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Within the present paper we investigate case-based representability as well as case-based learnability of indexed families of uniformly recursive languages. Since we are mainly interested in case-based learning with respect to an arbitrary fixed similarity measure, case-based learnability of an indexed family requires its representability, first. We show that every indexed family is case- based representable by positive and negative cases. If only positive cases are allowed the class of representable families is comparatively small. Furthermore, we present results that provide some bounds concerning the necessary size of case bases. We study, in detail, how the choice of a case selection strategy influences the learning capabilities of a case-based learner. We define different case selection strategies and compare their learning power to one another. Furthermore, we elaborate the relations to Gold-style language learning from positive and both positive and negative examples.

While symbolic learning approaches encode the knowledge provided by the presentation of the cases explicitly into a symbolic representation of the concept, e.g. formulas, rules, or decision trees, case-based approaches describe learned concepts implicitly by a pair (CB; d), i.e. by a set CB of cases and a distance measure d. Given the same information, symbolic as well as the case-based approach compute a classification when a new case is presented. This poses the question if there are any differences concerning the learning power of the two approaches. In this work we will study the relationship between the case base, the measure of distance, and the target concept of the learning process. To do so, we transform a simple symbolic learning algorithm (the version space algorithm) into an equivalent case-based variant. The achieved results strengthen the conjecture of the equivalence of the learning power of symbolic and casebased methods and show the interdependency between the measure used by a case-based algorithm and the target concept.

Contrary to symbolic learning approaches, which represent a learned concept explicitly, case-based approaches describe concepts implicitly by a pair (CB; sim), i.e. by a measure of similarity sim and a set CB of cases. This poses the question if there are any differences concerning the learning power of the two approaches. In this article we will study the relationship between the case base, the measure of similarity, and the target concept of the learning process. To do so, we transform a simple symbolic learning algorithm (the version space algorithm) into an equivalent case- based variant. The achieved results strengthen the hypothesis of the equivalence of the learning power of symbolic and case-based methods and show the interdependency between the measure used by a case-based algorithm and the target concept.

Contrary to symbolic learning approaches, that represent a learned concept explicitly, case-based approaches describe concepts implicitly by a pair (CB; sim), i.e. by a measure of similarity sim and a set CB of cases. This poses the question if there are any differences concerning the learning power of the two approaches. In this article we will study the relationship between the case base, the measure of similarity, and the target concept of the learning process. To do so, we transform a simple symbolic learning algorithm (the version space algorithm) into an equivalent case-based variant. The achieved results strengthen the hypothesis of the equivalence of the learning power of symbolic and casebased methods and show the interdependency between the measure used by a case-based algorithm and the target concept.