A modular approach to user-defined symbolic periodicities

Many applications in Artificial Intelligence and Data Bases deal with (domain and/or goal-dependent) temporal patterns that repeat regularly over time (periodicities). Hence the need for formal languages that allow users to define periodicities. Among proposals in the literature, symbolic languages are sets of operators for compositional and incremental definition. We propose a new methodology for designing symbolic languages, based on a preliminary analysis of the required expressiveness. The analysis is guided by a classification of the periodicities according to expressiveness properties that are mutually independent. Each of the properties will be then paired with a language operator such that the addition of that operator to a language adds the capability of defining all periodicities having the corresponding property. A modular family of languages with well-defined expressiveness is the result of this process. Moreover, in this paper we instantiate the general methodology by identifying a specific set of properties which we also use in order to classify the expressiveness of different symbolic approaches in the literature.