Understanding PML A Proof Markup Language Presented by

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 n Representation q q q n Proof traces of logical reasoning: reasoner, theory prover Provenance information: who? when? where? Multi-granular inference path: human/machine oriented Application q q q Portable proofs: proofs are available upon request Human understanding/browsing proof trace: filter out trivial steps Machine exchange/verify reasoning steps

PML Outline n Ontology Specification q q n Proof Provenance Ontology usage q q Hybrid reasoning in JTP Human friendly explanation

Proof Ontology (my understanding) Expression. Language has. EL 1 rdf: type Expression has. Conclusion 0* 1 Node. Set rdf: sequence has. Discharged. Assumption 1 has. Antecedents 1 has. Inference. Rule 0* has. Bidings has. Source Inference. Step 1 has. Engine 1 Time. Stampe Antecedents* Inference. Rule Variable. Biding Source Inference. Engine xsd: date. Time

Example

Example: GUI Proof Trace http: //belo. stanford. edu: 8080/iwbrowser/Wff. Browser? w=900&mg=1&st=Proof&fm=English&url=http: //www. ksl. stanford. edu/software/iw/ex/jtp/wine/tonysns 2_0. daml%23 tonysns 2_0

Example: DAML Proof trace (adapted from http: //www. ksl. stanford. edu/software/iw/ex/jtp/wine/tonysns 2_0. daml

Provenance Ontology (class hierarchy) Provenance. Element • URI • URL • Name • Submitter • Date. Time. Initial. Submission • Date. Time. Last. Submission • English. Description Inference. Engine Knowledge. Source Organization Person Publication Inference. Rule Declarative. Rule Represetation. Language Derived. Rule Expression. Language Team Primitive. Rule Method

Inference Web Framework Diagram http: //ksl. stanford. edu/software/IW/arch/IWOverview. Detail. gif

Hybrid reasoning in JTP n n n JTP architecture supports hybrid reasoning PML as interchange language Commands (truth maintenance related) q Tell: Given a sentence, tell conclusion n q 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 n When B as asked by A about C, B will tell a set of inference step that has C as conclusion

Human friendly explanation n Proof Len q q n Directly access to single proof step Hide trivial inference steps Web interface

Future work & Reference n More considerations… q q Relax logical proof to general justification Application in P 2 P network n n n Collaborative writing Privacy preserving proof sharing (justification) Reference Paulo Pinheiro da Silva, Deborah L. Mc. Guinness, and Richard E. Fikes, [A Proof Markup Language for Semantic Web Services], Technical Report KSL-04 -01. Knowledge Systems Laboratory, Stanford University. 2004.