Probabilistic causal logics : axiomatization, expressivity, complexity
Abstract/Contents
- Abstract
- This dissertation applies techniques and perspectives from logic to the study of probabilistic models of causality. It aims to shed light on recent questions and controversies by gaining a theoretical grasp on the potential and limitations of the latter. As a foundation, we first study logical languages capturing probabilities over a set of propositional atoms. We find that a division between those languages containing at most additive arithmetic and those containing any sort of multiplicative arithmetic robustly tracks a gap in computational complexity from NP-completeness to ETR-completeness respectively. We address expressivity and give several new axiomatization arguments. We next move to the analysis of causality, adopting the very popular structural framework. We axiomatize the logic of interventionist conditionals on deterministic structural models and show it to be NP-complete, and also obtain similar results for a few other related logics. The languages of the aforementioned sections express either probability or causality, but not both. The final part of the thesis combines the two notions. We define rich probabilistic logical languages delineating the three levels of the Causal Hierarchy: associational, interventional, and counterfactual. Inference then emerges as a special case of logical entailment. Interpreting our languages over probabilistic structural causal models, we give axiomatizations at each level and show that, in terms of expressivity, each level strictly exceeds those below it in almost-every causal model, thus revealing that additional model assumptions are necessary in a very strong sense to perform causal inference. However, in terms of computational complexity, the hierarchy 'collapses': we find that the satisfiability problem for all three languages is ETR-complete. Lastly, we turn to those additional assumptions that permit causal inference. Within the structural framework, these are frequently presented in the form of a mixed acyclic graph, on which methods like the do-calculus rely. We obtain a complete axiomatization of our counterfactual language over the model class of any graph that meets certain restrictions. Finally we formally define and axiomatize another popular causal framework, that of potential outcomes and Rubin causal models. Comparing the structural and potential outcomes approaches, we find that every Rubin model can be expressed as the abstraction of a structural model and that structural assumptions may appear implicitly in practice with potential outcomes, even though these two causal frameworks have sometimes been presented as though in conflict.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2024; ©2024 |
| Publication date | 2024; 2024 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Ibeling, Duligur Harm |
|---|---|
| Degree supervisor | Barrett, Clark |
| Degree supervisor | Icard, Thomas |
| Thesis advisor | Barrett, Clark |
| Thesis advisor | Icard, Thomas |
| Thesis advisor | Pratt, Vaughan R |
| Degree committee member | Pratt, Vaughan R |
| Associated with | Stanford University, School of Engineering |
| Associated with | Stanford University, Computer Science Department |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Duligur Harm Ibeling. |
|---|---|
| Note | Submitted to Computer Science Department. |
| Thesis | Thesis Ph.D. Stanford University 2024. |
| Location | https://purl.stanford.edu/hy978xx4379 |
Access conditions
- Copyright
- © 2024 by Duligur Harm Ibeling
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