Conceptual Language for Statistical Data Modeling

We describe a new language for statistical data modeling. The language offers a general framework for the representation of elementary and summary data, and have three main characteristics: i) the types of modeling primitives it provides are particularly suited for representing objects from a statistical point of view; ii) it includes a rich set of structuring mechanisms for both elementary and summary data, which are given a formal semantics by means of logic; iii) it is equipped with specialized inference procedures, allowing for performing different kinds of checks on the representation. The language is intended to be used during the specification phase of a statistical database, which we consider a knowledge-driven activity, where the availability of both powerful structuring mechanisms and suitable reasoning techniques constitute a valuable tool to the designer. The main focus of this paper is on the formal foundation of our approach. We describe the syntax and the semantics of the language, and we discuss its use in statistical data modeling. Also, we describe the basis for devising inference techniques for our language. Such techniques are based on an interesting correspondence between the language and propositional dynamic logic.