Subjective causal networks and indeterminate suppositional credences

Jiji ZHANG*, Teddy SEIDENFELD, Hailin LIU

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)

Abstract

This paper has two main parts. In the first part, we motivate a kind of indeterminate, suppositional credences by discussing the prospect for a subjective interpretation of a causal Bayesian network (CBN), an important tool for causal reasoning in artificial intelligence. A CBN consists of a causal graph and a collection of interventional probabilities. The subjective interpretation in question would take the causal graph in a CBN to represent the causal structure that is believed by an agent, and interventional probabilities in a CBN to represent suppositional credences. We review a difficulty noted in the literature with such an interpretation, and suggest that a natural way to address the challenge is to go for a generalization of CBN that allows indeterminate credences. In the second part, we develop a decision-theoretic foundation for such indeterminate suppositional credences, by generalizing a theory of coherent choice functions to accommodate some form of act-state dependence. The upshot is a decision-theoretic framework that is not only rich enough to, so to speak, ground the probabilities in a subjectively interpreted causal network, but also interesting in its own right, in that it accommodates both act-state dependence and imprecise probabilities.
Original languageEnglish
JournalSynthese
Early online date17 Dec 2019
DOIs
Publication statusE-pub ahead of print - 17 Dec 2019

Bibliographical note

This research was supported by the Research Grants Council of Hong Kong under the General Research Fund LU13600715, and by a Faculty Research Grant from Lingnan University. The research of the third author was supported by the Humanity and Social Science Youth Foundation of Ministry of Education of China (No. 16YJC72040001) and the MOE Project of Key Research Institute of Humanities and Social Sciences at Universities (No .17JJD720008).

Keywords

  • Causal Bayesian networks
  • Causal credal networks
  • Choice functions
  • Horse lotteries
  • Indeterminate credences
  • Interventions

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