Non-Monotonic Reasoning for the Semantic Web

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)

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)

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August HP Lab, pag. 4 A modern Semantic Network Tree of Porphyry, as drawn by Peter of Spain (1329)

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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)

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August HP Lab, pag. 7 An RDF assertion triple(“ “ “Ale”). <rdf:RDF xmlns:rdf=" xmlns:example=" Ale Ale

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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 

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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.

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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!!!

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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”

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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).

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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")

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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!

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August HP Lab, pag. 24 Towards ontology/schema integration? “How many people have written an ontology with a resource named student?”

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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!

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August 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

Bertino, Provetti & Salvetti, AGP03 Franco Salvetti Non-Monotonic Reasoning for the Semantic Web University of Colorado at Boulder 15, August HP Lab, pag. 27Acknowledgments  S. McIlraith (Stanford University)  R. King (Univerity of Colorado at Boulder)  B. Burg (HP Lab)

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