Kybernetika 51 no. 3, 525-539, 2015

On computations with causal compositional models

Vladislav Bína and Radim JiroušekDOI: 10.14736/kyb-2015-3-0525


The knowledge of causal relations provides a possibility to perform predictions and helps to decide about the most reasonable actions aiming at the desired objectives. Although the causal reasoning appears to be natural for the human thinking, most of the traditional statistical methods fail to address this issue. One of the well-known methodologies correctly representing the relations of cause and effect is Pearl's causality approach. The paper brings an alternative, purely algebraic methodology of causal compositional models. It presents the properties of operator of composition, on which a general methodology is based that makes it possible to evaluate the causal effects of some external action. The proposed methodology is applied to four illustrative examples. They illustrate that the effect of intervention can in some cases be evaluated even when the model contains latent (unobservable) variables.


conditioning, extension, causal model, intervention


65C50, 97K50


  1. A. Detwarasiti and R. D. Shachter: Influence diagrams for team decision analysis. Decision Analysis 2 (2005), 4, 207-228.   DOI:10.1287/deca.1050.0047
  2. Y. Hagmayer, S. Sloman, D. Lagnado and M. R. Waldmann: Causal reasoning through intervention. In: Causal Learning: Psychology, Philosophy, and Computation (A. Gopnik and L. Schulz, eds.), Oxford University Press 2007, pp. 86-101.   DOI:10.1093/acprof:oso/9780195176803.003.0007
  3. R. Jiroušek: Foundations of compositional model theory. Int. J. Gen. Syst. 40 (2011), 6, 623-678.   DOI:10.1080/03081079.2011.562627
  4. R. Jiroušek: On causal compositional models: Simple examples. In: Proc. 15th Int. Conf. on Inf. Processing and Management of Uncertainty - Part I. Springer 2014, pp. 517-526.   DOI:10.1007/978-3-319-08795-5_53
  5. F. M. Malvestuto: Equivalence of compositional expressions and independence relations in compositional models. Kybernetika 50 (2014), 3, 322-362.   DOI:10.14736/kyb-2014-3-0322
  6. F. M. Malvestuto: Marginalization in models generated by compositional expressions. To appear in Kybernetika 51 (2015), 4.   CrossRef
  7. J. Pearl: Causality: Models, Reasoning, and Inference. Cambridge University Press, NY 2009.   DOI:10.1017/cbo9780511803161
  8. M. Ryall and A. Bramson: Inference and Intervention: Causal Models for Business Analysis. Routledge, NY 2013.   DOI:10.4324/9780203076835
  9. R. Shachter: Evaluating influence diagrams. Oper. Res. 34 (1986), 6, 871-882.   DOI:10.1287/opre.34.6.871
  10. P. Spirtes, C. Glymour and R. Scheines: Causation, Prediction and Search. Springer Lecture Notes in Statistics, New York 1993.   DOI:10.1007/978-1-4612-2748-9
  11. R. R. Tucci: Introduction to Judea Pearl's Do-Calculus. arXiv:1305.5506v1 [cs.AI] (2013).   CrossRef