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ject. These constraints will be included in the fields of the metaobjects. For instance, the
tuples field will comprise the tuples that must belong or not belong (they will appear as
negated tuples) to the role described by the metarole. Each tuple, in turn, will include
a list of metaindividual names. Lets see an example of an environment describing a FB
in which the formula Owns(X, umbrella) ∧ P erson(X) is true. This environment is
{IND1(
, {Person}, {Owns}), IND2 (umbrella,
, {Owns}), CON1(Person, {IND1}),
ROLE1(Owns, {(IND1, IND2)})}. If there exists an object in the FB, for each metaob-
ject in the environment, that satisfies all the requirements imposed on it, then the given
formula will be true in the FB.
4 Operation of the method
In order to analyze the consistency of a DS, our method has to compute the context
associated to each IC. If this context results to be empty, that means that there is not any
valid initial FB that leads to the violation of the IC. The method implements a backward
chaining simulation of the real rule firing. The recursive calls finish when, in the pro-
cess of computing the context associated with a fact, this fact is external. Basically, the
method can be divided into two phases. In the first phase, the AND/OR deductive tree
associated with the IC is expanded. The leaves of this tree are rules that only contain ex-
ternal facts. During the first phase, some metaobjects are associated to the object names
and the variables in the rules, and they are propagated from a rule to another one, and
updated in each rule. In this updating process some constraints derived from the literals
and variable declarations are inserted into the metaobjects. Moreover, in this updating
process, the satisfacibility of the constraints in the metaobjects is checked w.r.t. the
TBox. To carry out the satisfiability test, our method relies on the calculus explained in
[4]. The computational properties of this calculus for the AL-languages family are also
discussed in [4].
In the second phase, the metaobjects associated to external facts are inserted in the sub-
contexts and the deductive tree is contracted by means of the context operations (these
operations are explained in [3]). Thus, all the metaobjects generated from external facts
are collected in the context associated with the IC.
References
1.
Levy, A.Y., Rousset, M.: Verification of knowledge bases on containment checking. Artificial
Intelligence 101 (1998) 227–250
2.
Donini, F.M., Lenzerini, M., Nardi, D., Schaerf, A.: AL-log: Integrating datalog and descrip-
tion logics. Journal of Intelligent Information Systems 10 (1998) 227–252
3. Ram
´
ırez, J., de Antonio, A.: Knowledge base semantic verification based on contexts propa-
gation, Notes of the AAAI-01 Symposium on Model-based Validation of Intelligence (2001)
4.
Donini, F.M., Lenzerini, M., Nardi, D., Nutt, W.: The complexity of concept languages.
Technical Report RR-95-07, Deutsches Forschungszentrum f
¨
ur K
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unstliche Intelligenz GmbH
Erwin-Schr
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odinger Strasse Postfach 2080 67608 Kaiserslautern Germany (1995)
5.
Horrocks, I.: Using an expressive description logic: FaCT or fiction? In Cohn, A.G., Schubert,
L., Shapiro, S.C., eds.: Principles of Knowledge Representation and Reasoning: Proceedings
of the Sixth International Conference (KR’98), Morgan Kaufmann Publishers, San Francisco,
California (1998) 636–647
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