**Dept. of Computer and Information science, Linköping University**

## IDA Technical Reports: abstract

*Generated: Tue, 27 Jan 2015 13:24:33 *

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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