An algorithm to compute circumscription
Artificial Intelligence
A circumscriptive theorem prover
Artificial Intelligence
Compiling circumscriptive theories into logic programs
Proceedings of the 2nd international workshop on Non-monotonic reasoning
Information Processing Letters
Handbook of logic in artificial intelligence and logic programming (vol. 3)
Computing Circumscription Revisited: A Reduction Algorithm
Journal of Automated Reasoning
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
ON NATURAL DEDUCTION IN FIRST-ORDER FIXPOINT LOGICS
Fundamenta Informaticae
Meta-Queries on Deductive Databases
Fundamenta Informaticae
General Domain Circumscription and its Effective Reductions
Fundamenta Informaticae
Automated Generation of Logical Constraints on Approximation Spaces Using Quantifier Elimination
Fundamenta Informaticae - To Andrzej Skowron on His 70th Birthday
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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 Ackermann's Lemma in order to deal with a subclass of universal formulas called semi-Horn formulas. Our results subsume previous results by Kolaitis and Papadimitriou regarding a characterization of circumscribed definite logic programs which are first-order expressible. The method for distinguishing which formulas are reducible is based on a boundedness criterion. The approach we use is to first reduce a circumscribed semi-Horn formula to a fixpoint formula which is reducible if the formula 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.