Comparative Uncertainty, Belief Functions and Accepted Beliefs
This work addresses foundational issues in belief management and uncertain reasoning for AI and logic communities, but is incremental as it builds on existing systems.
The paper establishes that the compatibility between classical deductive closure and uncertain reasoning exactly matches the nonmonotonic 'preferential' inference system of Kraus, Lehmann and Magidor, and identifies probability and Shafer's belief functions as special cases in generating belief sets.
This paper relates comparative belief structures and a general view of belief management in the setting of deductively closed logical representations of accepted beliefs. We show that the range of compatibility between the classical deductive closure and uncertain reasoning covers precisely the nonmonotonic 'preferential' inference system of Kraus, Lehmann and Magidor and nothing else. In terms of uncertain reasoning any possibility or necessity measure gives birth to a structure of accepted beliefs. The classes of probability functions and of Shafer's belief functions which yield belief sets prove to be very special ones.