Attributive Concept Descriptions with Unions and Complements

This paper investigates the consequences of adding unions and complements to the attributive concept descriptions employed in KL-ONE-like knowledge representation languages. It is shown that deciding consistency and subsumption of such descriptions are PSPACE-complete problems that can be decided with linear space

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

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

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

From Unstructured 3D Point Clouds to Structured Knowledge - A Semantics Approach

International audienc

Relational extensions to feature logic: applications to constraint based grammars

This thesis investigates the logical and computational foundations of unification-based or more appropriately constraint based grammars. The thesis explores extensions to feature logics (which provide the basic knowledge representation services to constraint based grammars) with multi-valued or relational features. These extensions are useful for knowledge representation tasks that cannot be expressed within current feature logics.The approach bridges the gap between concept languages (such as KL-ONE), which are the mainstay of knowledge representation languages in AI, and feature logics. Va¬ rious constraints on relational attributes are considered such as existential membership, universal membership, set descriptions, transitive relations and linear precedence con¬ straints.The specific contributions of this thesis can be summarised as follows: 1. Development of an integrated feature/concept logic 2. Development of a constraint logic for so called partial set descriptions 3. Development of a constraint logic for expressing linear precedence constraints 4. The design of a constraint language CL-ONE that incorporates the central ideas provided by the above study 5. A study of the application of CL-ONE for constraint based grammarsThe thesis takes into account current insights in the areas of constraint logic programming, object-oriented languages, computational linguistics and knowledge representation

Inductive Logic Programming in Databases: from Datalog to DL+log

In this paper we address an issue that has been brought to the attention of the database community with the advent of the Semantic Web, i.e. the issue of how ontologies (and semantics conveyed by them) can help solving typical database problems, through a better understanding of KR aspects related to databases. In particular, we investigate this issue from the ILP perspective by considering two database problems, (i) the definition of views and (ii) the definition of constraints, for a database whose schema is represented also by means of an ontology. Both can be reformulated as ILP problems and can benefit from the expressive and deductive power of the KR framework DL+log. We illustrate the application scenarios by means of examples. Keywords: Inductive Logic Programming, Relational Databases, Ontologies, Description Logics, Hybrid Knowledge Representation and Reasoning Systems. Note: To appear in Theory and Practice of Logic Programming (TPLP).Comment: 30 pages, 3 figures, 2 tables

A formal definition for the expressive power of knowledge representation languages

The notions "expressive power" or "expressiveness" of knowledge representation languages (KR-languages) can be found in most papers on knowledge representation; but these terms are usually just used in an intuitive sense. The papers contain only informal descriptions of what is meant by expressiveness. There are several reasons which speak in favour of a formal definition of expressiveness: For example, if we want to show that certain expressions in one language cannot be expressed in another language, we need a strict formalism which can be used in mathematical proofs. Though we shall only consider KL-ONE-based KR-language in our motivation and in the examples, the definition of expressive power which will be given in this paper can be used for all KR-languages with model-theoretic semantics. This definition will shed a new light on the tradeoff between expressiveness of a representation language and its computational tractability. There are KR-languages with identical expressive power, but different complexity results for reasoning. Sometimes, the tradeoff lies between convenience and computational tractability. The paper contains several examples which demonstrate how the definition of expressive power can be used in positive proofs -- that is, proofs where it is shown that one language can be expressed by another language -- as well as for negative proofs -- which show that a given language cannot be expressed by the other language