Werner Nutt

Bio: Werner Nutt is an academic researcher from Free University of Bozen-Bolzano. The author has contributed to research in topics: Knowledge representation and reasoning & Query language. The author has an hindex of 35, co-authored 151 publications receiving 4832 citations. Previous affiliations of Werner Nutt include Heriot-Watt University & German Research Centre for Artificial Intelligence.

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.

The Complexity of Concept Languages.

Abstract: Abstract A basic feature of Terminological Knowledge Representation Systems is to represent knowledge by means of taxonomies, here called terminologies, and to provide a specialized reasoning engine to do inferences on these structures. The taxonomy is built through a representation language called a concept language (or description logic ), which is given a well-defined set-theoretic semantics. The efficiency of reasoning has often been advocated as a primary motivation for the use of such systems. The main contributions of the paper are: (1) a complexity analysis of concept satisfiability and subsumption for a wide class of concept languages; (2) algorithms for these inferences that comply with the worst-case complexity of the reasoning task they perform.

The complexity of concept languages

Abstract: A basic feature of Terminological Knowledge Representation Systems is to represent knowledge by means of taxonomies, here called terminologies, and to provide a specialized reasoning engine to do inferences on these structures. The taxonomy is built through a representation language called a concept language (or description logic ), which is given a well-defined set-theoretic semantics. The efficiency of reasoning has often been advocated as a primary motivation for the use of such systems. The main contributions of the paper are: (1) a complexity analysis of concept satisfiability and subsumption for a wide class of concept languages; (2) algorithms for these inferences that comply with the worst-case complexity of the reasoning task they perform.

Rewriting aggregate queries using views

Abstract: We investigate the problem of rewriting queries with aggregate operators using views that may or may not contain aggregate operators. A rewriting of a query is a second query that uses view predicates such that evaluating first the views and then the rewriting yields the same result as evaluating the original query. In this sense, the original query and the rewriting are equivalent modulo the view definitions. The queries and views we consider correspond to unnested SQL queries, possibly with union, that employ the operators min, max, count, and sum. Our approach is based on syntactic characterizations of the equivalence of aggregate queries. One contribution of this paper are characterizations of the equivalence of disjunctive aggregate queries, which generalize our previous results for the conjunctive case. For each operator a, we introduce several types of queries using views as candidates for rewritings. We unfold such a candidate by replacing each occurrence of a view predicate with its definition, thus obtaining a regular aggregate query. The candidates have a different, usually more complex operator than a. We prove that unfolding the candidate, however, results in a regular aggregate query that is equivalent to the candidate modulo the view definitions. This property justifies considering these types of queries as natural candidates for rewritings. In this way, we reduce the problem of whether there exist rewritings of a particular type to a problem involving equivalence. We distinguish between partial rewritings that contain at least one view predicate and complete rewritings that contain only view predicates. In contrast to previous work on this topic, we not only give sufficient, but also necessary conditions for a rewriting to exist. More precisely, we show for each type of candidate that the existence of both, partial and complete rewritings is decidable, and we provide upper and lower complexity bounds.

Order-Sorted Equational Computation

Abstract: Publisher Summary This chapter discusses order-sorted equational computation. Many-sorted equational logic is the basis for algebraic specifications, rewriting techniques, unification theory, and equational programming. In the standard approach, sorts are unrelated and can be thought of as denoting disjoint sets. Order-sorted equational logic improves the expressivity of many-sorted equational logic by adding the notion of subsorts. The standard example of an abstract data type, stacks of natural numbers, is specified in order-sorted equational logic. It is known that defining a less or equal test for integers with unconditional equations not using subsorts is complicated; one has to introduce an auxiliary function and an auxiliary sort. These complications disappear if one uses conditional equations, but verification methods for the confluence of conditional rewriting systems are complicated and in most cases not practical. The chapter presents the verification methods for confluence extend to order-sorted unconditional rewriting systems.

Data integration: a theoretical perspective

Abstract: Data integration is the problem of combining data residing at different sources, and providing the user with a unified view of these data. The problem of designing data integration systems is important in current real world applications, and is characterized by a number of issues that are interesting from a theoretical point of view. This document presents on overview of the material to be presented in a tutorial on data integration. The tutorial is focused on some of the theoretical issues that are relevant for data integration. Special attention will be devoted to the following aspects: modeling a data integration application, processing queries in data integration, dealing with inconsistent data sources, and reasoning on queries.

The Description Logic Handbook

Abstract: This introduction presents the main motivations for the development of Description Logics (DLs) as a formalism for representing knowledge, as well as some important basic notions underlying all systems that have been created in the DL tradition. In addition, we provide the reader with an overview of the entire book and some guidelines for reading it. We first address the relationship between Description Logics and earlier semantic network and frame systems, which represent the original heritage of the field. We delve into some of the key problems encountered with the older efforts. Subsequently, we introduce the basic features of DL languages and related reasoning techniques. DL languages are then viewed as the core of knowledge representation systems, considering both the structure of a DL knowledge base and its associated reasoning services. The development of some implemented knowledge representation systems based on Description Logics and the first applications built with such systems are then reviewed. Finally, we address the relationship of Description Logics to other fields of Computer Science.We also discuss some extensions of the basic representation language machinery; these include features proposed for incorporation in the formalism that originally arose in implemented systems, and features proposed to cope with the needs of certain application domains.

Answering queries using views: A survey

Abstract: The problem of answering queries using views is to find efficient methods of answering a query using a set of previously defined materialized views over the database, rather than accessing the database relations. The problem has recently received significant attention because of its relevance to a wide variety of data management problems. In query optimization, finding a rewriting of a query using a set of materialized views can yield a more efficient query execution plan. To support the separation of the logical and physical views of data, a storage schema can be described using views over the logical schema. As a result, finding a query execution plan that accesses the storage amounts to solving the problem of answering queries using views. Finally, the problem arises in data integration systems, where data sources can be described as precomputed views over a mediated schema. This article surveys the state of the art on the problem of answering queries using views, and synthesizes the disparate works into a coherent framework. We describe the different applications of the problem, the algorithms proposed to solve it and the relevant theoretical results.

CHAPTER 6 – Rewrite Systems

Abstract: Publisher Summary This chapter focuses on rewrite systems, which are directed equations used to compute by repeatedly replacing sub-terms of a given formula with equal terms until the simplest form possible is obtained. As a formalism, rewrite systems have the full power of Turing machines and may be thought of as nondeterministic Markov algorithms over terms rather than strings. The theory of rewriting is in essence a theory of normal forms. To some extent, it is an outgrowth of the study of A. Church's Lambda Calculus and H. B. Curry's Combinatory Logic. The chapter discusses the syntax and semantics of equations from the algebraic, logical, and operational points of view. To use a rewrite system as a decision procedure, it must be convergent. The chapter describes this fundamental concept as an abstract property of binary relations. To use a rewrite system for computation or as a decision procedure for validity of identities, the termination property is crucial. The chapter presents the basic methods for proving termination. The chapter discusses the question of satisfiability of equations and the convergence property applied to rewriting.