Based on the causal ordering theory, the notion of conditional causality has been developed. Conditional causality allows for the development of conditional causal models, in which the world can be modeled as a set of variables. One variable can influence another by a direct link between the two. Besides a direct influence, a variable can also influence another variable conditionally by changing the nature of a relation between two directly related variables. Predicting (forward) reasoning in causal direction, from cause to effect, and postdicting (backward) reasoning, searching for possible causes of an effect, are possible in a conditional causal model. Currently, conditional causal models are being applied in veterinary diagnosis and in the analysis of dairy farm food and grassland management. This paper gives a formal description of the notion of conditional causal models, an overview of related literature, and a brief description of the applications currently under development.
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