Algorithms for possibility assessments: Coherence and extension

In this paper we study the computational aspects of coherence and extension of partial possibility assessments, both in an unconditional and a conditional setting, providing complexity results and algorithms for each problem. In particular, we propose an algorithm to check the coherence of a partial unconditional assessment which is based on propositional satisfiability. For the conditional case, we firstly prove a new characterization of coherent conditional assessments that allows us to define an algorithm again based on propositional satisfiability. The extension problem, in both settings, is solved by means of a search algorithm which relies on the corresponding coherence procedure.