Optimal Policy Generation for Partially Satisfiable Co-Safe LTL Specifications

We present a method to calculate cost-optimal poli-cies for task specifications in co-safe linear tem-poral logic over a Markov decision process model of a stochastic system. Our key contribution is to address scenarios in which the task may not be achievable with probability one. We formalise a task progression metric and, using multi-objective probabilistic model checking, generate policies that are formally guaranteed to, in decreasing order of priority: maximise the probability of finishing the task; maximise progress towards completion, if this is not possible; and minimise the expected time or cost required. We illustrate and evaluate our ap-proach in a robot task planning scenario, where the task is to visit a set of rooms that may be inaccessi-ble during execution.