This paper has two main parts. In the first part, we motivate a kind of indeterminate, suppositional credences by discussing the prospect for a subjective interpretation of a causal Bayesian network, an important tool for causal reasoning in artificial intelligence. A CBN consists of a causal graph and a collection of interventional probabilities. The subjective interpretation in question would take the causal graph in a CBN to represent the causal structure that is believed by an agent, and interventional probabilities in (...) a CBN to represent suppositional credences. We review a difficulty noted in the literature with such an interpretation, and suggest that a natural way to address the challenge is to go for a generalization of CBN that allows indeterminate credences. In the second part, we develop a decision-theoretic foundation for such indeterminate suppositional credences, by generalizing a theory of coherent choice functions to accommodate some form of act-state dependence. The upshot is a decision-theoretic framework that is not only rich enough to, so to speak, ground the probabilities in a subjectively interpreted causal network, but also interesting in its own right, in that it accommodates both act-state dependence and imprecise probabilities. (shrink)

The account of causal regularities in the influential INUS theory of causation has been refined in the recent developments of the regularity approach to causation and of the Boolean methods for inference of deterministic causal structures. A key element in the refinement is to strengthen the minimality or non-redundancy condition in the original INUS account. In this paper, we argue that the Boolean framework warrants a further strengthening of the minimality condition. We motivate our stronger condition by showing, first, that (...) a rationale for strengthening the original minimality condition in the INUS theory is also applicable to our proposal to go further, and second, that the new element of the stronger condition is a counterpart to a well-established minimality condition for probabilistic causal models. We also compare the various minimality conditions in terms of the difference-making criteria they imply and argue for the criterion implied by our condition. Finally, we show that putative counterexamples to our proposal can be addressed in the same way that the Boolean theorists defend the current minimality conditions in their framework. (shrink)

The framework of causal Bayes nets, currently influential in several scientific disciplines, provides a rich formalism to study the connection between causality and probability from an epistemological perspective. This article compares three assumptions in the literature that seem to constrain the connection between causality and probability in the style of Occam's razor. The trio includes two minimality assumptions—one formulated by Spirtes, Glymour, and Scheines (SGS) and the other due to Pearl—and the more well-known faithfulness or stability assumption. In terms of (...) logical strength, it is fairly obvious that the three form a sequence of increasingly stronger assumptions. The focus of this article, however, is to investigate the nature of their relative strength. The comparative analysis reveals an important sense in which Pearl's minimality assumption is as strong as the faithfulness assumption and identifies a useful condition under which it is as safe as SGS's relatively secure minimality assumption. Both findings have notable implications for the theory and practice of causal inference. 1 Introduction2 Background: Inference of Causal Structure in Markovian Causal Models3 Three Assumptions of Simplicity4 A Comparison of P-minimality and Faithfulness5 A Comparison of P-minimality and SGS-minimality6 Methodological Formulations and Prior Knowledge of Causal Order7 Conclusion. (shrink)

Though common sense says that causes must temporally precede their effects, the hugely influential interventionist account of causation makes no reference to temporal precedence. Does common sense lead us astray? In this paper, I evaluate the power of the commonsense assumption from within the interventionist approach to causal modeling. I first argue that if causes temporally precede their effects, then one need not consider the outcomes of interventions in order to infer causal relevance, and that one can instead use temporal (...) and probabilistic information to infer exactly when X is causally relevant to Y in each of the senses captured by Woodward’s interventionist treatment. Then, I consider the upshot of these findings for causal decision theory, and argue that the commonsense assumption is especially powerful when an agent seeks to determine whether so-called “dominance reasoning” is applicable. (shrink)

This article suggests a revision of the theory of causal nets. In section 1 we introduce an axiomatization of TCN based on a realistic understanding. It is shown that the causal Markov condition entails three independent principles. In section 2 we analyze indeterministic decay as the major counterexample to one of these principles: screening off by common causes. We call SCC-violating common causes interactive causes. In section 3 we develop a revised version of TCN, called TCN*, which accounts for interactive (...) causes. It is shown that there are interactive causal models that admit of no faithful noninteractive reconstruction. (shrink)

