Decomposition of Decidable First-Order Logics over Integers and Reals

We tackle the issue of representing infinite sets of realvalued 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.

• Type: Conference
• Year: 2008
• Where: TIME
• Authors: Florent Bouchy, Alain Finkel, Jérôme Leroux
• Keywords: Infinite Sets, Logical Reasoning, Logics Extending Presburger, Real Sets, TIME 2008