Resolution in the Smyth Powerdomain

The purposes of this paper are (i) to give a new, efficient representation of Smyth powerdomains as 0-inhabited information systems, following the style of Scott; (ii) to introduce, as a consequence of this representation, a generalized resolution method for an arbitrary Smyth powerdomain and show the soundness and completeness of this method. The connection of (i) with (ii) comes from the observation that the elements of a Smyth powerdomain are semantically equivalent to the basic notion of "clauses" as used in the area of logic programming. 1 Introduction This paper proposes a generalized resolution rule for an arbitrary Smyth powerdomain, which we believe gives some insight into the foundations of proof systems for different kinds of logics. It began as a paper in domain theory, the mathematical foundation for denotational semantics of programming languages, developed, as is well-known, by Dana Scott and others. It works with the concept of information systems, Scott's method for ..