Showing papers by "Franz Baader published in 1998"

Term rewriting and all that

Abstract: Preface 1. Motivating examples 2. Abstract reduction systems 3. Universal algebra 4. Equational problems 5. Termination 6. Confluence 7. Completion 8. Grobner bases and Buchberger's algorithm 9. Combination problems 10. Equational unification 11. Extensions Appendix 1. Ordered sets Appendix 2. A bluffer's guide to ML Bibliography Index.

Computing the Least Common Subsumer and the Most Specific Concept in the Presence of Cyclic ALN-Concept Descriptions

Abstract: Computing least common subsumers (lcs) and most specific concepts (msc) are inference tasks that can be used to support the ``bottom up'''' construction of knowledge bases for KR systems based on description logic. For the description logic ALN, the msc need not always exist if one restricts the attention to acyclic concept descriptions. In this paper, we extend the notions lcs and msc to cyclic descriptions, and show how they can be computed. Our approach is based on the automata-theoretic characterizations of fixed-point semantics for cyclic terminologies developed in previous papers.

Deciding the Word Problem in the Union of Equational Theories

Abstract: The main contribution of this paper is a new method for combining decision procedures for the word problem in equational theories. In contrast to previous methods, this method is based on transformation rules. Furthermore, it is not limited to theories with disjoint signatures but it also applies to theories sharing constructors.

Description Logics with Concrete Domains and Aggregation

Abstract: We extend different Description Logics by concrete domains (such as integers and reals) and by aggregation functions over these domains (such as min;max; count; sum), which are usually available in database systems. On the one hand, we show that this extension may lead to undecidability of the basic inference problems satisfiability and subsumption. This is true even for a very small Description Logic and very simple aggregation functions, provided that universal value restrictions are present. On the other hand, disallowing universal value restrictions yields decidability of satisfiability, provided that the concrete domain is not too expressive. An example of such a concrete domain is the set of (nonnegative) integers with comparisons (=, , n, ...) and the aggregation functions min;max; count.

Unification of Concept Terms in Description Logics.

Abstract: Unification of concept terms is a new kind of inference problem for description logics, which extends the equivalence problem by allowing one to replace certain concept names by concept terms before testing for equivalence. We show that this inference problem is of interest for applications, and present first decidability and complexity results for a small concept description language.

Structural Subsumption Considered from an Automata-Theoretic Point of View.

Abstract: This paper compares two approaches for deriving subsumption algorithms for the description logic ALN: structural subsumption and an automata-theoretic characterization of subsumption. It turns out that structural subsumption algorithms can be seen as special implementations of the automata-theoretic characterization.

Matching in Description Logics: Preliminary Results.

Abstract: Matching of concepts with variables (concept patterns) is a relatively new operation that has been introduced in the context of concept description languages (description logics), originally to help filter out unimportant aspects of large concepts appearing in industrial-strength knowledge bases. This paper proposes a new approach to performing matching, based on a “concept-centered” normal form, rather than the more standard “structural subsumption” normal form for concepts. As a result, matching can be performed (in polynomial time) using arbitrary concept patterns of the description language FL¬, thus removing restrictions from previous work. The paper also addresses the question of matching problems with additional “side conditions”, which were motivated by practical experience.

Least Common Subsumer Computation w.r.t. cyclic ALN-Terminologies.

Abstract: Computing least common subsumers (lcs) and most speciic concepts (msc) are inference tasks that can be used to support the \\bottom up\" construction of knowledge bases for KR systems based on description logic. For the description logic ALN, the msc need not always exist if one restricts the attention to acyclic concept descriptions. In this paper, we extend the notions lcs and msc to cyclic descriptions, and show how they can be computed. Our approach is based on the automata-theoretic characterizations of xed-point semantics for cyclic terminologies developed in previous papers.

The Guarded Fragment of Conceptual Graphs

Abstract: Conceptual graphs (CGs) are an expressive and intuitive formalism, which plays an important role in the area of knowledge representation. Due to their expressiveness, most interesting problems for CGs are inherently undecidable. We identify the syntactically defined guarded fragment of CGs, for which both subsumption and validity is decidable in deterministic exponential time.

Matching in Description Logics: Preliminary Results

Abstract: Matching of concepts with variables (concept patterns) is a relatively new operation that has been introduced in the context of concept description languages (description logics), originally to help filter out unimportant aspects of large concepts appearing in industrial-strength knowledge bases. This paper proposes a new approach to performing matching, based on a “concept-centered” normal form, rather than the more standard “structural subsumption” normal form for concepts. As a result, matching can be performed (in polynomial time) using arbitrary concept patterns of the description language FL¬, thus removing restrictions from previous work. The paper also addresses the question of matching problems with additional “side conditions”, which were motivated by practical experience.