Doherty, P., Lukaszewicz, W., and Salas, A. (1995). A Characterization Result for Circumscribed Normal Logic Programs. Technical Report LiTH-IDA-R-95-20, Department of Computer and Information Science, Linköping University, Sweden. (bibtex),
Abstract: Circumscription has been perceived as an elegant mathematical technique for modeling nonmonotonic and commonsense reasoning, but difficult to apply in practice due to the use of second-order formulas. One proposal for dealing with the computational problems is to identify classes of first-order formulas whose circumscription can be shown to be equivalent to a first-order formula. In previous work, we presented an algorithm which reduces certain classes of second-order circumscription axioms to logically equivalent first-order formulas. The basis for the algorithm is an elimination lemma due to Ackermann. In this paper, we capitalize on the use of a generalization of the Ackermann lemma in order to deal with a subclass of universal formulas used in normal logic programs. Our results subsume previous results by Kolaitis and Papadimitriou regarding a characterization of circumscribed definite logic programs which are first-order expressible. The means for distinguishing which programs are reducible is based on a boundedness criterion. The approach we use is to first reduce circumscribed normal logic programs to a fixpoint formula which is reducible if the program is bounded, otherwise not. In addition to a number of other extensions, we also present a fixpoint calculus which is shown to be sound and complete for bounded fixpoint formulas.
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