Holger Lausen (holger.lausen@deri.ie)

Reasoning about Anonymous Resources and Meta Statements on the Semantic WebGuizhen Yang and Michael Kifer Holger Lausen (holger.lausen@deri.ie) 1

Content • Preliminaries (RDF, F-Logic, HiLog) • Translation (RDF-> „F-Logic“) • Comparison RDF MT – “F-Logic” • Conclusion 2

Preliminaries RDF, F-Logic, HiLog 3

RDF (in less then 5 min ;) • <predicate> <subject> <object> • <predicate> is a property • <subject> is a resource • <object> is a resource or a literal •  labeled graph: • {creator, [http://www.w3.org/Home/Lassila], "Ora Lassila"} 4

Anonymous Resources • "http://www.w3.org/Home/Lassila has creator something and something has name Ora Lassila and email lassila@w3.org" • {creator, [http://www.w3.org/Home/Lassila], [X]} • {name, [x], „Ora Lassila“} • {email, [x], „lassilla@w3.org“} 5

Reification • {type, [X], [RDF:Statement]} • {predicate, [X], [creator]} • {subject, [X], [http://www.w3.org/Home/Lassila]} • {object, [X], "Ora Lassila"} 6

F-Logic • Explicit facts: • mary[spous->john, children->>{alice, nancy}]. • mary[children->>jack]. • mary[married]. • Inference Rule: • X[children->>{C}] :- Y[spouse->X, children->>{C}]. • Implicit Facts (generated by above Inference Rule): • john[children->>{alice, nancy, jack}] 7

HiLOG • Variables that range over function and predicate symbols •  Syntax for Reification: a statement can be an formula and an object at the same time • HiLog Example: • X[attributes->>{Attribute}] :- X[Attribute =>Range].(the set valued attribute „ attributes“ includes all defined Attributes for a particular class) 8

Translations RDF  „F-Logic“ 9

Translations • http://foo.org/bulb --> [http://foo.org/bulb] • Literals --> „Thomas Edison“ • Example: • Thomas Edison is the inventor of the bulb • {[inventor], [http://foo.org/TheBulb], ”Thomas Edison”} • ’http://foo.org/TheBulb’[inventor->>’Thomas Edison’]. 10

Translations – anonymous resources • Someone, named Thomas Edison, born in 1847, is the inventor of the resource http://foo.org/TheBulb. • RDF • {[name], [X], “Thomas Edison”} • {[born], [X], “1847”} • {[inventor], [http://foo.org/TheBulb], [X]} • Not In F-Logic, but in Flora-2 • _#: unnumbered anonymous ID symbol (each occurrence is a different ID) • _#1: numbered anonymous ID symbol(_#1 is identical to _#1 within the same scope) • ’http://foo.org/TheBulb’[inventor->>_#1], • _#1[name->>’Thomas Edison’, born->>’1847’]. 11

Translations – reified statements • Someone named John Doe believes that a person, called Thomas Edison, invented the bulb (resource http://foo.org/TheBulb). • RDF • {[type], [X], [RDF:Statement]} • {[predicate], [X], [inventor]} • {[subject], [X], [http://foo.org/TheBulb]} • {[object], [X], [Y]} • {[name], [Y], ”Thomas Edison”} • {[name], [Z], ”John Doe”} • {[believes], [Z], [X]} • Flora-2 (like) • _#[name->>’John Doe’, believes->>(’http://foo.org/TheBulb’[inventor->>_#1], _#1[name->>’Thomas Edison’]) ]. 12

Formal Syntax and Semantics (Section 4) 13

Syntax & Semantics • Believe me, there is one ;) 14

RDF MT vs F-Logic 15

Entailment • Strict • Does not hold for a proper instance and the graph itself: • { john[likes ->> food] } |{ #[likes ->> food] }  { #[likes ->> food] } • Relaxed • Does not hold for a proper instance and the graph itself: • { john[likes ->> food] } |~ { #[likes ->> food] }  { #[likes ->> food]}  Relaxed entailment is defined in RDF MT • Note: A proper instance of a graph is an instance in which a blank node has been replaced by a name, or two blank nodes in the graph have been mapped into the same node in the instance. The Paper does not make any claims which of the notions is the more appropriate one. 16

Compositionality of the Semantics • RDF MT has to differentiate between merge and union; It claims both has its suitable application: • MERGE: concatinate all triples, but rename identical blan nodes • UNION: concatinate all triples, no renaming of blank nodes • Example: • Document 1: {[loves], [X], [Mary]} • Document 2: {[inventor], [X], [Bulb]} • Union: • {[loves], [X], [Mary]} {[inventor], [X], [Bulb]} • Merge: • {[loves], [X], [Mary]} {[inventor], [Y], [Bulb]} • Thus this document: • {[loves], [John], [Mary]} {[inventor], [ThomasEdison], [Bulb]} Is a entailed by a merge, but not by a union of two graphs 17

Reification and blank nodes? • Reification uses blank nodes, thus making twice the same statement reified, we have two completly different statements (X,Y): • {[type], [X], [RDF:Statement]} • {[predicate], [X], [inventor]} • {[subject], [X], [http://foo.org/TheBulb]} • {[object], [X], [http://foo.org/ThomasEdison]} • {believes, [http://xyz.com/John], [X]} • With F-Logic Reification the statement itself has an ID: • ’http://foo.org/TheBulb’[inventor->>’http://foo.org/ThomasEdison’][ veracity->>true, authority->>’http://www.britannica.com/’]. • Statement <- Statement[veracity->> true]. • {[type], [Y], [RDF:Statement]} • {[predicate], [Y], [inventor]} • {[subject], [Y], [http://foo.org/TheBulb]} • {[object], [Y], [http://foo.org/ThomasEdison]} 18

Conclusion 19

Conclusion of the paper • F-Logic extended with anonymous resources and reification can serve as model theoretic semantics for RDF (as presented) • RDF MT has shortcomings: • Non-compositional semantics • Weaker then necessary treatment of reification • Identified at least 2 different treatments of RDF graph entailment • Claims F-Logic (rule / frame based) semantics have more possibilities to encode knowledge / have a bigger scope 20

Conclusion for WSM* • Anonymous IDs are useful • Nice not to build on RDF MT • Further explore reified statements 21

Holger Lausen (holger.lausen@deri.ie)