Partial Order Logic Programmingy

This paper shows the use of partial-order assertions and lattice domains for logic programming. We illustrate the paradigm using a variety of examples, ranging from program analysis to deductive databases. These applications are characterized by a need to solve circular constraints and perform aggregate operations. We show in this paper that deening functions with subset assertions and, more generally, partial-order assertions renders clear formulations to problems involving aggregate operations ((rst-order and inductive) and recursion. Indeed, as pointed out by Van Gelder V92], for many problems in which the use of aggregates has been proposed, the concept of subset is what is really necessary. We provide model-theoretic and operational semantics, and prove the correctness of the latter. Our proposed operational semantics employs a mixed strategy: top-down with memoization and bottom-up xed-point iteration. welcome, and may be sent to any of the authors.