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Representing Disjunction and Quantifiers in RDF

This paper by McDermott and Dou discusses the limitations of RDF in representing complex logical constructs, specifically highlighting its lack of support for quantifiers, negation, and disjunction. The authors explore methods for encoding predicate logic using reification and embedding more expressive languages such as PDDL within RDF. Examples illustrate how to represent logical statements and quantification through RDF triples, emphasizing the need for richer encoding capabilities in RDF. The relevance to WebPDDL and the potential for describing web services are also examined.

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Representing Disjunction and Quantifiers in RDF

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  1. Representing Disjunction and Quantifiers in RDF on the paper by McDermott and Douhttp://www.cs.yale.edu/~ddj/papers/ISWC02.pdf Eyal Oren DERI 2004/04/23

  2. Overview • RDF limitations • Encoding predicate logic using reification • Embedding PDDL in RDF

  3. RDF • simple logical system • assertions about things denoted with a URI • RDF: • <subject predicate object> • meaning of element depends on location in tag • no restrictions on value of properties (so arbitrary RDF node can be value of property) • easily merge different RDF sources

  4. Limitations of RDF • Limitations • no quantifiers, no negation, no disjunction • no arbitrary terms, only bags & sequences • Overcoming these: • extending RDF, user & developers opposition • embedding richer languagereification: using RDF to describe formulas in other language

  5. RDF triples corresponding RDF graph Example of reification Simple grammar Example sentence reification: the object of ‘second’is itself a triple

  6. encode terms, formulas, connectives (if, or) as RDF types: drs:If drs:antecedent drs:consequent drs:Atomic_formula drs:Term_seq drs:Functional_Term (P→Q) →R: Approach loves(Fred, Sally)<top rdf:type drs:Atomic_formula><top rdf:subject Fred><top rdf:pred loves><top rdf:obj Sally>

  7. Example functional terms child(C,M,F) child(Bates, mother(Bates), father(Bates))

  8. Quantifying Variables • introduce anonymous RDF variable • encode the properties of this variable (and the quantification) in the embedded language • forall X:Person → moralAgent(X) <var_1 rdf:Type Var><var_1 drs:name “x”><var_1 drs:type Person>

  9. Application to WebPDDL • extended PDDL (planning domain definition language) • “could be used to describe web services” • agent-centered • actions (an agent can take) • preconditions (for that actions) • effects (of that actions) • tractability not by limiting the syntax but: • every domain can set (computational) requirements, giving reasoners the opportunity to resign • WebPDDL ↔ RDF (DAML+OIL)

  10. Relevance to WSMO • about PDDL: interesting • about embedding logic in RDF • it is ‘just’ a syntactic embedding • looks awkward and very verbose • why use RDF in the first place • maybe I don’t understand the problem

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