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1. The explanatory nature of constraints: Law-based, mathematical, and causal

   https://doi.org/10.1007/s11229-023-04281-5  

   Ross, Lauren N. (August 2023, Synthese)

   This paper provides an analysis of explanatory constraints and their role in scientific explanation. This analysis clarifies main characteristics of explanatory constraints, ways in which they differ from “standard” explanatory factors, and the unique roles they play in scientific explanation. While current philosophical work appreciates two main types of explanatory constraints, this paper suggests a new taxonomy: law-based constraints, mathematical constraints, and causal constraints. This classification helps capture unique features of constraint types, the different roles they play in explanation, and it includes causal constraints, which are often overlooked in this literature. 

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2. Cascade versus Mechanism: The Diversity of Causal Structure in Science

   https://doi.org/10.1086/723623  

   Ross, Lauren N. (May 2023, The British Journal for the Philosophy of Science)

   According to mainstream philosophical views causal explanation in biology and neuroscience is mechanistic. As the term ‘mechanism’ gets regular use in these fields it is unsurprising that philosophers considerit important to scientific explanation. What is surprisingis that they consider it the only causal term of importance. This paper provides an analysis of a new causal concept—it examines the cascade concept in science and the causal structure it refers to. I argue that this conceptis importantly different from the notion of mechanism and that this difference matters for our understanding of causation and explanation in science. 

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3. Causal Approaches to Explanation

   Ross, Lauren N. (March 2023, Stanford encyclopedia of philosophy)

   Edward N. Zalta & Uri Nodelman (Ed.)

   This entry discusses some accounts of causal explanation developed after approximately 1990. Our focus in this entry is on the following three accounts – Section 1 those that focus on mechanisms and mechanistic explanations, Section 2 the kairetic account of explanation, and Section 3 interventionist accounts of causal explanation. All of these have as their target explanations of why or perhaps how some phenomenon occurs (in contrast to, say, explanations of what something is, which is generally taken to be non-causal) and they attempt to capture causal explanations that aim at such explananda. Section 4 then takes up some recent proposals having to do with how causal explanations may differ in explanatory depth or goodness. Section 5 discusses some issues having to do with what is distinctive about causal (as opposed to non-causal) explanations. 

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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. Triad Constraints for Learning Causal Structure of Latent Variables

   Ruichu Cai, Feng Xie (December 2019, Advances in neural information processing systems)

   Learning causal structure from observational data has attracted much attention,and it is notoriously challenging to find the underlying structure in the presenceof confounders (hidden direct common causes of two variables). In this paper,by properly leveraging the non-Gaussianity of the data, we propose to estimatethe structure over latent variables with the so-called Triad constraints: we design a form of "pseudo-residual" from three variables, and show that when causal relations are linear and noise terms are non-Gaussian, the causal direction between the latent variables for the three observed variables is identifiable by checking a certain kind of independence relationship. In other words, the Triad constraints help us to locate latent confounders and determine the causal direction between them. This goes far beyond the Tetrad constraints and reveals more information about the underlying structure from non-Gaussian data. Finally, based on the Triad constraints, we develop a two-step algorithm to learn the causal structure corresponding to measurement models. Experimental results on both synthetic and real data demonstrate the effectiveness and reliability of our method. 

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