How Lucky Are You to Know Your Way? A Probabilistic Approach to Knowing How Logics

We introduce a probabilistic version of knowing-how modal logics. More precisely, our logics extend extant approaches to model the ability of an agent to achieve a given goal with a certain probability. On the semantic side, we enrich the models of the logic with probability distributions over the agent's actions. Then, we investigate different languages to describe such structures. First, we consider a probabilistic version of the linear plan-based logic of knowing how, and discuss its properties. Then, we consider indistinguishability classes, and obtain two logics, one that has `non-adaptative' plans, and another with `adaptative' plans. In all cases we investigate the computational complexity of their model-checking problem, obtaining undecidability results for the first and the second logic, while for the last one the problem is decidable in polynomial time. We also explore the semantics of the new logics under non-probabilistic models to compare them to the original non-probabilistic ones.