Topology and Iterates in Computational Logic

We consider the problem of nding models for logic programs P via xed points of immediate consequence operators TP Certain extensions of syntax invalidate the classical approach adopted in the case of de nite programs using iterates of TP and the Knaster Tarski theorem We discuss alternatives to the use of this theorem based on elementary notions from topological dynamics This leads us to consider simple syntactic conditions on P employing level mappings taking values in a countable ordinal which ensure convergence to models and xed points of the requisite sequences of iterates We obtain as a result a constructive approach to the perfect model semantics of Przymusinski for locally strati ed programs somewhat along the lines of the approach adopted by Apt Blair and Walker for strati ed programs In particular when certain inequalities are sharp we show the existence of unique supported models which improves Przymusinski s results for perfect models This result is obtained by viewing a Scott domain as a generalized ultrametric space and applying a xed point theorem due to Priess Crampe and Ribenboim When happens to be these results extend Fitting s treatment by metric methods of certain non strati ed programs discussed by Apt and Pedreschi in termination problems Subject Classi cations Q H