As for BFL, these logics have been given semantics in terms of belief functions over a set of possible worlds. We are also investigating the use of these logics to model some aspects of the dynamics of belief, including belief combination and update. A major source of difficulties in modeling non-monotonic reasoning is that there are in general multiple ways to revise a belief set in order to recover from a contradiction. Thanks to their ability to reason about degrees of belief in a state of partial inconsistency, the logics above provide a framework to formalize preferences between alternative revisions. We have also used this framework to develop a new non-monotonic inference operator that solves many of the drawbacks of the existing approaches.
Logic is one of the main formal tools used to develop artificial intelligence products.
It provides a formal basis to most of the current work in knowledge representation and reasoning. However, classical logics only deal with the idealized case where knowledge is completely accurate. Our work on logics for quantified partial belief aims at extending the applicability of logic-based techniques to formalize domains where knowledge is incomplete, uncertain, and may contain errors and default assumptions. Most real-world domains are of this type. Selected References P. Smets Probability of provability and belief functions.