Topology and Iterates in Computational Logic
Anthony Karel Seda, Pascal Hitzler · 1997
We consider the problem of finding models for logic programs P via fixed points of immediate consequence operators, T P . Certain extensions of syntax invalidate the classical approach, adopted in the case of definite programs, using iterates of T P 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 fl, which ensure convergence (to models and fixed points) of the requisite sequences of iterates. We obtain, as a result, a constructive approach to the perfect model semantics of Przymusinski for locally stratified programs, somewhat along the lines of the approach adopted by Apt, Blair and Walker for stratified 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...