Aleatoric Predicates: Reasoning about Marbles

Aleatoric Logic is the logic of dice, where Boolean propositions are replaced by independent probabilistic events. In a first order extension of this notion, Aleatoric predicates are applied to domain elements selected via independent probabilistic events. An analogy for this is the classic marbles in an urn problem, where we might ask the probability of drawing three marbles of the same colour from an urn, or drawing only black marbles from an urn until a red marble is drawn. This paper formalises a syntax and semantics for propositions built from aleatoric predicates, and discusses how these predicates give a representation of an agent's beliefs that come through experience.