Decomposition of Decidable First-Order Logics over Integers and Reals

Florent Bouchy, Alain Finkel, Jérôme Leroux
2008 2008 15th International Symposium on Temporal Representation and Reasoning  
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.
doi:10.1109/time.2008.22 dblp:conf/time/BouchyFL08 fatcat:mmkslhpyrjg2rpqjzxoseoq6gq