Post on 14-Dec-2015
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…