Reasoning Under Inconsistency Based on Implicitly-Specified Partial Qualitative Probability Relations: A Unified Framework

Coherence-based approaches to inconsistency handling proceed by selecting preferred consistent subbases of the belief base according to a predefined method which takes advantage of explicitly stated priorities. We propose here a general framework where the preference relation between subsets of the belief base is induced by a system of constraints directly expressed by the user. Postulates taking their source in the qualitative modelling of uncertainty, either probabilistic or possibilistic, are used for completing the implicit specification of the preference relations. This enables us to define various types of preference relations, including as particular cases several well-known systems such as Brewka's preferred subtheories or the lexicographical system. Since the number of preferred consistent subbases may be prohibitive, we propose to compile the inconsistent belief base into a new one from which it is easier to select one preferred consistent subbase.