Communications of the ACM - Special issue on parallelism
Instance-Based Learning Algorithms
Machine Learning
Trading MIPS and memory for knowledge engineering
Communications of the ACM
Case-based representation and learning of pattern languages
Theoretical Computer Science - Special issue on algorithmic learning theory
Exact learning Boolean functions via the monotone theory
Information and Computation
Artificial Intelligence
Modeling Legal Arguments: Reasoning with Cases and Hypotheticals
Modeling Legal Arguments: Reasoning with Cases and Hypotheticals
Best-Case Results for Nearest-Neighbor Learning
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Concept Space and Hypothesis Space in Case-Based Learning Algorithms
ECML '95 Proceedings of the 8th European Conference on Machine Learning
Prism: A Case-Based Telex Classifier
IAAI '90 Proceedings of the The Second Conference on Innovative Applications of Artificial Intelligence
A Logical Representation for Relevance Criteria
EWCBR '93 Selected papers from the First European Workshop on Topics in Case-Based Reasoning
An Average Predictive Accuracy of the Nearest Neighbor Classifier
EWCBR '94 Selected papers from the Second European Workshop on Advances in Case-Based Reasoning
An Average-Case Analysis of k-Nearest Neighbor Classifier
ICCBR '95 Proceedings of the First International Conference on Case-Based Reasoning Research and Development
Learning Taxonomic Relation by Case-Based Reasoning
ALT '00 Proceedings of the 11th International Conference on Algorithmic Learning Theory
Constructing a Critical Casebase to Represent a Lattice-Based Relation
Progress in Discovery Science, Final Report of the Japanese Discovery Science Project
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Classification is one of major tasks in case-based reasoning (CBR) and many studies have been done for analyzing properties of case-based classification [1,14,10,15,12,9,13,7]. However, these studies only consider numerical similarity measures whereas there are other kinds of similarity measure for different tasks. Among these measures, HYPO system [2,3] in a legal domain uses a similarity measure based on set inclusion of differences of attributes in cases. In this paper, we give an analysis of representability of boolean functions in case-based classification using the above set inclusion based similarity. We show that such case-based classification has a strong connection between monotone theory studied in [4,11]. Monotone theory is originated from computational learning theory and is used to show learnability of boolean function with polynomial DNF size and polynomial CNF size [4] and is used for deductive reasoning as well [11]. In this paper, we analyze a case-based representability of boolean functions by using the above relationship between the case-based classification by set inclusion based similarity and the monotone theory. We show that any boolean function is representable by a casebase whose size is bounded in polynomial of its DNF size and its CNF size and thus, k-term DNF, k-clause CNF can be efficiently representable in a casebase using set inclusion similarity.