Applications of circumscription to formalizing common-sense knowledge
Artificial Intelligence
Relational queries computable in polynomial time
Information and Control
A theory of diagnosis from first principles
Artificial Intelligence
Information Processing Letters
Eliminating the fixed predicates from a circumscription
Artificial Intelligence
SIAM Journal on Computing
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
An efficient method for eliminating varying predicates from a circumscription
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
Handbook of logic in artificial intelligence and logic programming (vol. 3)
Artificial Intelligence
Knowledge compilation and theory approximation
Journal of the ACM (JACM)
Representing action: indeterminacy and ramifications
Artificial Intelligence
Circumscribing DATALOG: expressive power and complexity
Theoretical Computer Science
Formalizing narratives using nested circumscription
Artificial Intelligence
Abductive reasoning through filtering
Artificial Intelligence
Computational complexity of planning and approximate planning in the presence of incompleteness
Artificial Intelligence
Formalizing sensing actions—a transition function based approach
Artificial Intelligence
Decomposable negation normal form
Journal of the ACM (JACM)
Complexity and expressive power of logic programming
ACM Computing Surveys (CSUR)
Declarative problem-solving using the DLV system
Logic-based artificial intelligence
Computing Circumscription Revisited: A Reduction Algorithm
Journal of Automated Reasoning
An Algorithm to Evaluate Quantified Boolean Formulae and Its Experimental Evaluation
Journal of Automated Reasoning
Improvements to the Evaluation of Quantified Boolean Formulae
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Non-Monotonic Reasoning with Quantified Boolean Constraints
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
Modular Logic Programming and Generalized Quantifiers
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
A Distributed Algorithm to Evaluate Quantified Boolean Formulae
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Preprocessing of intractable problems
Information and Computation
A survey on knowledge compilation
AI Communications
Space efficiency of propositional knowledge representation formalisms
Journal of Artificial Intelligence Research
Change, change, change: three approaches
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Journal of Artificial Intelligence Research
The comparative linguistics of knowledge representation
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
A logical account of causal and topological maps
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
A circumscriptive formalization of the qualification problem
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Reasoning under minimal upper bounds in propositional logic
Theoretical Computer Science
Living with inconsistency and taming nonmonotonicity
Datalog'10 Proceedings of the First international conference on Datalog Reloaded
Hi-index | 0.01 |
Circumscription has been recognized as an important principle for knowledge representation and common-sense reasoning. The need for a circumscriptive formalism that allows for simple yet elegant modular problem representation has led Lifschitz (AIJ, 1995) to introduce nested abnormality theories (NATs) as a tool for modular knowledge representation, tailored for applying circumscription to minimize exceptional circumstances. Abstracting from this particular objective, we propose LCIRC, which is an extension of generic propositional circumscription by allowing propositional combinations and nesting of circumscriptive theories. As shown, NATs are naturally embedded into this language, and are in fact of equal expressive capability. We then analyze the complexity of LCIRC and NATs, and in particular the effect of nesting. The latter is found to be a source of complexity, which climbs the Polynomial Hierarchy as the nesting depth increases and reaches PSPACE-completeness in the general case. We also identify meaningful syntactic fragments of NATs which have lower complexity. In particular, we show that the generalization of Horn circumscription in the NAT framework remains coNP-complete, and that Horn NATs without fixed letters can be efficiently transformed into an equivalent Horn CNF, which implies polynomial solvability of principal reasoning tasks. Finally, we also study extensions of NATs and briefly address the complexity in the first-order case. Our results give insight into the “cost” of using LCIRC (respectively, NATs) as a host language for expressing other formalisms such as action theories, narratives, or spatial theories.