI, 1990
SWD key words: Künstliche Intelligenz
DDC notations: 004 Computer science, internet
Publikation type: Report
Abstract: Two approaches to equational unification can be distinguished. The syntactic approach relies heavily on the syntactic structure of the identities that define the equational theory. The semantic approach exploits the structure of the algebras that satisfy the theory. With this paper we pursue the semantic approach to unification. We consider the class of theories for which solving unification problems is equivalent to solving systems of linear equations over a semiring. This class has been introduced by the authors independently of each other as commutative theories (Baader) and monoidal theories (Nutt). The class encompasses important examples like the theories of abelian monoids, idempotent abelian monoids, and abelian groups. We identify a large subclass of commutative/monoidal theories that are of unification type zero by studying equations over the corresponding semiring. As a second result, we show with methods from linear algebra that unitary and finitary commutative/monoidal theories do not change their unification type when they are augmented by a finite monoid of homomorphisms, and how algorithms for the extended theory can be obtained from algorithms for the basic theory. The two results illustrate how using algebraic machinery can lead to general results and elegant proofs in unification theory.
Link to this record: urn:nbn:de:bsz:291-scidok-35601
Series name: Research report / Deutsches Forschungszentrum für Künstliche Intelligenz [ISSN 0946-008x]
Series volume: 90-16
Date of registration: 7-Apr-2011
Faculty: SE - Sonstige Einrichtungen
Department: SE - DFKI Deutsches Forschungszentrum für Künstliche Intelligenz
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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