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

� E R S V I T I N A U S S S A I S R N A E V I A Framework for Agent-Based Brokering of Reasoning Services E R S V I T I N A U Jürgen Zimmer S S S I A Universität des Saarlandes, Germany. S R N A E V I (University of Edinburgh, Scotland.) This work is supported by the European Union C ALCULEMUS IHP Training Network HPRN-CT-2000-00102 c 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 c 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 c J.Zimmer Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

✁ ✁ � Previous Experience Our first attempt was the M ATH W EB Software Bus [CADE’02]: Combines heterogeneous reasoning systems on 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). c 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. c J.Zimmer Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

� The New MathServ Framework MathWeb Software Web Services Bus MathServ AI Semantic Web Planning c 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. c 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! c 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. c 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) c J.Zimmer Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

� An Ontology for Service Descriptions Thing proofOf Proving−Problem Proof Result 1..1 Semi−Formal−Proof Formal−Proof is−a is−a proof FO−ATP− FO−Proving−Problem NL−Proof ND−Proof CNF−Refutation Result 0..1 TSTP− TSTP− CNF−Problem FOF−Problem 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. c 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. c 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) output 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). c 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 output parameters: ndProof ::ND-Proof pre-conditions: proof(atpResult, ?proof) type(?proof, TSTP-CNF-BrFP-Refutation) post-conditions: proofOf ( ndProof , fofProblem ) [WS7 on IJCAR’04] c 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 . c J.Zimmer Workshop on Logic, Proofs, and Programs, Nancy, 17–18th June, 2004

� The Broker’s Execution Plans TSTP−FOF−Problem( ) Γ |−− ψ TSTP−FOF−Problem( ) Γ |−− ψ FOF2CNF FOF2CNF Γ |−− ψ TSTP−CNF−Problem( ) proofOf EpATP OtterATP FO−ATP−Result Otterfier NDforFOF NDforFOF ND−Proof ND−Proof c 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. c 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