Embedding conditional event algebras into temporal calculus of conditionals

Abstract

In this paper we prove that all the existing conditional event algebras embed into a three-valued extension of temporal logic of discrete past time, which the authors of this paper have proposed in anothe paper as a general model of conditional events. First of all, we discuss the descriptive incompleteness of the cea's. In this direction, we show that some important notions, like independence of conditional events, cannot be properly addressed in the framework of conditional event algebras, while they can be precisely formulated and analyzed in the temporal setting. We also demonstrate that the embeddings allow one to use Markov chain algorithms (suitable for the temporal calculus) for computing probabilities of complex conditional expressions of the embedded conditional event algebras, and that these algorithms can outperform those previously known.