Clause-logical Aspects of the Smyth Powerdomain

Synopsis. In this paper we study the logical aspects of the Smyth powerdomain via clausal theories. The clause-theoretic view leads to an unexpectedly simple, operational, representation of the Smyth powerdomain. At the heart of this representation is a hyperresolution rule, whose completeness hinges upon a combinatorial lemma for the book-keeping of intermediate clauses. These results are motivated by the need to develop least xed-point semantics for disjunctive logic programming. We show that, indeed, the clause-theoretic representation of the Smyth powerdomain provides a clean and correct xed-point semantics for disjunctive logic programs. Correctness is established by proving that clauses in the xed-point theory induced by a logic program coincide with those that are logical consequences of the program.