Showing papers by "Franz Baader published in 2003"

The Description Logic Handbook: Theory, Implementation and Applications

Abstract: Description logics are embodied in several knowledge-based systems and are used to develop various real-life applications. Now in paperback, The Description Logic Handbook provides a thorough account of the subject, covering all aspects of research in this field, namely: theory, implementation, and applications. Its appeal will be broad, ranging from more theoretically oriented readers, to those with more practically oriented interests who need a sound and modern understanding of knowledge representation systems based on description logics. As well as general revision throughout the book, this new edition presents a new chapter on ontology languages for the semantic web, an area of great importance for the future development of the web. In sum, the book will serve as a unique resource for the subject, and can also be used for self-study or as a reference for knowledge representation and artificial intelligence courses.

Basic description logics

Abstract: This chapter provides an introduction to Description Logics as a formal language for representing knowledge and reasoning about it. It first gives a short overview of the ideas underlying Description Logics. Then it introduces syntax and semantics, covering the basic constructors that are used in systems or have been introduced in the literature, and the way these constructors can be used to build knowledge bases. Finally, it defines the typical inference problems, shows how they are interrelated, and describes different approaches for effectively solving these problems. Some of the topics that are only briefly mentioned in this chapter will be treated in more detail in subsequent chapters.

Terminological cycles in a description logic with existential restrictions

Abstract: Cyclic definitions in description logics have until now been investigated only for description logics allowing for value restrictions. Even for the most basic language FL0, which allows for conjunction and value restrictions only, deciding subsumption in the presence of terminological cycles is a PSPACE-complete problem. This paper investigates subsumption in the presence of terminological cycles for the language EL, Which allows for conjunction, existential restrictions, and the topconcept. In contrast to the results for FL0., subsumption in EL remains polynomial, independent of whether we use least fixpoint semantics, greatest fixpoint semantics, or descriptive semantics.

Least common subsumers and most specific concepts in a description logic with existential restrictions and terminological cycles

Abstract: Computing least common subsumers (Ics) and most specific concepts (msc) are inference tasks that can support the bottom-up construction of knowledge bases in description logics. In description logics with existential restrictions, the most specific concept need not exist if one restricts the attention to concept descriptions or acyclic TBoxes. In this paper, we extend the notions les and msc to cyclic TBoxes. For the description logic EC (which allows for conjunctions, existential restrictions, and the top-concept), we show that the les and msc always exist and can be computed in polynomial time if we interpret cyclic definitions with greatest fixpoint semantics.

Extensions to description logics

Abstract: This chapter considers, on the one hand, extensions of Description Logics by features not available in the basic framework, but considered important for using Description Logics as a modeling language. In particular, it addresses the extensions concerning: concrete domain constraints; modal, epistemic, and temporal operators; probabilities and fuzzy logic; and defaults.On the other hand, it considers non-standard inference problems for Description Logics, i.e., inference problems that - unlike subsumption or instance checking - are not available in all systems, but have turned out to be useful in applications. In particular, it addresses the non-standard inference problems: least common subsumer and most specific concept; unification and matching of concepts; and rewriting.

From tableaux to automata for description logics

Abstract: This paper investigates the relationship between automata- and tableau-based inference procedures for description logics. To be more precise, we develop an abstract notion of what a tableau-based algorithm is, and then show, on this abstract level, how tableau-based algorithms can be converted into automata-based algorithms. In particular, this allows us to characterize a large class of tableau-based algorithms that imply an ExpTime upper-bound for reasoning in the description logics for which such an algorithm exists.

