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1. Approximate causal abstraction

   Beckers, Sander; Eberhardt, Frederick; Halpern, Joseph Y. (July 2019, 35th Conference on Uncertainty in AI (UAI 2019))

   Scientific models describe natural phenomena at different levels of abstraction. Abstract descriptions can provide the basis for interventions on the system and explanation of observed phenomena at a level of granularity that is coarser than the most fundamental account of the system. Beckers and Halpern [2019], building on work of Rubenstein et al.[2017], developed an account of \emph{abstraction} for causal models that is exact. Here we extend this account to the more realistic case where an abstract causal model offers only an approximation of the underlying system. We show how the resulting account handles the discrepancy that can arise between low- and high-level causal models of the same system, and in the process provide an account of how one causal model approximates another, a topic of independent interest. Finally, we extend the account of approximate abstractions to probabilistic causal models, indicating how and where uncertainty can enter into an approximate abstraction. 

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2. Abstracting causal models

   Beckers, Sander; Halpern, Joseph Y. (January 2019, Abstracting causal models, Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence)

   We consider a sequence of successively more restrictive definitions of abstraction for causal models, starting with a notion introduced by Rubenstein et al. called exact transformation that applies to probabilistic causal models, moving to a notion of uniform transformation that applies to deterministic causal models and does not allow differences to be hidden by the ``right'' choice of distribution, and then to abstraction, where the interventions of interest are determined by the map from low-level states to high-level states, and strong abstraction, which takes more seriously all potential interventions in a model, not just the allowed interventions. We show that procedures for combining micro-variables into macro-variables are instances of our notion of strong abstraction, as are all the examples considered by Rubenstein et al. 

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3. Supporting Student System Modelling Practice Through Curriculum and Technology Design

   https://doi.org/10.1007/s10956-021-09943-y  

   Bielik, Tom; Stephens, Lynn; McIntyre, Cynthia; Damelin, Daniel; Krajcik, Joseph S. (October 2021, Journal of Science Education and Technology)

   Abstract Developing and using models to make sense of phenomena or to design solutions to problems is a key science and engineering practice. Classroom use of technology-based tools can promote the development of students’ modelling practice, systems thinking, and causal reasoning by providing opportunities to develop and use models to explore phenomena. In previous work, we presented four aspects of system modelling that emerged during our development and initial testing of an online system modelling tool. In this study, we provide an in-depth examination and detailed evidence of 10th grade students engaging in those four aspects during a classroom enactment of a system modelling unit. We look at the choices students made when constructing their models, whether they described evidence and reasoning for those choices, and whether they described the behavior of their models in connection with model usefulness in explaining and making predictions about the phenomena of interest. We conclude with a set of recommendations for designing curricular materials that leverage digital tools to facilitate the iterative constructing, using, evaluating, and revising of models. 

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4. Causal models with constraints

   S. Beckers; C. Hitchcock; J. Y. Halpern (April 2023, Proceedings of the Second Conference on Causal Learning and Reasoning)

   Causal models have proven extremely useful in offering formal representations of causal relationships between a set of variables. Yet in many situations, there are non-causal relationships among variables. For example, we may want variables LDL, HDL, and TOT that represent the level of low-density lipoprotein cholesterol, the level of lipoprotein high-density lipoprotein cholesterol, and total cholesterol level, with the relation LDL+HDL=\OT. This cannot be done in standard causal models, because we can intervene simultaneously on all three variables. The goal of this paper is to extend standard causal models to allow for constraints on settings of variables. Although the extension is relatively straightforward, to make it useful we have to define a new intervention operation that disconnects a variable from a causal equation. We give examples showing the usefulness of this extension, and provide a sound and complete axiomatization for causal models with constraints. 

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5. It's complicated: Improving decisions on causally complex topics

   Kleinberg, Samantha; Marsh, Jessecae K. (January 2021, Proceedings of the 43rd Annual Meeting of the Cognitive Science Society)

   Fitch., T.; Lamm, C.; Leder, H.; Teßmar-Raible, K. (Ed.)

   We make frequent decisions about how to manage our health, yet do so with information that is highly complex or received piecemeal. Causal models can provide guidance about how components of a complex system interact, yet models that provide a complete causal story may be more complex than people can reason about. Prior work has provided mixed insights into our ability to make decisions with causal models, showing that people can use them in novel domains but that they may impede decisions in familiar ones. We examine how tailoring causal information to the question at hand may aid decision making, using simple diagrams with only the relevant causal paths (Experiment 1) or those paths highlighted within a complex causal model (Experiment 2). We find that diagrams tailored to a choice improve decision accuracy over complex diagrams or prior knowledge, providing new evidence for how causal models can aid decisions. 

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