Social Consolidations: Rational Belief in a Many-Valued Logic of Evidence and Peerhood

We explore an interpretation of FVEL, a four-valued logic of evidence, where states represent agents, the propositional layer corresponds to the evidence available to these agents, and the relation corresponds to peerhood connections between them. Belief is determined based on the agent’s evidence, but also on her peers’ evidence. Consolidation functions are proposed, which map evidence situations to belief attitudes. We adapt some postulates of Social Choice Theory to our belief formation setting and, with them, we separate rational from irrational consolidations. We define a dynamic operator for addition and removal of evidence, which serves as a basis for some essential dynamic postulates and also for future developments on consolidations that take amounts of evidence into account. Our main technical result is a characterisation of a class of consolidations satisfying most of our rationality postulates.