The paper compares two kinds of models for logics of knowledge and belief, neighbourhood models and epistemic weight models. We give sound and complete calculi for both, and we show that our calculus for neighbourhood models is sound but not complete for epistemic weight models. Epistemic weight models combine knowledge and probability by using epistemic accessibility relations and weights to define subjective probabilities. Our Probability Comparison Calculus for this class of models is a further simplification of the calculus that was presented in AIML 2014.

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Conference on Advances in Modal Logic
Software Analysis and Transformation

van Eijck, J., & Renne, B. (2016). Update, probability, knowledge and belief. In Advances in Modal Logic (pp. 551–570).