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What does a conditional knowledge base entail?
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Probabilistic semantics for nonmonotonic reasoning: a survey
Proceedings of the first international conference on Principles of knowledge representation and reasoning
Constraint propagation with imprecise conditional probabilities
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What does a conditional knowledge base entail?
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Conditional entailment: bridging two approaches to default reasoning
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Qualitative reasoning with imprecise probabilities
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Qualitative probabilities for default reasoning, belief revision, and causal modeling
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From statistical knowledge bases to degrees of belief
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Nonmonotonic reasoning, conditional objects and possibility theory
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Belief functions and default reasoning
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Default reasoning from conditional knowledge bases: complexity and tractable cases
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Probabilistic logic programming with conditional constraints
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Probabilistic Reasoning Under Coherence in System P
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Probabilistic Default Reasoning with Conditional Constraints
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IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
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Annals of Mathematics and Artificial Intelligence
A probabilistic logic based on the acceptability of gambles
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Web Semantics: Science, Services and Agents on the World Wide Web
Expressive probabilistic description logics
Artificial Intelligence
Handling uncertainty and defeasibility in a possibilistic logic setting
International Journal of Approximate Reasoning
Managing uncertainty and vagueness in description logics for the Semantic Web
Web Semantics: Science, Services and Agents on the World Wide Web
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We present an approach where probabilistic logic is combined with default reasoning from conditional knowledge bases in Kraus et al.'s System P, Pearl's System Z, and Lehmann's lexicographic entailment. The resulting probabilistic generalizations of default reasoning from conditional knowledge bases allow for handling in a uniform framework strict logical knowledge, default logical knowledge, as well as purely probabilistic knowledge. Interestingly, probabilistic entailment in System P coincides with probabilistic entailment under g-coherence from imprecise probability assessments. We then analyze the semantic and nonmonotonic properties of the new formalisms. It turns out that they all are proper generalizations of their classical counterparts and have similar properties as them. In particular, they all satisfy the rationality postulates of System P and some Conditioning property. Moreover, probabilistic entailment in System Z and probabilistic lexicographic entailment both satisfy the property of Rational Monotonicity and some Irrelevance property, while probabilistic entailment in System P does not. We also analyze the relationships between the new formalisms. Here, probabilistic entailment in System P is weaker than probabilistic entailment in System Z, which in turn is weaker than probabilistic lexicographic entailment. Moreover, they all are weaker than entailment in probabilistic logic where default sentences are interpreted as strict sentences. Under natural conditions, probabilistic entailment in System Z and lexicographic entailment even coincide with such entailment in probabilistic logic, while probabilistic entailment in System P does not. Finally, we also present algorithms for reasoning under probabilistic entailment in System Z and probabilistic lexicographic entailment, and we give a precise picture of its complexity.