Uncertainty as a Modality over t-norm Based Logics

In this work we propose a general approach for representing uncertainty measures in the framework of t-norm based logics. This approach is extended also to classes of measures like probability, possibility, necessity, lower and upper probability. We show that, under certain conditions, the logical consistency of a theory of uncertainty is tantamount to the coherence of a related assessment of rational values. Finally, we characterize the basic requirements that guarantee the compactness of coherent assessments.