Subsumption Algorithms for Some Attributive Concept Description Languages

This paper investigates subsumption algorithms for logic-based knowledge representation languages of the KL-ONE family. We amalgamate the attributive concept description language ALC, that contains value restrictions, intersections, unions and complements with number restrictions, role hierarchies (to model the KL-ONE’s roleset differentiation), and Feature Logic, respectively. We show that deciding consistency and subsumption of ALC extended with number restrictions and ALC extended with role hierarchies is PSPACE-complete. Furthermore, for all these languages we give subsumption algorithms

Qualifying number restrictions in concept languages

We investigate the subsumption problem in logic-based knowledge representation languages of the KL-ONE family. The language presented in this paper provides the constructs for conjunction, disjunction, and negation of concepts, as well as qualifying number restrictions. The latter ones generalize the well-known role quantifications (such as value restrictions) and ordinary number restrictions, which are present in almost all KL-ONE based systems. Until now, only little attempts were made to integrate qualifying number restrictions into concept languages. It turns out that all known subsumption algorithms which try to handle these constructs are incomplete, and thus detecting only few subsumption relations between concepts. We present a subsumption algorithm for our language which is sound and complete. Subsequently we discuss why the subsumption problem in this language is rather hard from a computational point of view. This leads to an idea of how to recognize concepts which cause tractable problems

Subsumption algorithms for concept languages

We investigate the subsumption problem in logic-based knowledge representation languages of the KL-ONE family and give decision procedures. All our languages contain as a kernel the logical connectives conjunction, disjunction, and negation for concepts, as well as role quantification. The algorithms are rule-based and can be understood as variants of tableaux calculus with a special control strategy. In the first part of the paper, we add number restrictions and conjunction of roles to the kernel language. We show that subsumption in this language is decidable, and we investigate sublanguages for which the problem of deciding subsumption is PSPACE-complete. In the second part, we amalgamate the kernel language with feature descriptions as used in computational linguistics. We show that feature descriptions do not increase the complexity of the subsumption problem

Embedding defaults into terminological knowledge representation formalisms

We consider the problem of integrating Reiter\u27s default logic into terminological representation systems. It turns out that such an integration is less straightforward than we expected, considering the fact that the terminological language is a decidable sublanguage of first-order logic. Semantically, one has the unpleasant effect that the consequences of a terminological default theory may be rather unintuitive, and may even vary with the syntactic structure of equivalent concept expressions. This is due to the unsatisfactory treatment of open defaults via Skolemization in Reiter\u27s semantics. On the algorithmic side, we show that this treatment may lead to an undecidable default consequence relation, even though our base language is decidable, and we have only finitely many (open) defaults. Because of these problems, we then consider a restricted semantics for open defaults in our terminological default theories: default rules are only applied to individuals that are explicitly present in the knowledge base. In this semantics it is possible to compute all extensions of a finite terminological default theory, which means that this type of default reasoning is decidable

Cardinality restrictions on concepts

The concept description formalisms of existing terminological systems allow the user to express local cardinality restrictions on the fillers of a particular role. It is not possible, however, to introduce global restrictions on the number of instances of a given concept. The paper argues that such cardinality restrictions on concepts are of importance in applications such as configuration of technical systems, an application domain of terminological systems that is currently gaining in interest. It shows that including such restrictions into the description language leaves the important inference problems such as instance testing decidable. The algorithm combines and simplifies the ideas developed for the treatment of qualifying number restrictions and of general terminological axioms

An empirical analysis of optimization techniques for terminological representation systems : or: \u27Making KRIS get a move on\u27

We consider different methods of optimizing the classification process of terminological representation systems, and evaluate their effect on three different types of test data. Though these techniques can probably be found in many existing systems, until now there has been no coherent description of these techniques and their impact on the performance of a system. One goal of this paper is to make such a description available for future implementors of terminological systems. Building the optimizations that came off best into the KRIS system greatly enhanced its efficiency

Task acquisition with a description logic reasoner

In many knowledge based systems the application domain is modeled in an object-centered formalism. Research in knowledge acquisition has given evidence that this approach allows one to adequately model the conceptual structures of human experts. However, when a novice user wants to describe a particular task to be solved by such a system he has to be well acquainted with the underlying domain model, and therefore is charged with the burden of making himself familiar with it. We aim at giving automated support to a user in this process, which we call task acquisition. This paper describes the TACOS system, which guides a user through an object-centered domain model and gives support to him in specifying his task. A characteristic of TACOS is that the user can enter only information that is meaningful and consistent with the domain model. In order to identify such information, TACOS exploits the ability of a description logic based knowledge representation system to reason about such models

The complexity of existential quantification in concept languages

Much of the research on concept languages, also called terminological languages, has focused on the computational complexity of subsumption. The intractability results can be divided into two groups. First, it has been shown that extending the basic language FL- with constructs containing some form of logical disjunction leads to co-NP-hard subsumption problems. Second, adding negation to FL- makes subsumption PSPACE-complete. The main result of this paper is that extending FL- with unrestricted existential quantification makes subsumption NP-complete. This is the first proof of intractability for a concept language containing no construct expressing disjunction--whether explicitly or implicitly. Unrestricted existential quantification is therefore, alongside disjunction, a source of computational complexity in concept languages

Concept logics

Concept languages (as used in BACK, KL-ONE, KRYPTON, LOOM) are employed as knowledge representation formalisms in Artificial Intelligence. Their main purpose is to represent the generic concepts and the taxonomical hierarchies of the domain to be modeled. This paper addresses the combination of the fast taxonomical reasoning algorithms (e.g. subsumption, the classifier etc.) that come with these languages and reasoning in first order predicate logic. The interface between these two different modes of reasoning is accomplished by a new rule of inference, called constrained resolution. Correctness, completeness as well as the decidability of the constraints (in a restricted constraint language) are shown