Kleene's logic with equality

Plotkin's Powerdomain facilitates a rational reconstruction of Kleene's Logic from Predicate Logic and we use this to apply the techniques developed in previous studies of powerdomains in semantics and static analysis of programs for suggesting natural formulae for interpreting new logical operators. It follows that the so-called summary predicate, considered in previous applications of Kleene's Logic for static analysis of programs, can be derived from equality; this leads to a substantial simplification in the notion of approximation between structures.