Mathematical Service Discovery - Semantic Scholar

Mathematical Service Discovery Julian Padget Department of Computer Science University of Bath, UK

20060913 / ENGAGE: Jakarta

Julian Padget (CS Dept, Bath UK)

Mathematical Service Discovery


1 / 26

Outline

1

Project history Context OpenMath MONET

2

Recent work GENSS

3

Current and future work KNOOGLE Conclusion




2 / 26

Project history

Context

People, places, projects...

Universit of Bath: Bill Naylor, Julian Padget Cardiff Universit : Simone Ludwig, Tom Goodale, Omer Rana NAG Ltd., Stilo Ltd., University of Eindhoven, Université de Nice/INRIA Sophia Antipolis, University of Manchester, University of Western Ontario OpenMath, MONET, GENSS, KNOOGLE: running from mid 1990s until now




3 / 26

Project history

Context

The Vision Identification, composition and invocation of (mathematical) web services from functional description: e-scientist .. . mathematical web services .. . software agent

Plumbing is (relatively) easy, saying what you want is not Julian Padget (CS Dept, Bath UK)



4 / 26

Project history

Context

Matchmaking and Brokerage

Matchmaking: identifying candidate services Brokerage: matchmaking + selection + invocation Problem: establishing “degree” of match between task and capability. Outcomes to expect: Exact match No match Partial match—how? what does this mean? what are the criteria?

Mathematical capability descriptions are a blessing and a curse: Precise service descriptions possible But service matching can rapidly become intractable




5 / 26

Project history

OpenMath

The OpenMath Project Objective: Framework for an extensible mathematical ontology OpenMath: http://www.openmath.org, EU, 1997–2000 and 2001–2004 OpenMath 1.1 Standard (October 2002) OpenMath 2.0 Standard (June 2004) Defines mathematical symbols and concepts, organized by content dictionaries (CDs) Simple markup encompassing application (OMA), integer (OMI), symbol (OMS) and variable (OMV) Extensible, in contrast to MATHML[-C] Defined as the escape language for MATHML[-C]




6 / 26

Project history

OpenMath

OpenMath example OpenMath representation of x 2 − y 2 : 2 2

Note: old style XML, heavy use of attributes, no namespaces. Changed in OpenMath 2.0 (2004).




7 / 26

Project history

MONET

The MONET Project Objective: Demonstrate end-to-end functionality from query through service discovery to invocation MONET: http://monet.nag.co.uk, EU, 2002–2004 Schema definition: Mathematical Service Description Language, Mathematical Problem Description Language, Mathematical Explanation Language Basic ontologies: hardware, software, algorithms, problems Link to and extend GAMS gams.nist.gov Brokerage, service selection by ontological reasoning, orchestration with BPEL4WS Some project-specific solutions to meet deliverables See [Caprotti et al., 2004]




8 / 26

Project history

MONET

The MONET Architecture MONET (OWL) ontologies

provider

MSDL

MQDL

OpenMath ontologies

MPDL

client

MEL

lem prob

lts su re

MONET broker Registry Manager

y er qu description repository (instance store) Racer


rv se

Execution Manager BPEL4WS/Jelly

Plan Manager

s ice service A axis/tomcat


service B axis/tomcat


9 / 26

Recent work

GENSS

The GENSS Project

Objectives: Mathematical reasoning to identify suitable services; Integration with UK e-Science program (semantic grids theme) GENSS: http://genss.cs.bath.ac.uk, EPSRC, 2004–2006 Extend matching to capabilities and effects Diversify range of services Move towards integration with Grid See [Ludwig et al., 2006] (mathematical service matching) and [Goodale et al., 2006] (matchmaking/brokerage architecture)




10 / 26

Recent work

GENSS

The GENSS Architecture ···

HTTP/SOAP

Ontology server (OWL) @ Cardiff

TCP Portal

HT

AP /SO TP

UDDI registry @ Cardiff Matching algorithms

Broker Rule-based + (Java) Reasoner

HT

HTTP/SOAP

Java Beans

Web Services (Matching algorithms) @ Cardiff

Authorization Server


Ontology server (OWL) @ Bath

TP /SO AP

MSQL database @ Cardiff Mathematical service descriptions

··· Numeric and Symbolic Services @ Bath



11 / 26

Recent work

GENSS

GENSS Matchmaking Strategy Two phases: Service registration: Convert service to normal form Put in registry

Conversion to normal form dominates complexity. Service lookup: Convert query to normal form Traverse registry, calculating a similarity value between the query and each service Return a list of service URLs ordered on the similarity value.

Traversal of the registry dominates complexity.




12 / 26

Recent work

GENSS

Normalization Dissimilar (mathematical) expressions can be equivalent No absolute normal form exists But can normalize for purpose: Logical equivalences – standard rewrites Associative operators – flattened Context dependent equivalences Alpha conversions – consistent naming Commutative operators – reorder arguments Conversion to disjunctive normal form (cost: O(2n ))

Conditions and effects take the form Q(L(R)): Q is a quantifier block e.g. ∀x∃y s.t. · · · L is a block of logical connectives e.g. ∧, ∨, ⇒, · · · R is a block of relations. e.g. =, ≤, ≥, 6=, · · ·




13 / 26

Recent work

GENSS

Matching techniques 1/2

Structural Task and capability match exactly

Syntax+Ontology: Compare elements and attributes in task and capability using taxonomic structure of types to test for inclusion

Ontological reasoning (demonstrated in MONET): Translate task description into OWL Compute match using Description Logic reasoner (Racer) Sort capabilities that satisfy: Tin ≥ Cin ∧ Tout ≤ Cout




14 / 26

Recent work

GENSS

Matching techniques 2/2

Function: Use conditions and effects: Tcond ⇒ Ccond ∧ Ceff ⇒ Teff Algebraic equivalence: show that Q − S = 0 algebraically. In general undecidable, but often works in practice. eg. x 2 − y 2 and (x + y )(x − y ). Value substitution: show that Q − S = 0 by substituting random values into the expression and evaluating (Richardson’s Theorem). Result is evidence, not proof.

