There are many probabilistic methods for performing temporal inference using models such as Dynamic Bayesian Networks and Temporal Markov Random Fields, but the patterns that are hardcoded into these models about time can be abstracted to a more general representation. More general representations have the advantage in learning problems of being able to reuse learned patterns in describing complex relationships.
The more general pattern that can be abstracted from temporal inference betworks are transitive relationships. Transitive inference networks would allow inference along any number of axes, not only the temporal axis. Obvious examples of transitive inference are relating the concepts of dimensionality, such as space and time. Thinking about moving forward in a spatial dimension is similar in many ways to thinking backwards in time and the primitive patterns used to learn these relationships could be used to distinguish differences and establish a deeper understanding of similarity within patterned data.
Traditional approaches to the temporal inference problem, such as dividing the inference space into duplicate slices of the entire state space are too naive an approach for a general transitive inference problem as the number of dimensions approaches the number of relationships within the model. Size, shape, quantity, brightness, speed, all of these share in defining transition relationships among data. The model cannot simply be naivy expanded in all of these dimensions resulting in explosive requirements for memory and computational resources.