Applications of circumscription to formalizing common-sense knowledge
Artificial Intelligence
Inferring negative information from disjunctive databases
Journal of Automated Reasoning
Propositional circumscription and extended closed-world reasoning are &Pgr;p2-complete
Theoretical Computer Science
Negation in disjunctive logic programs
ICLP'93 Proceedings of the tenth international conference on logic programming on Logic programming
Reasoning with Incomplete Information
Reasoning with Incomplete Information
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Possible World Semantics for Disjunctive Databases
IEEE Transactions on Knowledge and Data Engineering
The equivalence problem for regular expressions with squaring requires exponential space
SWAT '72 Proceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)
On the complexity of theory curbing
LPAR'00 Proceedings of the 7th international conference on Logic for programming and automated reasoning
Yuri, logic, and computer science
Fields of logic and computation
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We introduce curbing, a new nonmonotonic technique of commonsense reasoning that is based on model minimality but unlike circumscription treats disjunction inclusively. A finitely axiomatized first-order theory T is transformed to a formula Curb(T) whose set of models is defined as the smallest collection of models which contains all minimal models of T and which is closed under formation of minimal upper bounds with respect to inclusion. We first give an intuitive definition of Curb in third-order logic and then show how Curb can be equivalently expressed in second-order logic. We study the complexity of inferencing from a curbed propositional theory and present a PSPACE algorithm for this problem. Finally, we address different possibilities to approximate the curb of a theory.