This work is part of the larger project INTEGRITY. Integrity develops a conceptual frame integrating beliefs
with individual (and consensual group) decision making and action based on belief awareness. Comments and
criticisms are most welcome via email.
Starting with a thorough discussion of the conceptual embedding in existing schools of thought and liter-
ature we develop a framework that aims to be empirically adequate yet scalable to epistemic states where an
agent might testify to uncertainly believe a propositional formula based on the acceptance that a propositional
formula is possible, called accepted truth. The familiarity of human agents with probability assignments make
probabilism particularly appealing as quantitative modelling framework for defeasible reasoning that aspires
empirical adequacy for gradual belief expressed as credence functions. We employ the inner measure induced
by the probability measure, going back to Halmos, interpreted as estimate for uncertainty. Doing so omits
generally requiring direct probability assignments testi�ed as strength of belief and uncertainty by a human
agent. We provide a logical setting of the two concepts uncertain belief and accepted truth, completely relying
on the the formal frameworks of 'Reasoning about Probabilities' developed by Fagin, Halpern and Megiddo and
the 'Metaepistemic logic MEL' developed by Banerjee and Dubois. The purport of Probabilistic Uncertainty is
a framework allowing with a single quantitative concept (an inner measure induced by a probability measure)
expressing two epistemological concepts: possibilities as belief simpliciter called accepted truth, and the agents'
credence called uncertain belief for a criterion of evaluation, called rationality. The propositions accepted to be
possible form the meta-epistemic context(s) in which the agent can reason and testify uncertain belief or suspend
judgement
