Abstract
We present a proof-theoretical and model-theoretical approach to reasoning about knowledge and conditional probability. We extend both the language of epistemic logic and the language of linear weight formulas, allowing statements like “Agent Ag knows that the probability of A given B is at least a half”. We axiomatize this logic, provide corresponding semantics and prove that the axiomatization is sound and strongly complete. We also show that the logic is decidable.
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Acknowledgments
This work has been partially funded by the Science Fund of the Republic of Serbia through the project Advanced artificial intelligence techniques for analysis and design of system components based on trustworthy BlockChain technology - AI4TrustBC (the first and the third author).
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Dautović, Š., Doder, D., Ognjanović, Z. (2021). An Epistemic Probabilistic Logic with Conditional Probabilities. In: Faber, W., Friedrich, G., Gebser, M., Morak, M. (eds) Logics in Artificial Intelligence. JELIA 2021. Lecture Notes in Computer Science(), vol 12678. Springer, Cham. https://doi.org/10.1007/978-3-030-75775-5_19
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