Modelling causal reasoning

Although human causal reasoning is widely acknowledged as an object of scientific enquiry, there is little consensus on an appropriate measure of progress. Up-to-date evidence of the standard method of research in the field shows that this method has been rejected at the birth of modern science. We describe an instance of the standard scientific method for modelling causal reasoning (causal calculators). The method allows for uniform proofs of three relevant computational properties: correctness of the model with respect to the intended model, full abstraction of the model (function) with respect to the equivalence of reasoning scenarios (input), and formal relations of equivalence and subsumption between models. The method extends and exploits the systematic paradigm [Handbook of Logic in Artificial Intelligence and Logic Programming, volume IV, p. 439-498, Oxford 1995] to fit with our interpretation of it. Using the described method, we present results for some major models, with an updated summary spanning seventy-two years of research in the field.