  We propose a framework for learning a fragment of probabilistic computation
tree logic (pCTL) formulae from a set of states that are labeled as safe or
unsafe. We work in a relational setting and combine ideas from relational
Markov Decision Processes with pCTL model-checking. More specifically, we
assume that there is an unknown relational pCTL target formula that is
satisfied by only safe states, and has a horizon of maximum $k$ steps and a
threshold probability $\alpha$. The task then consists of learning this unknown
formula from states that are labeled as safe or unsafe by a domain expert. We
apply principles of relational learning to induce a pCTL formula that is
satisfied by all safe states and none of the unsafe ones. This formula can then
be used as a safety specification for this domain, so that the system can avoid
getting into dangerous situations in future. Following relational learning
principles, we introduce a candidate formula generation process, as well as a
method for deciding which candidate formula is a satisfactory specification for
the given labeled states. The cases where the expert knows and does not know
the system policy are treated, however, much of the learning process is the
same for both cases. We evaluate our approach on a synthetic relational domain.

Artificial Intelligence