An efficient method for eliminating varying predicates from a circumscription

doi:10.1016/0004-3702(92)90051-X

Artificial Intelligence

Volume 54, Issue 3, April 1992, Pages 397-410

https://doi.org/10.1016/0004-3702(92)90051-X Get rights and content

Abstract

Circumscription appears to be the most powerful and well-studied technique used in formalizing common-sense reasoning. The general form of predicate circumscription allows for fixed and varying (floating) predicates. We show that the inference problem under this form of circumscription is efficiently reducible to inferencing under circumscription without varying predicates. In fact, we transform this problem even into circumscription without fixed and varying predicates, that is where all predicates are minimized. Thus any theorem prover or algorithm for inferencing under circumscription without fixed and varying predicates is able to handle inferencing under the general form of predicate circumscription. As a consequence, algorithms that compute circumscription for an inference task can be simplified.

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Cited by (15)

Note about cardinality-based circumscription
2000, Artificial Intelligence
In a very interesting paper, Liberatore and Schaerf showed how to express the leading proposals of belief revision using a circumscription. In order to deal with one of the belief revision theories, they had to introduce a new circumscription, based on the cardinality instead of the classical set inclusion. We give a few properties of this new circumscription. In doing so, we prove that in the finite case, there is inter-definability between ordinary circumscription and cardinality-based circumscription. We show why a technical result published in the initial paper cannot be true, and we give a related result which is true instead, where the respective roles of the varying or fixed propositions are reversed. This result could help automatic computation. We use the logical properties of circumscriptions and cardinality-based circumscriptions in order to highlight the behavior of cardinality-based circumscription and the importance of the fixed propositions. This study allows a full description of the expressive power of cardinality-based circumscription in the finite case, and it provides some limitations in the infinite case.
Reducing belief revision to circumscription (and vice versa)
1997, Artificial Intelligence
Nonmonotonic formalisms and belief revision operators have been introduced as useful tools to describe and reason about evolving scenarios. Both approaches have been proven effective in a number of different situations. However, little is known about their relationship. Previous work by Winslett has shown some correlations between a specific operator and circumscription. In this paper we greatly extend Winslett's work by establishing new relations between circumscription and a large number of belief revision operators. This highlights similarities and differences between these formalisms. Furthermore, these connections provide us with the possibility of importing results in one field into the other one.
An extension of pointwise circumscription
1996, Artificial Intelligence
In this paper we generalize Lifschitz's pointwise circumscription ander the first-order framework. The generalized version has the ability for simultaneously minimizing several predicates at finitely many pinpoints in a pointwise manner. We show that if an anderlying first-order theory is almost existential, then the extended pointwise circumscription is complete with respect to minimal model semantics. Almost existential formulas are in the dual form of almost universal formulas, which was proposed by Lifschitz to investigate the satisfiability of circumscription. This completeness result is a generalization of the result by Kolaitis and Papadimitriou, who regarded the case of existential formulas. We also give a partial answer to the question for exponential growth of the size of first-order formulas equivalent to circumscription. Moreover we clarify that Lifschitz's pointwise circumscription is complete in a slightly wider class of positive formulas.
The complexity of propositional closed world reasoning and circumscription
1994, Journal of Computer and System Sciences
Closed world reasoning is a common nonmonotonic technique that allows for dealing with negative information in knowledge and data bases. Several forms of closed world reasoning have been proposed in the literature, ranging from the closed world assumption, introduced in the context of data bases, to the extended closed world assumption, which is equivalent to circumscription. The aim of this paper is to present a detailed analysis of the computational complexity of the different forms of closed world reasoning for various fragments of propositional logic. Such an analysis allows us to draw a complete picture of the boundary between tractability and intractability of such a form of nonmonotonic reasoning. We also discuss how to use our results in order to characterize the computational complexity of other nonmonotonic reasoning problems, namely nonmonotonic inheritance, diagnosis, and default reasoning.
A survey of complexity results for non-monotonic logics
1993, The Journal of Logic Programming
This paper surveys the main results appearing in the literature on the computational complexity of non-monotonic inference tasks. We not only give results about the tractability/intractability of the individual problems but we also analyze sources of complexity and explain intuitively the nature of easy/hard cases. We focus mainly on non-monotonic formalisms, like default logic, autoepistemic logic, circumscription, closed-world reasoning, and abduction, whose relations with logic programming are clear and well studied. Complexity as well as recursion-theoretic results are surveyed.
Computing general first-order parallel and prioritized circumscription
2014, Proceedings of the National Conference on Artificial Intelligence

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Research noteAn efficient method for eliminating varying predicates from a circumscription

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Ann. Pure Appl. Logic

Research note
An efficient method for eliminating varying predicates from a circumscription