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We propose modal Markov logic as an extension of propositional Markov logicto reason under the principle of maximum entropy for modal logics K45, KD45,and S5. Analogous to propositional Markov logic, the knowledge base consists ofweighted formulas, whose weights are learned from data. However, in contrast toMarkov logic, in our framework we use the knowledge base to define aprobability distribution over non-equivalent epistemic situations (pointedKripke structures) rather than over atoms, and use this distribution to assignprobabilities to modal formulas. As in all probabilistic representations, thecentral task in our framework is inference. Although the size of the statespace grows doubly exponentially in the number of propositions in the domain,we provide an algorithm that scales only exponentially in the size of theknowledge base. Finally, we briefly discuss the case of languages with aninfinite number of propositions.

Reasoning Under the Principle of Maximum Entropy for Modal Logics K45, KD45, and S5