Logical Aspects of Set Constraints

Set constraints are inclusion relations between sets of ground terms over a ranked alphabet They have been used extensively in pro gram analysis and type inference Here we present an equational axiom atization of the algebra of set constraints Models of these axioms are called termset algebras They are related to the Boolean algebras with operators of J onsson and Tarski We also de ne a family of combinato rial models called topological term automata which are essentially the term automata studied by Kozen Palsberg and Schwartzbach endowed with a topology such that all relevant operations are continuous These models are similar to Kripke frames for modal or dynamic logic We es tablish a Stone duality between termset algebras and topological term automata and use this to derive a completeness theorem for a related multidimensional modal logic Finally we prove a small model property by ltration and argue that this result contains the essence of several algorithms appearing in the literature on set constraints