A Framework for Agent-Based Brokering of Reasoning Services E R S - - PowerPoint PPT Presentation

U N I V E R S I T A S S A R A V I E N S I S

U N I V E R S I T A S S A R A V I E N S I S

A Framework for Agent-Based Brokering of Reasoning Services

Jürgen Zimmer

Universität des Saarlandes, Germany. (University of Edinburgh, Scotland.) This work is supported by the European Union CALCULEMUS IHP Training Network HPRN-CT-2000-00102

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

Overview

Motivation: Combination of Reasoning Systems A new Framework for Online Reasoning Services Formal Descriptions of Reasoning Services Theorem Proving and Proof Transformation Services Brokering of Theorem Proving Services Conclusion & Future Work

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

Motivation

Many specialized reasoning systems are currently available: Deduction Systems: Automated Theorem Provers (e.g. Otter, SPASS, Vampire) Model Generators (e.g. MACE, SEM) Proof Assistants (e.g. Isabelle) Computation Systems (e.g., Maple, GAP , Matlab) Problem: Systems are not open and only usable by experts. Goal: Make systems interoperable for automated combination and coordination of specialized systems

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

Previous Experience

Our first attempt was the MATHWEB Software Bus [CADE’02]: Combines heterogeneous reasoning systems

• n the system level (ATPs, MGs, CAS, HR,

• Clam, PVS).

Similar to CORBA distribution middle-ware. Offers standard protocols (HTTP , XML-RPC) Used by OMEGA, INKA,

• Clam.

HR (Automated theory formation). DORIS (NLP).

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

Limitations of MathWeb Software Bus

Despite its successful use, it had some limitations: Client applications still have to know which reasoning system to use, and how to access the system (API). User has to coordinate different reasoning systems to solve a problem.

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

The New MathServ Framework

Semantic Web AI Planning Web Services

MathServ

MathWeb Software Bus

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

The MathServ Framework

A new framework for semantic reasoning services: Based on Web Service technology. Agents offering reasoning services described in the Mathematical Service Description Language (MSDL):

Developed by MONET and MathBroker project.

Ideas from Semantic Web activity (Semantic WS).

Based on commonly agreed ontology. Brokering mechanism retrieves and combines reasoning services using modified POP planner.

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

Benefits of MathServ

The MathServ framework can be used by humans or machines to... retrieve reasoning services (human

machine) given a semantic description of a problem. automatically combine services to tackle a problem. tackle subproblems in automatic or interactive theorem proving. No need to know the underlying reasoning system!

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

Ongoing Work

For our framework, we have to integrate systems in Web Service framework. develop an ontology for service descriptions. describe systems’ capabilities in MSDL. develop brokering mechanism for MSDL services.

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

System Integration

We are currently integrating proving and transformation services: Automated Theorem Proving (ATP) systems for First-order predicate logic with equality. Tools for transformation between different formats. (TSTP , OpenMath, OMDoc, POST) Tools for proof transformation. (Resolution and Natural Deduction calculus)

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

An Ontology for Service Descriptions

1..1 0..1

Thing Proof Proving−Problem is−a TSTP− CNF−Problem

proofOf

FO−Proving−Problem Result Result is−a

proof

FO−ATP− CNF−Refutation TSTP− FOF−Problem Formal−Proof Semi−Formal−Proof NL−Proof ND−Proof

Developed in Web Ontology Language (OWL) with Protégé Tool. ND-Proof represents proofs in Natural Deduction calculus. NL-Proof stands for proofs in Natural Language.

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

The Mathematical Service Description Language (MSDL)

MSDL describes... Classification of a service (Taxonomy, etc.). Input and Outputs of a service. Pre- and Post-conditions. Properties of underlying algorithms, hardware and software. MSDL has been used to... Describe fine-grained computation services (symbolic & numeric), e.g., given

and

, compute

. Semantic retrieval of service matching a query.

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

An ATP Service in MSDL

The central part of an MSDL description [MICAI’04]: Service:

input parameters: problem::TSTP-CNF-Problem (OWL class)

• utput parameters:

result::FO-ATP-Result pre-conditions:

post-conditions: mweb#proof(?result, ?proof)

RDF#type(?proof, TSTP-CNF-Refutation) We completely omit XML details. Conditions in Semantic Web Rule Language (SWRL) (RDF-triples, conjunction, implications).

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

A Proof Transformation Service

The

system can create ND proofs for first-order problems: Service:

input parameters: fofProblem::TSTP-FOF-Problem atpResult::FO-ATP-Result

• utput parameters:

ndProof::ND-Proof pre-conditions: proof(atpResult, ?proof)

type(?proof, TSTP-CNF-BrFP-Refutation) post-conditions: proofOf(ndProof, fofProblem) [WS7 on IJCAR’04]

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

Brokering of Services (Example)

Scenario: Brokering of proving (transformation) services. Available Services:

: clause normal form generator.

/

: first-order theorem proving services.

: transforms arbitrary refutation proofs in resolution proofs in restricted Otter calculus (BrFP).

: Transforms refutation proofs in BrFP calculus into ND. Query: Given: Higher-order conjecture

. Want: ND proof object

.

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

The Broker’s Execution Plans

NDforFOF

ND−Proof

EpATP Otterfier

Γ |−− ψ Γ |−− ψ

FOF2CNF

TSTP−FOF−Problem( ) TSTP−CNF−Problem( )

proofOf

FO−ATP−Result

NDforFOF

ND−Proof

OtterATP

Γ |−− ψ

FOF2CNF

TSTP−FOF−Problem( )

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

Conclusion

We presented the MathServ framework which offers... ... semantically described reasoning services. ... a semantic brokering and coordination mechanism. We started describing theorem provers and proof transformation tools. Our broker can provide customized execution plans for a given query.

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• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

Ongoing and Future Work

Service Grounding: “How a service is invoked”

MONET plan executor? Description of other reasoning systems (e.g., model generators, decision procedures). More fine-grained services (like MONET). (e.g., given

, prove that

is prime). Advanced brokering with reasoning on ontology (subsumption test, etc.). disjunctive plans (or re-planning).

c

• J.Zimmer

Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004