Planned: Reputation metrics/third-party annotation Planned: Semantic textual analysis




15 / 26

Recent work

GENSS

The Broker from Triana 1/2




16 / 26

Recent work

GENSS

The Broker from Triana 2/2




17 / 26

Recent work

GENSS

Generation of Semantic Descriptions

Sources: Manual authoring... Documentation — hence textual analysis Synthesis from type information (note: very preliminary): Experimentation with a two-level polymorphic dependent type system (Aldor) Automatic wrapper generation Automatic generation of OpenMath for service description Depends on availability of appropriate CDs




18 / 26

Recent work

GENSS

GENSS Outcomes

Development of a prototype matchmaker shell allowing Domain-specific ontologies Co-existence of multiple match modes Combination of results from multiple match modes Automated access to numerical web services

Development of plug-ins for the matchmaker shell Demonstration of the approach with Maple-based mathematical services Investigation of scalability of the shell and rule-based reasoner (OWLJessKB) Integration with the Triana workflow engine www.triana.org




19 / 26

Current and future work

KNOOGLE

The KNOOGLE Project

Objectives: Refactoring of GENSS architecture to produce generic tools; Demonstrators based on current UK e-Science projects Open Middleware Infrastructure Institute (OMII), 2006–2007 Provide minimalist brokerage functions for e-Science: Where to find descriptions of entities to match against How to match the query against a description How to choose between the matched descriptions

Implement a re-configurable, re-targettable architecture for matchmaking and brokerage




20 / 26


KNOOGLE

Options for Brokerage Specialization vs. late-binding of function creates three options: No fixed actions One fixed action: the matching service comes with A set of registries or A set of matchers or A selection function

Two fixed actions: the matching service comes with A set of registries and a set of matchers or A set of registries and a selection function or A set of matchers and a selection function

Three fixed actions: a set of registries and a set of matchers and a selection function




21 / 26


KNOOGLE

The KNOOGLE Architecture

··· Web Services (Matching algorithms)

HT

AP /SO TP

BROKER WORK-FLOW match plugin Command Line Interface

HTTP SOAP

user query

match plugin

GRIMOIRES REGISTRY Matching algorithms ranking function GRIMOIRES REGISTRY Grid service descriptions

match plugin HT

TP /SO AP

··· Grid Services




22 / 26


Conclusion

Summary

OpenMath provides an extensible framework for the authoring of mathematical ontologies MONET demonstrates feasibility of semantic processing from user query to service invocation [Caprotti et al., 2004] GENSS generalizes the matchmaking/brokerage component [Ludwig et al., 2006] and extends matching to conditions and effects [Naylor and Padget, 2006] KNOOGLE implements an open architecture for matchmaking and brokerage [Goodale et al., 2006]




23 / 26


Conclusion

Outlook

Over the next year: Basic command-line tools for broker and registry manipulation by October 2006 Integration with OMII stack (OMII project: Southampton) Integration with GridSAM (OMII project: Imperial) Integration with Taverna (OMII project: Manchester) Development of a range of matchers (including e.g. ClassAds) and selection policies Tools for end-user construction and deployment of brokers




24 / 26


Conclusion

Open issues

Reputation/Recommender systems and third-party annotations Semantics textual analysis Shim service: discovery/generation Early adopters: GridSAM (e-Protein, Application Hosting Environment) my Grid — bioinformatics RealityGrid —a range of applications in physics and chemistry and ...?




25 / 26


Conclusion

References Caprotti, O., Dewar, M., Davenport, J., and Padget, J. (2004). Mathematics on the (Semantic) Net. In Bussler, C., Davies, J., Fensel, D., and Studer, R., editors, Proceedings of the European Symposium on the Semantic Web, volume 3053 of LNCS, pages 213–224. Springer Verlag. ISBN 3-540-21999-4. Goodale, T., Ludwig, S. A., Naylor, W., Padget, J., and Rana, O. F. (2006). Service-oriented matchmaking and brokerage. In Watson, P., editor, Proceedings of UK e-Science All Hands conference. EPSRC. Ludwig, S., Rana, O., Naylor, W., and Padget, J. (2006). Matchmaking framework for mathematical web services. Journal of Grid Computing, pages 1–16. Available via http://dx.doi.org/10.1007/s10723-005-9019-z. ISSN: 1570-7873 (Paper) 1572-9814 (Online). Naylor, W. and Padget, J. (2006). Semantic matching for mathematical services. In Kohlhase, M., editor, Mathematical Knowledge Management: 4th International Conference, MKM 2005, volume 3863 of LNCS, pages 174–189. Springer Verlag. ISBN: 3-540-31430-X. Available via http://dx.doi.org/10.1007/11618027_12. Julian Padget (CS Dept, Bath UK)



26 / 26