A Decision Procedure for a Fragment of Set Theory Involving Monotone, Additive, and Multiplicative Functions
Résumé
2LS is a decidable many-sorted set-theoretic language involving one sort for elements and one sort for sets of elements. In this report we extend 2LS with constructs for expressing monotonicity, additivity, and multiplicativity properties of set-to-set functions. We call the resulting language 2LSmf. We prove that 2LSmf is decidable by reducing the problem of determining the satisfiability of its sentences to the problem of determining the satisfiability of sentences of 2LS. Furthermore, we prove that the language 2LSmf is stably infinite with respect to the sort of elements. Therefore, using a many-sorted version of the Nelson-Oppen combination method, 2LSmf can be combined with other languages modeling the sort of elements.