Towards a Logical Model for Patterns

Nowadays, the vast volume of collected digital data obliges us to employ processing methods like pattern recognition and data mining in order to reduce the complexity of data management. In this paper, we present the architecture and the logical foundations for the management of the produced knowledge artifacts, which we call patterns. To this end, we first introduce the concept of Pattern-Base Management System; then, we provide the logical foundations of a general framework based on the notions of pattern types and pattern classes, which stand for the intensional and extensional description of pattern instances, respectively. The framework is general and extensible enough to cover a broad range of real-world patterns, each of which is characterized by its structure, the related underlying data, an expression that carries the semantics of the pattern, and measurements of how successful the representation of raw data is. Finally, some remarkable types of relationships between patterns are discussed.