Causal reasoning from almost first principles

A formal theory of causal reasoning is presented that encompasses both Pearl's approach to causality and several key formalisms of nonmonotonic reasoning in Artificial Intelligence. This theory will be derived from a single rationality principle of causal acceptance for propositions. However, this principle will also set the theory of causal reasoning apart from common representational approaches to reasoning formalisms

Your Brain as the Source of Free Will Worth Wanting: Understanding Free Will in the Age of Neuroscience

Philosophical debates about free will have focused on determinism—a potential ‘threat from behind’ because determinism entails that there are conditions in the distant past that, in accord with the laws of nature, are sufficient for all of our decisions. Neuroscience is consistent with indeterminism, so it is better understood as posing a ‘threat from below’: If our decision-making processes are carried out by neural processes, then it might seem that our decisions are not based on our prior conscious deliberations or reasoning. The response to this threat will require a neurophilosophical theory of mind that makes sense of the causal role of our conscious reasons and reasoning. Without such a theory, our conscious self seems bypassed by the neural processes in our brains, and this view seems to explain why many scientists assume that neuroscience challenges free will. However, I argue that most people are amenable to the possibility of a future theory of mind that is physicalist (if not reductionist), yet preserves much of our ordinary experience and understanding of conscious decision-making and self-control. I outline such a theory using the resources of causal interventionism. I argue that this view is best understood as a minimal revision to our understanding of free will, rather than an elimination of it. And I argue that this view has more reasonable and effective implications for our moral and legal practices than an eliminativist or skeptical theory of free will

RankPL: A Qualitative Probabilistic Programming Language

In this paper we introduce RankPL, a modeling language that can be thought of as a qualitative variant of a probabilistic programming language with a semantics based on Spohn's ranking theory. Broadly speaking, RankPL can be used to represent and reason about processes that exhibit uncertainty expressible by distinguishing "normal" from" surprising" events. RankPL allows (iterated) revision of rankings over alternative program states and supports various types of reasoning, including abduction and causal inference. We present the language, its denotational semantics, and a number of practical examples. We also discuss an implementation of RankPL that is available for download

Justifying additive-noise-model based causal discovery via algorithmic information theory

A recent method for causal discovery is in many cases able to infer whether X causes Y or Y causes X for just two observed variables X and Y. It is based on the observation that there exist (non-Gaussian) joint distributions P(X,Y) for which Y may be written as a function of X up to an additive noise term that is independent of X and no such model exists from Y to X. Whenever this is the case, one prefers the causal model X--> Y. Here we justify this method by showing that the causal hypothesis Y--> X is unlikely because it requires a specific tuning between P(Y) and P(X|Y) to generate a distribution that admits an additive noise model from X to Y. To quantify the amount of tuning required we derive lower bounds on the algorithmic information shared by P(Y) and P(X|Y). This way, our justification is consistent with recent approaches for using algorithmic information theory for causal reasoning. We extend this principle to the case where P(X,Y) almost admits an additive noise model. Our results suggest that the above conclusion is more reliable if the complexity of P(Y) is high.Comment: 17 pages, 1 Figur

A quantum probability account of individual differences in causal reasoning

We use quantum probability (QP) theory to investigate individual differences in causal reasoning. By analyzing data sets from Rehder (2014) on comparative judgments, and from Rehder & Waldmann (2016) on absolute judgments, we show that a QP model can both account for individual differences in causal judgments, and why these judgments sometimes violate the properties of causal Bayes nets. We implement this and previously proposed models of causal reasoning (including classical probability models) within the same hierarchical Bayesian inferential framework to provide a detailed comparison between these models, including computing Bayes factors. Analysis of the inferred parameters of the QP model illustrates how these can be interpreted in terms of putative cognitive mechanisms of causal reasoning. Additionally, we implement a latent classification mechanism that identifies subcategories of reasoners based on properties of the inferred cognitive process, rather than post hoc clustering. The QP model also provides a parsimonious explanation for aggregate behavior, which alternatively can only be explained by a mixture of multiple existing models. Investigating individual differences through the lens of a QP model reveals simple but strong alternatives to existing explanations for the dichotomies often observed in how people make causal inferences. These alternative explanations arise from the cognitive interpretation of the parameters and structure of the quantum probability model