What are other theories of causality besides graphical models and Bayesian networks? I am trying to find some data structures/mathemetical theories to represent causal relationships which differ from graphical models or Bayesian Networks. Any ideas?
 A: The standard account of causality is Lewis's theory of counterfactuals. He wrote a small, very readable book called Counterfactuals, which the SEP summarizes here. The idea is to take the viewpoint of modal logic, and interpret the counterfactual conditional $A \;\boxdot\!\!\!\to B$ (read "if A were the case, then B would be the case") as holding if $B$ holds in the nearest world in which $A$ holds. Obviously this requires enriching modal logic with a notion of similarity of worlds, as well. 
A lot of other people have worked on this subject; personally I am most fond of McCain-Turner causality, since Graham White has given it a nice proof-theoretic formulation. 
A: With several variables connected by asymmetric causal relations, it's not so likely that a mathematical theory of causality will escape graphical representation. Neel mentioned above Lewis's counterfactual analysis, and this has a close affinity with aspects of Judea Pearl's work on casual Bayesian networks, see p. 239 of http://books.google.co.uk/books?id=wnGU_TsW3BQC.
Among quantitative approaches, a variant on the usual statistical approach is Janzing and Schoelkopf's use of algorithmic dependence to determine causal relations: http://www.kyb.mpg.de/publications/attachments/paper_IEEE_version3_webseite_6526%5B1%5D.pdf.
A: Burks, A.W. (1977), Chance, Cause, Reason : An Inquiry into the Nature of Scientific Evidence, University of Chicago Press, Chicago, IL.
