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Non-Monotonic Reasoning for the Semantic Web
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Bertino, Provetti & Salvetti, AGP03 Bertino, Provetti, Salvetti Non-Monotonic Reasoning for the Semantic Web AGP03, pag. 2Agenda Default reasoning Closed World Assumption Belief vs truth A possible non-monotonic Semantic Web Different semantics for rdf:type Results Unique Name Assumption (the names problem)
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Bertino, Provetti & Salvetti, AGP03 Semantic Web “The Semantic Web is not a Web of documents, but a Web of relations between resources denoting real world objects, i.e., objects such as people, places and events.” - (Guha, McCool, Miller)
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 4 A modern Semantic Network Tree of Porphyry, as drawn by Peter of Spain (1329)
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 5 Semantic Web =? Semantic Network Yes/No... Maybe Semantic Network introduced few years later the Peano’s work for First Order Logic (Peirce 1882) FOL =? Semantic Networks DAML-OIL FOL (KSL, Stanford 2001)
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 6 Knowledge Base We want to describe the world using RDF assertions (Subject, Predicate, Object) RDF does not have inference, yet a description- logic semantics is available (Horrocks et al.) RDF assertions can be seen as equivalent to facts: –triple(”subject”,”predicate”,”object”). We can translate DAML-OIL to LP/ASP
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 7 An RDF assertion triple(“http://example.org/LCWA”, “http://example.org/author”, “Ale”). <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#” xmlns:example="http://example.org/"> Ale http://example.org/LCWA http://example.org/author Ale
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 8 Why rules and inference? Rules are a compact way to describe the world Inference is the formal mechanism for passing from facts and rules to new facts We need inference if we want to use rules to describe in a compact way our domain
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 9 Why default reasoning? “Any classification of the world has exceptions.” Default rules are a way to deal with exceptions If is true and we can assume , we can believe –If there is a proof for and there is no proof of we can believe in
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 10 Example of a default rules “Normally Swedish people are pale unless they are skiers”. swedish : skier pale pale :- swedish, not skier. :- pale, n_pale. It is consistent assuming that you are skier if there is no proof that you are a skier
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 11 …and the inference? we admit contraddiction, swedish is pale (from inference) and swedish is tanned for a fact: she lives in ski resort the whole year. The default reasoning consider pale as a belief and tanned a truth, therefore there is no contraddiction
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 12 Stable Models and ASP capture maximal consistent sets of beliefs (Gelfond & Lifschitz 1991) Anwer Set Programming is the confluence of Deductive Database and Logic Programming DATALOG with negation and negation as failure Big difference between “the train is not coming” and “I do not have a proof that the train is coming” In the SW provability is an issue.
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 13 Negation as failure and CWA The negation as failure, used in a default rule to produce a beleif is based on the CWA CWA: “everything that does not have a formal proof is false” We think that the truth of things relevant for our reasoning is captured in the KB
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 14 Can we rely on CWA for the SW? NO We cannot make inference on the whole Web Do two agents need to reason on the whole Web? NO Can they define their world? YES They can declare which “pages” are relevant
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 15 All together! We want to do default reasoning because is compact way to dealt with exceptions in classification Default rules are good candidates We need negation as failure Negation as failure needs CWA We introduce a Local CWA for the Web
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 16 rdf:type and rdfs:subClassOf rdf:type is monotonic, it means that if we say that B is a rdfs:subClassOf A and x is rdf:type B we can infer that x is rdf:type of A however, any system of classification sooner or later fails due to exceptions Idea: transform rdf:type into its non monotonic version
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 17 some new knowledge arrives rdf:type is monotonic, it means that if we say that B is a rdfs:subClassOf A and x is rdf:type B we can infer that x is rdf:type of A Here we have made an implicit inference Now we discover that x is rdf:type of C and C is daml:complementOf A x is, not A and A... This is really bad!!!
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 18 Does it happen? YES Do you know Pingu? (Minsky, McCarthy) “Normally birds fly” “Penguins rdfs:subClassOf Birds” “Penguins do not fly!” “Magic is a magic Penguin that flies!” “Pingu is a Penguin”
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 19 Flying, in RDF triple(S, "rdfs:subClassOf", O) :- d(S), d(O), d(B), d(C), triple(S, "rdfs:subClassOf", B), triple(B, "rdfs:subClassOf", O), not cannotBeSubClassOf(S,O). cannotBeSubClassOf(X,C) :- d(X), d(C), d(A), triple(X, "rdfs:subClassOf", A), triple(A, "daml:complementOf", C). triple(S, "rdf:type", O) :- d(S), d(C), d(B), d(O), triple(S, "rdf:type", B), triple(B, "rdfs:subClassOf", O), not cannotBeTypeOf(S,O). cannotBeTypeOf(X,C) :- d(X), d(C), d(A), triple(X, "rdf:type", A), triple(A, "daml:complementOf", C).
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 20 Two consistent s-models Answer: 1 Stable Model: type("magic","Flying") type("pingu","Flying") type("magic","Penguin") type("pingu","Penguin") type("magic","Bird") type("pingu","Bird") subClassOf("Bird","Flying") subClassOf("Penguin","n_Flying") subClassOf("Penguin","Bird") Answer: 2 Stable Model: type("magic","Flying") type("pingu","n_Flying") type("magic","Penguin") type("pingu","Penguin") type("magic","Bird") type("pingu","Bird") subClassOf("Bird","Flying") subClassOf("Penguin","n_Flying") subClassOf("Penguin","Bird")
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 21 An explicit semantics in ASP triple(S,Super,O) :- d(S), d(Super), d(O), d(Son), triple(Son, "rdfs:subPropertyOf", Super), triple(S, Son, O). q p
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 22Results Using the LCWA we can use the negation as failure for the SW with negation as failure we can do default reasoning We can discover alternative interpretations of our knowledge ASP inference engines, e.g., smodels can do that
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 23 Is the CWA the only assumption? NO The Unique Names Assumption (UNA) is normally used in logic programming Can we rely on that in the Semantic Web? Yes/No... Maybe Maybe No! No!
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 24 Towards ontology/schema integration? “How many people have written an ontology with a resource named student?”
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 25 Is there a solution? The problem of schema or ontology integration is an open, maybe unsolvable problem Do we hope in Darwin? Is there a cooperative way to build ontologies? Is Linux a good example? Reintroducing names is stupid!
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 26Conclusions A non monotonic semantic for RDF is needed for capturing an environment, the Web, that is not monotonic W3C semantics for RDF is monotonic, the Web ain’t Default and ASP are a possible practical solution LCWA is a must A different way to build ontologies has to be found
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Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 2003 - HP Lab, pag. 27Acknowledgments S. McIlraith (Stanford University) R. King (Univerity of Colorado at Boulder) B. Burg (HP Lab)
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Non-Monotonic Reasoning for the Semantic Web questions…
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thank you
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