## Logical aspects of set constraints (1993)

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Venue: | in Proc. 1993 Conf. Computer Science Logic |

Citations: | 27 - 5 self |

### BibTeX

@INPROCEEDINGS{Kozen93logicalaspects,

author = {Dexter Kozen},

title = {Logical aspects of set constraints},

booktitle = {in Proc. 1993 Conf. Computer Science Logic},

year = {1993},

pages = {175--188},

publisher = {Springer}

}

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### Abstract

Abstract. Set constraints are inclusion relations between sets of ground terms over a ranked alphabet. They have been used extensively in program analysis and type inference. Here we present an equational axiomatization of the algebra of set constraints. Models of these axioms are called termset algebras. They are related to the Boolean algebras with operators of Jonsson and Tarski. We also de ne a family of combinatorial 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 establish 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, weproveasmall model property by ltration, and argue that this result contains the essence of several algorithms appearing in the literature on set constraints. 1