Matchmaking framework for mathematical web services

Service discovery and matchmaking in a distributed environment has been an active research issue for some time now. Previous work on matchmaking has typically presented the problem and service descriptions as free or structured (marked-up) text, so that keyword searches, tree-matching or simple constraint solving are sufficient to identify matches. In this paper, we discuss the problem of matchmaking for mathematical services, where the semantics play a critical role in determining the applicability or otherwise of a service and for which we use OpenMath descriptions of pre- and post-conditions. We describe a matchmaking architecture supporting the use of match plug-ins and describe five kinds of plug-in that we have developed to date: (i) A basic structural match, (ii) a syntax and ontology match, (iii) a value substitution match, (iv) an algebraic equivalence match and (v) a decomposition match. The matchmaker uses the individual match scores from the plug-ins to compute a ranking by applicability of the services. We consider the effect of pre- and post-conditions of mathematical service descriptions on matching, and how and why to reduce queries into Disjunctive Normal Form (DNF) before matching. A case study demonstrates in detail how the matching process works for all four algorithms. © Springer Science+Business Media, Inc. 2006.