Haziness for Common Sensical Inference from Uncertain and Inconsistent Linear Knowledge Base

We theoretically address the problem of reasoning common sensically in uncertain and inconsistent linear knowledge bases.Those bases linearly combine degrees of belief about sentences of a propositional logic, where degrees of belief are assumed to be probabilities. A knowledge base is inconsistent iff no probability function satisfies it. We propose a new process that consistently infers information from such bases. Contrary to ordinary inference processes, ours tackles inconsistencies by trusting every single item of knowledge, where trust can be an application-specific parameter. Moreover, our inference process behaves common sensically when applied to a consistent knowledge base, since it coincides with the maximum entropy inference process. Besides, we provide new measures of inconsistency and similarity that deal with possibly inconsistent knowledge bases. Injecting a bit of common sense into decision systems should make them more easily trustworthy.