On the relationship between circumscription and negation as failure
Artificial Intelligence
Propositional circumscription and extended closed-world reasoning are &Pgr;p2-complete
Theoretical Computer Science
The complexity of propositional closed world reasoning and circumscription
Journal of Computer and System Sciences
On compact representations of propositional circumscription
Theoretical Computer Science
Theories of computability
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
The Inference Problem for Propositional Circumscription of Affine Formulas Is coNP-Complete
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The complexity of minimal satisfiability problems
Information and Computation
The Complexity of Reasoning for Fragments of Default Logic
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
The complexity of generalized satisfiability for linear temporal logic
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Sets of boolean connectives that make argumentation easier
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
The Complexity of Reasoning for Fragments of Autoepistemic Logic
ACM Transactions on Computational Logic (TOCL)
On the applicability of Post's lattice
Information Processing Letters
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Circumscription is one of the most important formalisms for reasoning with incomplete information. It is equivalent to reasoning under the extended closed world assumption , which allows to conclude that the facts derivable from a given knowledge base are all facts that satisfy a given property. In this paper, we study the computational complexity of several formalizations of inference in propositional circumscription for the case that the knowledge base is described by a propositional theory using only a restricted set of Boolean functions. To systematically cover all possible sets of Boolean functions, we use Post's lattice. With its help, we determine the complexity of circumscriptive inference for all but two possible classes of Boolean functions. Each of these problems is shown to be either ${\Pi^{\rm p}_{2}}$-complete, coNP-complete, or contained in L. In particular, we show that in the general case, unless P = NP, only literal theories admit polynomial-time algorithms, while for some restricted variants the tractability border is the same as for classical propositional inference.