Description Logic Terminology

Abstract: The purpose of this appendix is to introduce (in a compact manner) the syntax and semantics of the most prominent DLs occurring in this handbook. More information and explanations as well as some less familiar DLs can be found in the respective chapters. For DL constructors whose semantics cannot be described in a compact manner, we will only introduce the syntax and refer the reader to the respective chapter for the semantics. Following Chapter 2 on Basic Description Logics, we will first introduce the basic DL AL, and then describe several of its extensions. Thereby, we will also fix the notation employed in this handbook. Finally, we will comment on the naming schemes for DLs that are employed in the literature and in this handbook. Before starting with the definitions, let us introduce some notational conventions. The letters A, B will often be used for atomic concepts, and C, D for concept descriptions. For roles, we often use the letters R, S, and for functional roles (features, attributes) the letters f, g. Nonnegative integers (in number restrictions) are often denoted by n, m, and individuals by a, b. In all cases, we may also use subscripts. This convention is followed when defining syntax and semantics and in abstract examples. In concrete examples, the following conventions are used: concept names start with an uppercase letter followed by lowercase letters (e.g., Human, Male), role names (also functional ones) start with a lowercase letter (e.g., hasChild, marriedTo), and individual names are all uppercase (e.g., CHARLES, MARY).

The Instance Problem and the Most Specific Concept in the Description Logic \mathcal{EL} w.r.t. Terminological Cycles with Descriptive Semantics

Abstract: Previously, we have investigated both standard and non-standard inferences in the presence of terminological cycles for the description logic \(\mathcal{EL}\), which allows for conjunctions, existential restrictions, and the top concept. The present paper is concerned with two problems left open by this previous work, namely the instance problem and the problem of computing most specific concepts w.r.t. descriptive semantics, which is the usual first-order semantics for description logics. We will show that—like subsumption—the instance problem is polynomial in this context. Similar to the case of the least common subsumer, the most specific concept w.r.t. descriptive semantics need not exist, but we are able to characterize the cases in which it exists and give a decidable sufficient condition for the existence of the most specific concept. Under this condition, it can be computed in polynomial time.

Computing the Least Common Subsumer in the Description Logic \mathcal{EL} w.r.t. Terminological Cycles with Descriptive Semantics

Abstract: Computing the least common subsumer (lcs) is one of the most prominent non-standard inference in description logics. Baader, Kusters, and Molitor have shown that the lcs of concept descriptions in the description logic \(\mathcal{EL}\) always exists and can be computed in polynomial time. In the present paper, we try to extend this result from concept descriptions to concepts defined in a (possibly cyclic) \(\mathcal{EL}\)-terminology interpreted with descriptive semantics, which is the usual first-order semantics for description logics. In this setting, the lcs need not exist. However, we are able to define possible candidates P k (k ≥ 0) for the lcs, and can show that the lcs exists iff one of these candidates is the lcs. Since each of these candidates is a common subsumer, they can also be used to approximate the lcs even if it does not exist. In addition, we give a sufficient condition for the lcs to exist, and show that, under this condition, it can be computed in polynomial time.

Restricted Role-value-maps in a Description Logic with Existential Restrictions and Terminological Cycles.

Abstract: In a previous paper we have investigated subsumption in the presence of terminological cycles for the description logic EL, which allows conjunctions, existential restrictions, and the top concept, and have shown that the subsumption problem remains polynomial for all three types of semantics usually considered for cyclic definitions in description logics. In this paper we show that subsumption in EL (with or without cyclic definitions) remains polynomial even if one adds a certain restricted form of global role-value-maps to EL. In particular, this kind of role-value-maps can express transitivity of roles.

Appendix: description logic terminology

Abstract: The purpose of this appendix is to introduce (in a compact manner) the syntax and semantics of the most prominent DLs occurring in this handbook. More information and explanations as well as some less familiar Description Logics can be found in the respective chapters. For DL constructors whose semantics cannot be described in a compact manner, we will only introduce the syntax and refer the reader to the respective chapter for the semantics. Following Chapter 2 on basic Description Logics, we will first introduce the basic Description Logic AL, and then describe several of its extensions. Thereby, we will also fix the notation employed in this handbook. Finally, we will comment on the naming schemes for Description Logics that are employed in the literature and in this handbook.

Automated Deduction – CADE-19

Abstract: Abstraction reduces the problem of whether an infinite state system satisfies a temporal logic property to model checking that property on a finite state abstract version. The most common abstractions are quotients of the original system. We present a simple method of defining quotient abstractions by means of equations collapsing the set of states. Our method yields the minimal quotient system together with a set of proof obligations that guarantee its executability and can be discharged with tools such as those in the Maude formal environment.