Artificial Intelligence
Higher order probability and intervals
International Journal of Approximate Reasoning
On probability distributions over possible worlds
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Representing and reasoning with probabilistic knowledge
Representing and reasoning with probabilistic knowledge
Reasoning about knowledge and probability
TARK '88 Proceedings of the 2nd conference on Theoretical aspects of reasoning about knowledge
Extending Markov Logic to Model Probability Distributions in Relational Domains
KI '07 Proceedings of the 30th annual German conference on Advances in Artificial Intelligence
Pr$\mathcal{SH}$: A Belief Description Logic
KES-AMSTA '07 Proceedings of the 1st KES International Symposium on Agent and Multi-Agent Systems: Technologies and Applications
PrDLs: a new kind of probabilistic description logics about belief
IEA/AIE'07 Proceedings of the 20th international conference on Industrial, engineering, and other applications of applied intelligent systems
The future of knowledge representation
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 2
A logic and time nets for probabilistic inference
AAAI'91 Proceedings of the ninth National conference on Artificial intelligence - Volume 1
Default reasoning from statistics
AAAI'91 Proceedings of the ninth National conference on Artificial intelligence - Volume 1
A logic of knowledge and belief for recursive modeling: a preliminary report
AAAI'92 Proceedings of the tenth national conference on Artificial intelligence
A partition-based first-order probabilistic logic to represent interactive beliefs
SUM'11 Proceedings of the 5th international conference on Scalable uncertainty management
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Forecasting sleep apnea with dynamic network models
UAI'93 Proceedings of the Ninth international conference on Uncertainty in artificial intelligence
Compressed constraints in probabilistic logic and their revision
UAI'91 Proceedings of the Seventh conference on Uncertainty in Artificial Intelligence
Probabilistic logic with strong independence
IBERAMIA-SBIA'06 Proceedings of the 2nd international joint conference, and Proceedings of the 10th Ibero-American Conference on AI 18th Brazilian conference on Advances in Artificial Intelligence
Learning stochastic logical automaton
JSAI'05 Proceedings of the 2005 international conference on New Frontiers in Artificial Intelligence
A Fuzzy Modal Logic for Belief Functions
Fundamenta Informaticae - The 1st International Workshop on Knowledge Representation and Approximate Reasoning (KR&AR)
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We consider two approaches to giving semantics to first order logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a (typical) bird flies is greater than. 9." The second approach puts a probability on possible worlds, and is appropriate for giving semantics to formulas describing degrees of belief, such as "The probability that Tweety (a particular bird) flies is greater than.9." We show that the two approaches can be easily combined, allowing us to reason in a straightforward way about statistical information and degrees of belief. We then consider axiornatizing these logics. In general, it can be shown that no complete axiomatization is possible. We provide axiom systems that are sound and complete in cases where a complete axiomatization is possible, showing that they do allow us capture a great deal of interesting reasoning about probability.