Locally strong coherence and inference with lower-upper probabilities

We introduce an operational way to reduce the spatial complexity in inference processes based on conditional lower–upper probabilities assessments. To reach such goal we must suitably exploit zero probabilities taking account of logical conditions characterizing locally strong coherence. We actually re-formulate for conditional lower–upper probabilities the notion of locally strong coherence already introduced for conditional precise probabilities. Thanks to the characterization, we avoid to build all atoms, so that several real problems become feasible. In fact, the real complexity problem is connected to the number of atoms. Since for an inferential process with lower–upper probabilities several sequences of constraints must be fulfilled, our simplification can have either a ‘‘global’’ or a ‘‘partial’’ effect, being applicable to all or just to some sequences. The whole procedure has been implemented by XLisp-Stat language. A comparison with other approaches will be done by an example.