William Naylor

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.

Semantic matching for mathematical services

The amount of machine oriented data on the web as well as the deployment of agent/Web Services are simultaneously increasing. This poses a service-discovery problem for client agents wishing to discover Web Services to perform tasks. We discuss a prototype mathematical service broker and look at an approach to circumventing the ambiguities arising from alternative but equivalent mathematical representations occurring in mathematical descriptions of tasks and capabilities.

Matchmaking of mathematical web services

Service discovery and matchmaking in a distributed environment has been an active research issue since at least the mid 1990s. 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. 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 four kinds of plug-in that we have developed to date.

From untyped to polymorphically typed objects in mathematical web services

OpenMath is a widely recognised approach to the semantic markup of mathematics that is often used for communication between OpenMath compliant systems. The Aldor language has a sophisticated category-based type system that was specifically developed for the purpose of modelling mathematical structures, while the system itself supports the creation of small-footprint applications suitable for deployment as web services. In this paper we present our first results of how one may perform translations from generic OpenMath objects into values in specific Aldor domains, describing how the Aldor interface domain ExpressionTree is used to achieve this. We outline our Aldor implementation of an OpenMath translator, and describe an efficient extension of this to the Parser category. In addition, the Aldor service creation and invocation mechanism are explained. Thus we are in a position to develop and deploy mathematical web services whose descriptions may be directly derived from Aldors rich type language.

Agent-based matchmaking of mathematical web services

Service discovery and matchmaking in a distributed environment has been an active research issue since at least the mid 1990s. 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. 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.

Mathematical matchmaker for numeric and symbolic services

Service discovery and matchmaking in a distributed environment has been an active research issue since at least the mid 1990s. 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. 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 mathematical matchmaker supporting the use of match plug-ins.