Non-Monotonic Reasoning for the Semantic Web. Bertino, Provetti & Salvetti, AGP03 Bertino, Provetti,...

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Non-Monotonic Non-Monotonic Reasoning Reasoning for the Semantic Web for the Semantic Web

Transcript of Non-Monotonic Reasoning for the Semantic Web. Bertino, Provetti & Salvetti, AGP03 Bertino, Provetti,...

Non-Monotonic ReasoningNon-Monotonic Reasoning

for the Semantic Webfor the Semantic Web

Bertino, Provetti & Salvetti, AGP03Bertino, Provetti, Salvetti

Non-Monotonic Reasoning for the Semantic WebAGP03, pag. 2

AgendaAgenda

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 WebSemantic 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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 4

A modern Semantic NetworkA modern Semantic Network

Tree of Porphyry, as drawn by Peter of Spain (1329)

Bertino, Provetti & Salvetti, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 5

Semantic Web =? Semantic NetworkSemantic 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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 6

Knowledge BaseKnowledge 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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 7

An RDF assertionAn RDF assertion

triple(“http://example.org/LCWA”, “http://example.org/author”, “Ale”).

<?xml version="1.0"?><rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#” xmlns:example="http://example.org/"><rdf:Description rdf:about="http://example.org/paper_LCWA"> <example:author> Ale </example:author></rdf:Description></rdf:RDF>

http://example.org/LCWA http://example.org/author Ale

Bertino, Provetti & Salvetti, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 8

Why rules and inference?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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 9

Why default reasoning?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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 10

Example of a default rulesExample 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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 11

……and the inference?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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 12

Stable Models and ASPStable 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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 13

Negation as failure and CWANegation 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, AGP03Franco 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?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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 15

All together!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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 16

rdf:type and rdfs:subClassOfrdf: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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 17

some new knowledge arrives 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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 18

Does it happen? 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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 19

Flying, in RDFFlying, 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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 20

Two consistent s-models Two consistent s-models

Answer: 1Stable 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: 2Stable 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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 21

An explicit semantics in ASPAn 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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 22

Results Results

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, AGP03Franco 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? 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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 24

Towards ontology/schema integration? Towards ontology/schema integration?

“How many people have written an ontology with a resource named

student?”

Bertino, Provetti & Salvetti, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 25

Is there a solution? 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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 26

ConclusionsConclusions

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, AGP03Franco Salvetti

Non-Monotonic Reasoning for the Semantic Web

University of Colorado at Boulder

15, August 2003 - HP Lab, pag. 27

AcknowledgmentsAcknowledgments

S. McIlraith (Stanford University)

R. King (Univerity of Colorado at Boulder)

B. Burg (HP Lab)

Non-Monotonic ReasoningNon-Monotonic Reasoningfor the Semantic Webfor the Semantic Web

questions…questions…

Non-Monotonic ReasoningNon-Monotonic Reasoningfor the Semantic Webfor the Semantic Web

thank youthank you