Understanding PML A Proof Markup Language

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Understanding PMLA Proof Markup Language

• Presented by Li Ding
• ding.li_at_umbc.edu

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Motivation

• Explicitly represent the proof trace 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

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PML Outline

• Ontology Specification
• Proof
• Provenance
• Ontology usage
• Hybrid reasoning in JTP
• Human friendly explanation

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Proof Ontology (my understanding)
rdftype
Expression
ExpressionLanguage
hasEL
hasConclusion
0
hasDischargedAssumption
1
1
NodeSet
1
hasAntecedents
Antecedents
1
hasInferenceRule
InferenceRule
rdfsequence
0
hasBidings
VariableBiding
hasSource
Source
InferenceStep
1
hasEngine
InferenceEngine
1
TimeStampe
xsddateTime
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Example
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Example GUI Proof Trace
http//belo.stanford.edu8080/iwbrowser/WffBrowser
?w900mg1stProoffmEnglishurlhttp//www.ksl
.stanford.edu/software/iw/ex/jtp/wine/tonysns2_0.d
aml23tonysns2_0
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Example DAML Proof trace
(adapted from http//www.ksl.stanford.edu/software
/iw/ex/jtp/wine/tonysns2_0.daml
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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
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Inference Web Framework Diagram
http//ksl.stanford.edu/software/IW/arch/IWOvervie
wDetail.gif
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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

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Human friendly explanation

• Proof Len
• Directly access to single proof step
• Hide trivial inference steps
• Web interface

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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.