Decomposition of Decidable First-Order Logics over Integers and Reals
Florent Bouchy, Alain Finkel, Jérôme Leroux · 2008
We tackle the issue of representing infinite sets of real-valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our decomposition splits a logic into two parts: one integer, and one decimal (i.e. on the interval [0, 1[). We also give a basis for an implementation of our representation.