Extending and Automating Basic Probability Theory with Propositional Computability Logic

Classical probability theory[2] is formulated using sets. Unfortuna tely, the language of sets lacks expressiveness and is, in a sense, a low-level'assembly language' of the probability theory. In this paper, we develop a'high -level approach' to classical probability theory with propositional compu tability logic[1] (CoL). Unlike other formalisms such as sets, logic and linear log ic, computability logic is built on the notion of events/games, which is cent ral to probability theory. Therefore, CoL is a perfect place to begin th e study of automating probability theory. To be specific, CoL is well-suited to describing complex (sequential/parallel) experiments and events, and more expressive than set operation s. In contrast, classical probability theory - based on,, etc - is designed to represent mainly the simple/additive events - the events that occur under a single experiment. Naturally, we need to talk about composite/multiplicative events - events that occur under two different experiments. Developing probability along this line requires a new, powerful language.