  We propose a new task-specification language for Markov decision processes
that is designed to be an improvement over reward functions by being
environment independent. The language is a variant of Linear Temporal Logic
(LTL) that is extended to probabilistic specifications in a way that permits
approximations to be learned in finite time. We provide several small
environments that demonstrate the advantages of our geometric LTL (GLTL)
language and illustrate how it can be used to specify standard
reinforcement-learning tasks straightforwardly.
