A drawback which concept languages based on kl-one have is that all the terminological knowledge has to be defined on an abstract logical level. In many applications, one would like to be able to refer to concrete domains and predicates on these domains when defining concepts. Examples for such concrete domains are the integers, the real numbers, or also non-arithmetic domains, and predicates could be equality, inequality, or more complex predicates. In the present paper we shall propose a scheme for integrating such concrete domains into concept languages rather than describing a particular extension by some specific concrete domain. We shall define a terminological and an assertional language, and consider the important inference problems such as subsumption, instantiation, and consistency. The formal semantics as well as the reasoning algorithms are given on the scheme level. In contrast to existing kl-one based systems, these algorithms will be not only sound but also complete. The...

Description logics and reasoners, which are descendants of the kl-one language, have been studied in depth in Artificial Intelligence. After a brief introduction, we survey in this paper their application to the problems of information management, using the framework of an abstract information server equipped with several operations -- each involving one or more languages. Specifically, we indicate how one can achieve enhanced access to data and knowledge by using descriptions in languages for schema design and integration, queries, answers, updates, rules, and constraints.

This paper analyzes the correctness of the subsumption algorithm used in classic, a description logic-based knowledge representation system that is being used in practical applications. In order to deal efficiently with individuals in classic descriptions, the developers have had to use an algorithm that is incomplete with respect to the standard, model-theoretic semantics for description logics. We provide a variant semantics for descriptions with respect to which the current implementation is complete, and which can be independently motivated. The soundness and completeness of the polynomial-time subsumption algorithm is established using description graphs, which are an abstracted version of the implementation structures used in classic, and are of independent interest. 1. Introduction to Description Logics Data and knowledge bases are models of some part of the natural world. Such models are often built from individual objects that are inter-related by relationships and g...

We present a series of theoretical and experimental results on the learnability of description logics. We first extend previous formal learnability results on simple description logics to C-Classic, a description logic expressive enough to be practically useful. We then experimentally evaluate two extensions of a learning algorithm suggested by the formal analysis. The first extension learns C-Classic descriptions from individuals. (The formal results assume that examples are themselves descriptions.) The second extension learns disjunctions of C-Classic descriptions from individuals. The experiments, which were conducted using several hundred target concepts from a number of domains, indicate that both extensions reliably learn complex natural concepts. 1 INTRODUCTION One well-known family of formalisms for representing knowledge are description logics, sometimes also called terminological logics or KL-ONE-type languages. Description logics have been applied in a number of contexts...

Description logics are a popular formalism for knowledge representation and reasoning. This paper introduces a new operation for description logics: computing the "least common subsumer" of a pair of descriptions. This operation computes the largest set of commonalities between two descriptions. After arguing for the usefulness of this operation, we analyze it by relating computation of the least common subsumer to the well-understood problem of testing subsumption; a close connection is shown in the restricted case of "structural subsumption". We also present a method for computing the least common subsumer of "attribute chain equalities", and analyze the tractability of computing the least common subsumer of a set of descriptions---an important operation in inductive learning.

This paper explores the explanation of subsumption reasoning in Description Logics that are implemented using normalization methods, focusing on the perspective of knowledge engineers. The notion of explanation is specified using a proof-theoretic framework for presenting the inferences supported in these systems. The problem of overly long explanations is addressed by decomposing them into smaller, independent steps, using the notions of “atomic description” and “atomic justification”. Implementation aspects are explored by considering the design space and some desiderata for explanation modules. This approach has been implemented for the classic knowledge representation system.

Although there is an increasing amount of experimental research on learning concepts expressed in first-order logic, there are still relatively few formal results on the polynomial learnability of first-order representations from examples. Most previous analyses in the pac-model have focused on subsets of Prolog, and only a few highly restricted subsets have been shown to be learnable. In this paper, we will study instead the learnability of the restricted first-order logics known as "description logics", also sometimes called "terminological logics" or "KL-ONE-type languages". Description logics are also subsets of predicate calculus, but are expressed using a different syntax, allowing a different set of syntactic restrictions to be explored. We first define a simple description logic, summarize some results on its expressive power, and then analyze its learnability. It is shown that the full logic cannot be tractably learned. However, syntactic restrictions exist that enable tractable learning from positive examples alone, independent of the size of the vocabulary used to describe examples. The learnable sublanguage appears to be incomparable in expressive power to any subset of first-order logic previously known to be learnable.

. Description logics, also called terminological logics, are commonly used in knowledgebased systems to describe objects and their relationships. We investigate the learnability of a typical description logic, Classic, and show that Classic sentences are learnable in polynomial time in the exact learning model using equivalence queries and membership queries (which are in essence, "subsumption queries"---we show a prediction hardness result for the more traditional membership queries that convey information about specific individuals). We show that membership queries alone are insufficient for polynomial time learning of Classic sentences. Combined with earlier negative results (Cohen & Hirsh, 1994a) showing that, given standard complexity theoretic assumptions, equivalence queries alone are insufficient (or random examples alone in the PAC setting are insufficient), this shows that both sources of information are necessary for efficient learning in that neither type alone is sufficie...

This paper considers the learnability of subsets of first-order logic. Prior work has established two boundaries of learnability: Haussler [ 1989 ] has shown that conjunctions in first-order logic cannot be learned in the Valiant model, even if the form of the conjunction is highly restricted; on the other hand, Valiant [ 1984 ] has shown that propositional conjunctions are learnable. In this

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