Applications of circumscription to formalizing common-sense knowledge
Artificial Intelligence
A logical framework for default reasoning
Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Representing and reasoning with probabilistic knowledge: a logical approach to probabilities
Representing and reasoning with probabilistic knowledge: a logical approach to probabilities
What does a conditional knowledge base entail?
Proceedings of the first international conference on Principles of knowledge representation and reasoning
On Spohn's rule for revision of beliefs
International Journal of Approximate Reasoning
Some properties of plausible reasoning
Proceedings of the seventh conference (1991) on Uncertainty in artificial intelligence
Conditional logics for default reasoning and belief revision
Conditional logics for default reasoning and belief revision
On the semantics of updates in databases
PODS '83 Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems
Default reasoning: causal and conditional theories
Default reasoning: causal and conditional theories
System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning
TARK '90 Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge
Preferred subtheories: an extended logical framework for default reasoning
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Nonmonotonic logics: meaning and utility
IJCAI'87 Proceedings of the 10th international joint conference on Artificial intelligence - Volume 1
A maximum entropy approach to nonmonotonic reasoning
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
System-Z+: a formalism for reasoning with variable-strength defaults
AAAI'91 Proceedings of the ninth National conference on Artificial intelligence - Volume 1
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We recently described a formalism for reasoning with if-then rules that are expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude of disbelief, which impose constraints over possible rankings of worlds. It was shown that, once we compute a priority function Z+ on the rules, the degree to which a given query is confirmed or denied can be computed in O(log n) propositional satisfiability tests, where n is the number of rules in the knowledge base. In this paper, we show that computing Z+ requires O(n2 × log n) satisfiability tests, not an exponential number as was conjectured in [18], which reduces to polynomial complexity in the case of Horn expressions. We also show how reasoning with imprecise observations can be incorporated in our formalism and how the popular notions of belief revision and epistemic entrenchment are embodied naturally and tractably.