Complexity results for structure-based causality

  • Authors:

  • Thomas Eiter;Thomas Lukasiewicz

  • Affiliations:

  • Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040 Vienna, Austria;Dipartimento di Informatica e Sistemistica, Università di Roma "La Sapienza", Via Salaria 113, I-00198 Rome, Italy and Institut für Informationssysteme, Technische Universität Wien, ...

  • Venue:
  • Artificial Intelligence
  • Year:
  • 2002

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Abstract

We give a precise picture of the computational complexity of causal relationships in Pearl's structural models, where we focus on causality between variables, event causality, and probabilistic causality. As for causality between variables, we consider the notions of causal irrelevance, cause, cause in a context, direct cause, and indirect cause. As for event causality, we analyze the complexity of the notions of necessary and possible cause, and of the sophisticated notions of weak and actual cause by Halpern and Pearl. In the course of this, we also prove an open conjecture by Halpern and Pearl, and establish other semantic results. We then analyze the complexity of the probabilistic notions of probabilistic causal irrelevance, likely causes of events, and occurrences of events despite other events. Moreover, we consider decision and optimization problems involving counterfactual formulas. To our knowledge, no complexity aspects of causal relationships in the structural-model approach have been considered so far, and our results shed light on this issue.