Computing prioritized circumscription via compilation into stratified logic programs

Our previous extension of Gelfond and Lifs chitz´s compiling circurnscriptive theories into logic programs sometimes allows to compute prioritized circumscription even if its axiom set contains clauses which violate syntactically the requirements of stratification. It is very effective since, for exam ple, under such a syntactical violation, it enables to compute a meeting scheduling problem which needs non-monotonic reasoning. However it is not applicable to a tree-structured inheritance system with exception due to multiple positive occurrences of an abnormal predicate which causes the violation of the required stratification. A translational method pro posed in this paper strengthens our previous extension so that it can overcome this difficulty. This method translates a query evaluation problem with respect to a given circumscription into that of its reduced circumscription where the problem of the multiple positive occurrences of a harmful predicate is reduced into the problem of its single occurrence to which our previous method is applicable. Its the oretical foundation is also given in this paper.