Conceptual Classifications Guided by a Concept Hierarchy

already paid for the studies on the learnabilities on those languages, the goal of this preliminary paper di ers from them at the following points: 1. A concept hierarchy is itself a knowledge source. At the same time, it is the target of knowledge revision when we nd some inadequateness in it. So some part of hierarchy may be utilizable to revise and resolve anomalies in the hierarchy itself. So a system we suppose in this paper revises knowledge and refers it at the same time. 2. Normally, a concept hierarchy has the root or top node, meaning "everything". Hence in the worst case, some individual concept may be classi ed to the top. However the classi cation has no information in this case. Similarly, when the hierarchy has only too abstract concepts subsuming very particular instances, the user also feels that something intermediate between them are missed, although the subsumption is logically valid. Taking these points into account, we present a framework with the following invocation condition, a strategy and a key notion to solve the problem. Given a concept hierarchy and a set of instances of multiple concepts, the primary concepts subsuming the instances are judged inadequate by a user. The basic strategy to resolve this con ict is to utilize the information the hierarchy involves in order to classify the instance set and to form a set of severl intermediate concepts, each from each class. We refer to the strategy of this kind as hierarchy-guided classi cation. For this purpose, we check similarities between concepts in the hierarchy and the instances so that the similarities are invariant even when we generalize those instances to some concept at the middle. This condition is called a Similarity Independence Condition (SIC). This paper is organized as follows. First in Section2, we give some de nitions about CoreClassic according to the literature [2]. In Section 3, we informally introduce a classi cation problem and exemplify it. In Section 4, we present Similarity Independence Condition and show some properties about it. In Section 5, we present a formal de nition of classi cation task and a corresponding algorithm, and show what classi cations it actually performs. In Section6, we summarize this paper.
Abstract.
1 Introduction
We propose in this preliminary paper an algorithm to classify a set of instances and to form new concepts based on the classi cation. Such a classi cation task normally depends on what kinds of concepts and instances we concern. Both the concepts and instances which we consider here are conceptual structure represented by some knowledge representation languages. One of important issues about them seems related to the tasks for building and revising thesaurus or MRD, machine readable dictionary. It is generally convinced that building thesaurus is a hard task and needs much cost. Some support systems for reducing such a task have been designed. For instance, a computational system DODDLE [5] with the input WordNet, a kind of large MRD, has strategies to identify some anomalies we encounter in applying WordNet to some particular domain for which the MRD is not yet suciently developed. The anomalies found by DODDLE are inadequateness of the subsumption relationship between terms in a concept hierarchy involved in the dictionary. However, DODDLE does not contain semantic information, such as types and roles, on conceptual terms, so the detection of anomalies is much restricted. This papaer is directly motivated by DODDLE, and tries to present a framework for those systems revising concept hierarchy, using the semantic information. For this purpose, we suppose a Classic [1, 2], particularly a CoreClassic [2], as a knowledge representation language. Although much e orts have been
2 Descriptions
We rst de ne our language to describe concepts, CoreClassic, and introduce the standard lattice operations for computing the least common subsumer and uni cations of two or more concepts, that are key to handle our space of concepts. In CoreClassic, a description is formally a nite set of constraints for individual objects, and is used to denote a set of individuals satisfying all the constraints in the description, where we suppose descriptions in the form of conjunctive normal forms without loss of generality. To describe various relationships between individuals, CoreClassic provides three kinds of symbols: primitive
Conceptual Classi cations Guided by a Concept Hierarchy
Yuhsuke ITOH and Makoto HARAGUCHI
Division of Electronics and Information Engineering Hokkaido University N-13 W-8, Kita-ku, Sapporo 060-8628, JAPAN makoto@db-ei.eng.hokudai.ac.jp Given a concept hierarchy and a set of instances of multiple concepts, we consider the revision problem that the primary concepts subsuming the instances are judged inadequate by a uselve this con ict is to utilize the information the hierarchy involves in order to classify the instance set and to form a set of several intermediate concepts. We refer to the strategy of this kind as hierarchyguided classi cation. For this purpose, we make a condition, Similarity Independence Condition, that checks similarities between the hierarchy and the instances so that the similarities are invariant even when we generalize those instances to some concept at the middle. Based on the condition, we present an algorithm for classifying instances and for modifying the concept hierarchy.