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Understanding PML A Proof Markup Language

Understanding PML A Proof Markup Language. Presented by Li Ding ding.li@umbc.edu. Motivation. Explicitly represent the proof trace to enable better understanding and justification Representation Proof traces of logical reasoning: reasoner, theory prover

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Understanding PML A Proof Markup Language

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  1. Understanding PMLA Proof Markup Language Presented by Li Ding ding.li@umbc.edu

  2. Motivation Explicitly represent the prooftrace to enable better understanding and justification • Representation • Proof traces of logical reasoning: reasoner, theory prover • Provenance information: who? when? where? • Multi-granular inference path: human/machine oriented • Application • Portable proofs: proofs are available upon request • Human understanding/browsing proof trace: filter out trivial steps • Machine exchange/verify reasoning steps

  3. PML Outline • Ontology Specification • Proof • Provenance • Ontology usage • Hybrid reasoning in JTP • Human friendly explanation

  4. Proof Ontology (my understanding) rdf:type ExpressionLanguage Expression hasEL hasConclusion 0* hasDischargedAssumption 1 1 NodeSet 1 hasAntecedents Antecedents* 1 hasInferenceRule InferenceRule rdf:sequence 0* hasBidings VariableBiding hasSource Source InferenceStep 1 hasEngine InferenceEngine 1 TimeStampe xsd:dateTime

  5. Example

  6. Example: GUI Proof Trace http://belo.stanford.edu:8080/iwbrowser/WffBrowser?w=900&mg=1&st=Proof&fm=English&url=http://www.ksl.stanford.edu/software/iw/ex/jtp/wine/tonysns2_0.daml%23tonysns2_0

  7. Example: DAML Proof trace (adapted from http://www.ksl.stanford.edu/software/iw/ex/jtp/wine/tonysns2_0.daml

  8. Provenance Ontology (class hierarchy) • ProvenanceElement • URI • URL • Name • Submitter • DateTimeInitialSubmission • DateTimeLastSubmission • EnglishDescription InferenceEngine KnowledgeSource Organization Source Person Publication InferenceRule RepresetationLanguage ExpressionLanguage DerivedRule DeclarativeRule Team PrimitiveRule Method

  9. Inference Web Framework Diagram http://ksl.stanford.edu/software/IW/arch/IWOverviewDetail.gif

  10. Hybrid reasoning in JTP • JTP architecture supports hybrid reasoning • PML as interchange language • Commands (truth maintenance related) • Tell: Given a sentence, tell conclusion • When B was told by A about sentence S, B will add S to its KB if no contradiction detected. B will acknowledge A about the result: new proof or contradiction • Ask: Given a conclusion, tell inference steps that cause it • When B as asked by A about C, B will tell a set of inference step that has C as conclusion

  11. Human friendly explanation • Proof Len • Directly access to single proof step • Hide trivial inference steps • Web interface

  12. Future work & Reference • More considerations… • Relax logical proof to general justification • Application in P2P network • Collaborative writing • Privacy preserving proof sharing (justification) • Reference Paulo Pinheiro da Silva, Deborah L. McGuinness, and Richard E. Fikes, [A Proof Markup Language for Semantic Web Services], Technical Report KSL-04-01. Knowledge Systems Laboratory, Stanford University. 2004.

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