Appropriate causal models and the stability of causation
type: Item
instance of: scholarly article
zbMATH Open document ID: 1383.03026
DOI: 10.1017/S1755020315000246
author: Joseph Y. Halpern
published in: The Review of Symbolic Logic
publication date: 2016-04-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1412.3518
Mathematics Subject Classification ID: 03B42
Mathematics Subject Classification ID: 03B80
Mathematics Subject Classification ID: 68T30
zbMATH DE Number: 6575406
zbMATH Keywords: causal model
zbMATH Keywords: structural equations
zbMATH Keywords: Halpern-Pearl definition of causality
zbMATH Keywords: model normality
zbMATH Keywords: causality stability
MaRDI profile type: Publication
arXiv ID: 1412.3518
cites work: Complexity results for structure-based causality.
cites work: Causal Powers
cites work: Causes and Explanations: A Structural-Model Approach. Part I: Causes
cites work: Actual causation: a stone soup essay
cites work: Graded Causation and Defaults
cites work: Explaining counterexamples using causality
cites work: Actual causation and simple voting scenarios
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title: Appropriate causal models and the stability of causation
review text: A \textit{causal model} is a pair \((\mathcal{S},\mathcal{F})\) where \(\mathcal S\), the model's \textit{signature}, lists endogenous and exogenous variables together with their possible values, and \(\mathcal F\) is a set of \textit{modifiable structural equations} that relate the values of the variables. The focus is on \textit{acyclic} models for which there exists a strict ordering \(\prec\) on the set of endogenous variables such that if \(X\prec Y\) then the value of \(X\) may affect the value of \(Y\), but not the other way around; so given a \textit{context}, that is, an assignment of values to the exogenous variables, there is a unique solution for all equations, obtained by solving the equations for each variable in the order given by \(\prec\) (starting with the \(\prec\)-minimal endogenous variables, whose values are immediately determined by the values of the exogenous variables). Six examples are discussed in the paper. The first one, also to be found in [\textit{J. Y. Halpern} and \textit{J. Pearl}, Br. J. Philos. Sci. 56, No. 4, 843--887 (2005; Zbl 1092.03003)], is the following.NEWLINENEWLINE``Suzy and Billy both pick up rocks and throw them at a bottle. Suzy's rock gets there first, shattering the bottle.''NEWLINENEWLINEA suitable model should capture the fact that Suzy's throw is a cause of the bottle shattering, while Billy's is not. Halpern and Pearl proposed a model (the HP model) based on counterfactuals, the idea being that \(A\) is a cause of \(B\) if, if \(A\) hadn't occurred (although it did), then \(B\) would not have occurred -- still the model is more complicated as this definition is too naive to work. A simplistic model has three endogenous variables \(\mathrm{ST}\), \(\mathrm{BT}\), and \(\mathrm{BS}\) for ``Suzy throws'', ``Billy throws'', and ``bottle shatters'', respectively, all taking the value 0 or 1 (False or True). There is the equation: \(\mathrm{BS} = \mathrm{ST}\vee\mathrm{BT}\), plus equations that, thanks to one endogen…
reviewed by: Éric Martin
description: scientific article; zbMATH DE number 6575406