This paper describes the continuing development of the system SPII (here is the version 2) which is a simple backward chaining inference engine equipped with powerful fuzzy logic capabilities. Fundamentally, SPII-2 is able to accommodate both imprecision and uncertainty in the homogeneous framework of possibility theory. More specifically, in addition to evaluating the certainty of fixed hypotheses (which is about all what most present approximate reasoning systems can do) SPII-2 can take into account judgemental expertise about problems which require computation as well as reasoning on numerical quantities that may be pervaded by fuzziness. Beside presenting SPII-2 under various aspects (knowledge representation, techniques for approximate reasoning and computation, functioning issues), this paper discusses an application to an important petroleum geology problem that is the one of prospect appraisal.