A semantics for weak, question-sensitive belief

Recent work in epistemology defends the unorthodox theses that (1) belief is an evidentially weak, (2) question-sensitive attitude, and that (3) rationally permissible belief is sometimes a matter of guessing. These theses fit together naturally to form a unified account of weak, question-sensitive belief. A formal account of weak, question-sensitive belief as a coherent phenomenon is still forthcoming, however. The main aim of this article is to develop a formal account that captures belief’s weakness and question-sensitivity in the setting of epistemic logic. We introduce a class of models in which the points of evaluation are situations, or world-evidence pairs, with evidence understood liberally to include sets of live possibilities, measures of uncertainty, and QUDs. A proposition is believed at a situation just in case it is implied by the most informative probabilistically dominant answer to the QUD, on some way of specifying the threshold of probabilistic dominance. The second aim of the article is to explore two sets of epistemological implications in our formal setting. First, we consider whether beliefs are preserved between situations upon shifting the QUD parameter; specifically, we consider whether beliefs are preserved upon updating with learned information, under refining and coarsening questions, and whether belief is closed under conjunction. Second, we consider the interaction of knowledge and belief; specifically, we consider whether the principles governing the interaction of knowledge and belief in Stalnaker’s KD45 also hold in our setting.