Reasoning about knowledge in economics
Proceedings of the 1986 Conference on Theoretical aspects of reasoning about knowledge
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Towards a probabilistic modal logic for semantic-based information retrieval
SIGIR '92 Proceedings of the 15th annual international ACM SIGIR conference on Research and development in information retrieval
Handbook of logic in artificial intelligence and logic programming (vol. 1)
Reasoning about knowledge
An Introduction to Variational Methods for Graphical Models
Machine Learning
Automata and Computability
The modal logic of probability
TARK '98 Proceedings of the 7th conference on Theoretical aspects of rationality and knowledge
Modal probability, belief, and actions
Fundamenta Informaticae
A knowledge-based framework for belief change part I: foundations
TARK '94 Proceedings of the 5th conference on Theoretical aspects of reasoning about knowledge
Reasoning about knowledge and probability
TARK '88 Proceedings of the 2nd conference on Theoretical aspects of reasoning about knowledge
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Probabilistic and Logical Beliefs
Languages, Methodologies and Development Tools for Multi-Agent Systems
Probabilistic modelling, inference and learning using logical theories
Annals of Mathematics and Artificial Intelligence
Factored models for probabilistic modal logic
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
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A modal logic is any logic for handling modalities: concepts like possibility, necessity, and knowledge. Artificial intelligence uses modal logics most heavily to represent and reason about knowledge of agents about others' knowledge. This type of reasoning occurs in dialog, collaboration, and competition. In many applications it is also important to be able to reason about the probability of beliefs and events. In this paper we provide a formal system that represents probabilistic knowledge about probabilistic knowledge. We also present exact and approximate algorithms for reasoning about the truth value of queries that are encoded as probabilistic modal logic formulas. We provide an exact algorithm which takes a probabilistic Kripke stntcture and answers probabilistic modal queries in polynomial-time in the size of the model. Then, we introduce an approximate method for applications in which we have very many or infinitely many states. Exact methods are impractical in these applications and we show that our method returns a close estimate efficiently.