Building Logical Specifications of Temporal Granularities through Algebraic Operators

Logical and algebraic approaches have been proposed in the literature for the definition and the management of time granularities. In the algebraic framework, a bottom granularity is assumed, and new granularities are created by means of suitable algebraic operators. In the logical framework, mathematical structures are used to represent time granularities, and logical formulae are used to specify meaningful properties between them. In this paper we extend the logical approach of Combi et al. for representing and reasoning about temporal granularities, defining logical formulae corresponding to calendar algebra operators. This approach allows one to define a large set of granularities,possibly corresponding to complex formulae, in a natural way. Indeed, it gives the possibility of specifying granularity-related formulae in an easier way through operators that are intuitive and natural as the algebraic ones, still maintaining the capability of reasoning on granularities through the (formal) techniques that have been deeply investigated for the logical framework.