Decomposition of Decidable First-Order Logics over Integers and Reals

Florent Bouchy (1) , Alain Finkel (1) , Jérôme Leroux (2)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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.

Domaines: Logique en informatique [cs.LO]; Algorithme et structure de données [cs.DS]

Florent Bouchy, Alain Finkel, Jérôme Leroux. Decomposition of Decidable First-Order Logics over Integers and Reals. Temporal Representation and Reasoning, 2008. TIME '08. 15th International Symposium on, 2008, Montreal, QC, Canada. pp.147-155, ⟨10.1109/TIME.2008.22⟩. ⟨hal-00345998⟩