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# Modeling Markov Decision Processes with Imprecise Probabilities Using Probabilistic Logic Programming

; Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:49-60, 2017.

#### Abstract

We study languages that specify Markov Decision Processes with Imprecise Probabilities (MDPIPs) by mixing probabilities and logic programming. We propose a novel language that can capture MDPIPs and Markov Decision Processes with Set-valued Transitions (MDPSTs) we then obtain the complexity of one-step inference for the resulting MDPIPs and MDPSTs. We also present results of independent interest on the complexity of inference with probabilistic logic programs containing interval-valued probabilistic assessments. Finally, we also discuss policy generation techniques.