MoL-2002-05: Automated Reasoning with Boolean ABoxes

MoL-2002-05: Hernández, Bernadette Martínez (2002) Automated Reasoning with Boolean ABoxes. [Report]

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Description Logics (DL) is a family of knowledge representation (KR) formalisms tailored to represent the knowledge of an application domain by first defining the basic and derived concepts of the domain, and then using these concepts to specify properties of objects and individuals in the domain. Therefore a DL knowledge base (KB) is made up of two parts, the terminological part (TBox) where the definitions of the basic and derived notions are stored, and the assertional part (ABox), which records facts about individuals. A common property of a group of individuals is described by a concept. Concepts can be considered as unary predicates and interpreted as sets of objects. Roles are interpreted as binary relations between objects. Thus, an ABox resembles superficially a relational database with only unary and binary relations. However a database represents only one interpretation, while an ABox encodes a set of interpretations, namely all its models. The ABox does not assume its information to be complete, but in a database the absence of information is regarded as negative information. The partial knowledge of an ABox comes out not only from lack of information, but also from disjunctive assertions like i:C |_| D. Such possibility of partial knowledge is very restricted, it only allows conjunction of assertions. A less restricted representation is usually needed to deal with interesting problems as planning and diagnosis. To be useful it would have to have good expressivity to describe partial knowledge by means of disjunctions or boolean constraints. One way to tackle this problem is to use the Boolean ABoxes (BABoxes), in which boolean combinations of ABox assertions are permitted. Given a TBox T and a BABox B, to find whether (T;B) has a model we treat all the assertions of the BABox as propositions. Then, all the propositional models, which are ABoxes, can be obtained. If one of these models A, together with T has a model; then (T;B) has a model. This process may be expensive because of the exhaustive search. Therefore, a suitable translation from BABox to a regular KB could make it better. In [ABM02] such translation has been proposed. However it is not clear if this translation is really more effcient than an optimized method which tries out all propositional models. The research reported in this thesis was done in order to clarify this issue. Our main results are that the translation approach is an adequate option for BABoxes containing propositionally non trivial information, specifically when the BABoxes are modally constrained. We give examples of DL's in which the translation approach is always needed. Our work has several important consequences. We created a number of examples which turned out to be revealing. They showed several mistakes in RACER. We developed several optimizations to both the translation and the model generation approach. Furthermore we created a random generator of test examples. Chapter 2 is a short introduction to Description Logics. Boolean ABoxes are defined here as well. The two main approaches to check the consistency of Boolean ABoxes, their algorithms and their optimizations are described in Chapter 3. The last chapter contains the description of the implementations of these algorithms, the testing and the description of the random generator of test sets. In Appendix A we include the code of the algorithms and in Appendix B we can find the formulation of some puzzles that were part of the preliminary test of the implementations.

Item Type: Report
Report Nr: MoL-2002-05
Series Name: Master of Logic Thesis (MoL) Series
Year: 2002
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38

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