Brokering of Theorem Proving Services Described in MSDL

Transcription

1 U N S A R I V E R S A V I E I T A S N I S S Brokering of Theorem Proving Services Descried in MSDL Jürgen Zimmer University of Edinurgh, Scotland Universität des Saarlandes, Germany This work is supported y the CALCULEMUS IHP Training Network HPRN-CT

2 Overview Motivation Our Agent Framework An Ontology for Deductive Services First-order ATP Services Classification of Theorem Proving Prolems Broker for FO-ATP Services A Little Demonstration

3 Motivation DORIS Client (Prolog) request service reference UED Broker (Mozart) λclam PP Spass ATP Ωmega PP MathWe Clients Ωmega Client (Lisp) Broker UBIR forward request (un ) register Broker USAAR Maple CAS MBase KB MathWe Servers HR Client (Java) Broker Broker RDL ATP UED tptp2x Trans UGE Vampire ATP roker to roker communication client to roker communication (Mozart, XMLRPC, HTTP) server to roker communication (service offers/requests)

4 Motivation Despite its success, MathWe-SB some limitations: Client applications still have to know which reasoning system to use, and how to access the system. User has to coordinate different reasoning systems to solve a prolem. The MathWe-SB is not designed for asynchronous communication. Technical Prolems (OS, Firewalls, Proxies)

5 A New Agent Framework From MathWe-SB to the Semantic MathWe-SB:... ased on FIPA compliant agent platform (JADE)... agents offering reasoning services descried in service description language: currently MSDL (developed in MONET and MathBroker) in the future also OWL-S (OWL)?... a rokering mechanism for reasoning services.

6 Ongoing Work Implementing agents and communication in JADE Designing an Ontology in Protégé-2000 tool (Protégé-2 supports OWL). Descriing first-order Automated Theorem Provers (ATPs) in MSDL using our ontology. Mapping MSDL to Java classes. Implementing simple rokering: analysing prolems in queries. find most suitale service.

7 An Ontology for Deduction Services Thing Logic Prolem Resource Result ProverState logic is a is a... is a a.. Suconcept Proving time Time time Prolem 0..1 Resource 0..1 formal Slot(+Restriction) Instance OMDoc logic Proof calc Calculus proof 0..1 FO ATP Result state Theorem FO ATP State Unsatisfiale Satisfiale

8 " $ " )! & '! & '! &% ' # *, / $, * One Ontology for All JADE Agent Ontology: Protege Ontology: Beangenerator! %& # %& ( % %& ( % ) %& ( JiBX? Ontology for Services (MSDL): +, + * *,.

9 First-order Theorem Proving Services Every first-order proving service accepts standard prolem formats TSTP and OMDoc.... returns a proof oject in standard format (TSTP).... is specialized on a particular domain. For an ontology for first-order ATPs use: Experience with the MathWe-SB. Recent work with Geoff Sutcliffe and Stephan Schulz on ATP states.

10 = > 1 = ; 0 ; > E F 0 =1 =2 G = 2H I First-order Theorem Proving Prolems FO proving prolems classified using known features (Sutcliffe & Suttner 2001): Logical Class of prolem: :<;= A ; 3 4 ; 1 7? (finite Herrand Universe) Equality:, BDCE, BDCE BDCE Presentation: vs. F G? = ; F G? = ; (first-order formulae) (clause normal form) 16 Specialists Prolems Classes (SPC) Performance data of well-known ATPs is availale for every SPC.

11 J J K J c ]\[ c _t s r`\ t y` r r` r][ The ATP SPASS in MSDL Service: SpassProver classification: Classification with Taxonomy of services or link to Ontology ( service interface: ( implementation details: spass prolem description ZY XW TRVU MS RQ LNMPO ) Information aout hardware, software (calculus, etc.) QPQ) input parameters: output parameters: pre-conditions: name: name: spass prolem description ^_a` }k\] a z({, signature:, signature: mnpoq l ikj i e gh dfe nx u ovw i e gh d e ^_` ~ ]\[ _ { z zt ]y (Ontology concept) (Ontology concept) (OpenMath Oject) ^_a` ~ ]\[ _ zt k {s y ] ^_a` ~ ]\[ ƒ ] \ ƒ ] post-conditions:

12 J J K J c ]\[ c _t s r`\ { `\ [ y The ATP E in MSDL Service: EProver classification: Classification with Taxonomy of services or link to Ontology ( service interface: ( implementation details: e prolem description ZY XW TRVU MS RQ LNMPO ) Information aout hardware, software (calculus, etc.) QPQ) input parameters: output parameters: pre-conditions: name: name: e prolem description ^_a`, signature:, signature: ^_a` ~ ]\[ `\ \ t z \r _ mnpoq l ikj i e gh dfe nx u ovw i e gh d e (Ontology concept) (Ontology concept) ^_a` ~ ]\[ _ zt k {s `\s ^_a` ~ ]\[ _ zt k {s } `\s zt y ] y post-conditions:

13 I A First Broker Our roker analyses incoming proving prolems using TSTP classifier (G. Sutcliffe).... annotates prolems with new preconditions puts prolem in SPC.... matches new prolem with availale services using tuprolog engine (DEIS, Università di Bologna).... calls the first matching service.

14 ž š Ž Ž Ž ª Ÿ š Ž A little Demo Two services: EProver & SpassProver Two queries: Query 1: Did Agatha commit suicide? Agatha hates x Butler hates x,... classified as, ˆŠ Œ žÿ, 6œ 6 Š Ž Query 1: Prolem in group theory: ˆŠ Œ ˆŠ Œ ˆŠ Ž ˆŠ Œ œ Ž «6, 6œ Ž, Ž classified as Consequently, roker selects SpassProver for Query 1 and EProver for Query 2.

15 ± Prolems To Solve Among others... Binding of MSDL to agent Ontology Currently, we use JiBX. Mathroker uses JAXB. I/O parameters of MSDL astract prolems: vs. XML-serialisation of Java Ojects (FO-ATP-Prolem) Invocation of service through JADE agent ehaviours (conversations). Comination of ehaviours.

16 ² Future Work Knowledge retrieval from ATP users and developers. Case study to show enefit of rokering. Extend ontology to logics & calculi. SOAP inding for MONET and Mathroker. Ontology in OWL ( Protege-2.0 & HarmonIA). Description of other reasoning systems (e.g., model generators). Advanced rokering (dynamic comination of services).

17 A Dream: MSDL Service Authoring Tool Logic a.. logic Prolem Proving time Time time state FO ATP FO ATP Prolem 0..1 Resource 0..1 Result State formal OMDoc Proof Theorem Satisfiale logic Suconcept Unsatisfiale Slot(+Restriction) Instance Calculus is a Ontology Thing Resource is a calc proof 0..1 Result... ProverState is a Repository of already specified JADE Agent Behaviours <DialogicFramework id="fishdialfrw" contentlanguage <Ontology id="fishonto" specificationlanguage="o <Role id="boss" type="internalrole"> <Behaviour id="open" type="simplebehaviour"/> <Behaviour id="discuss" type="compositebehavio <Behaviour id="initialresolution" type="oneshot revise use <Behaviour id="finalresolution" type="oneshotb </Behaviour> Service Editor