(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2003)
A generalized version of the declarative semantics of Horn clause programs on abstract structures with parameters is presented. The parameters are subsets of the domain of the structure. They are treated as effectively enumerable sets. The main feature of the semantics is that it does not admit searching in the domain of the structure. The obtained programming language is closed under recursion and has the greatest expressive power among the languages satisfying certain natural model-theoretic properties. It is shown that the obtained notion of computability is transitive.