A Decision Procedure for a Sublanguage of Set Theory Involving Monotone, Additive, and Multiplicative Functions

MLSS is a decidable sublanguage of set theory involving the predicates membership, set equality, set inclusion, and the operators union, intersection, set difference, and singleton. In this paper we extend MLSS with constructs for expressing monotonicity, additivity, and multiplicativity properties of set-to-set functions. We prove that the resulting language is decidable by reducing the problem of determining the satisfiability of its sentences to the problem of determining the satisfiability of sentences of MLSS. ⋆ This research has been partially supported by MURST Grant prot. 2001017741 under project “Ragionamento su aggregati e numeri a supporto della programmazione e relative verifiche”. 1 Email: [email protected]. 2 Email: [email protected]. 3 Email: [email protected]. This is a preliminary version. The final version will be published in Electronic Notes in Theoretical Computer Science URL: www.elsevier.nl/locate/entcs Cantone, Schwartz, and Zarba