Probabilities with Gaps and Gluts
Abstract
Belnap-Dunn logic (BD), sometimes also known as First Degree Entailment, is a four-valued propositional logic that complements the classical truth values of True and False with two non-classical truth values Neither and Both. The latter two are to account for the possibility of the available information being incomplete or providing contradictory evidence. In this paper, we present a probabilistic extension of BD that permits agents to have probabilistic beliefs about the truth and falsity of a proposition. We provide a sound and complete axiomatization for the framework defined and also identify policies for conditionalization and aggregation. Concretely, we introduce four-valued equivalents of Bayes' and Jeffrey updating and also suggest mechanisms for aggregating information from different sources.
Keywords
Cite
@article{arxiv.2003.07408,
title = {Probabilities with Gaps and Gluts},
author = {Dominik Klein and Ondrej Majer and Soroush Rafiee Rad},
journal= {arXiv preprint arXiv:2003.07408},
year = {2020}
}