We start this paper by arguing that causality should, in analogy with force in Newtonian physics, be understood as a theoretical concept that is not explicated by a single definition, but by the axioms of a theory. Such an understanding of causality implicitly underlies the well-known theory of causal nets and has been explicitly promoted by Glymour. In this paper we investigate the explanatory warrant and empirical content of TCN. We sketch how the assumption of directed cause–effect relations can be (...) philosophically justified by an inference to the best explanation. We then ask whether the explanations provided by TCN are merely post-facto or have independently testable empirical content. To answer this question we develop a fine-grained axiomatization of TCN, including a distinction of different kinds of faithfulness. A number of theorems show that although the core axioms of TCN are empirically empty, extended versions of TCN have successively increasing empirical content. (shrink)

Independence of Conditionals (IC) has recently been proposed as a basic rule for causal structure learning. If a Bayesian network represents the causal structure, its Conditional Probability Distributions (CPDs) should be algorithmically independent. In this paper we compare IC with causal faithfulness (FF), stating that only those conditional independences that are implied by the causal Markov condition hold true. The latter is a basic postulate in common approaches to causal structure learning. The common spirit of FF and IC is to (...) reject causal graphs for which the joint distribution looks ‘non-generic’. The difference lies in the notion of genericity: FF sometimes rejects models just because one of the CPDs is simple, for instance if the CPD describes a deterministic relation. IC does not behave in this undesirable way. It only rejects a model when there is a non-generic relation between different CPDs although each CPD looks generic when considered separately. Moreover, it detects relations between CPDs that cannot be captured by conditional independences. IC therefore helps in distinguishing causal graphs that induce the same conditional independences (i.e., they belong to the same Markov equivalence class). The usual justification for FF implicitly assumes a prior that is a probability density on the parameter space. IC can be justified by Solomonoff’s universal prior, assigning non-zero probability to those points in parameter space that have a finite description. In this way, it favours simple CPDs, and therefore respects Occam’s razor. Since Kolmogorov complexity is uncomputable, IC is not directly applicable in practice. We argue that it is nevertheless helpful, since it has already served as inspiration and justification for novel causal inference algorithms. (shrink)

Goldman (1967) proposed that a subject s knows p if and only if p is appropriately causally connected to s’s believing p. He later on abandoned this theory (Goldman, 1976). The main objection to the theory is that the causal connection required by Goldman is compatible with certain problematic forms of luck. In this paper we argue that Goldman’s causal theory of knowledge can overcome the luck problem if causation is understood along interventionist lines. We also show that the modified (...) theory leads to the correct results in contexts involving other prominent forms of epistemic luck and compare it with other accounts on the market. (shrink)

In this paper I reconstruct and evaluate the validity of two versions of causal exclusion arguments within the theory of causal Bayes nets. I argue that supervenience relations formally behave like causal relations. If this is correct, then it turns out that both versions of the exclusion argument are valid when assuming the causal Markov condition and the causal minimality condition. I also investigate some consequences for the recent discussion of causal exclusion arguments in the light of an interventionist theory (...) of causation such as Woodward's (2003) and discuss a possible objection to my causal Bayes net reconstruction. (shrink)

Kim’s causal exclusion argument purports to demonstrate that the non-reductive physicalist must treat mental properties (and macro-level properties in general) as causally inert. A number of authors have attempted to resist Kim’s conclusion by utilizing the conceptual resources of Woodward’s interventionist conception of causation. The viability of these responses has been challenged by Gebharter, who argues that the causal exclusion argument is vindicated by the theory of causal Bayesian networks (CBNs). Since the interventionist conception of causation relies crucially on CBNs (...) for its foundations, Gebharter’s argument appears to cast significant doubt on interventionism’s anti-reductionist credentials. In the present article, we both (1) demonstrate that Gebharter’s CBN-theoretic formulation of the exclusion argument relies on some unmotivated and philosophically significant assumptions (especially regarding the relationship between CBNs and the metaphysics of causal relevance), and (2) use Bayesian networks to develop a general theory of causal inference for multi-level systems that can serve as the foundation for an anti-reductionist interventionist account of causation.1. (shrink)

Spirtes, Glymour and Scheines [Causation, Prediction, and Search Springer] described a pointwise consistent estimator of the Markov equivalence class of any causal structure that can be represented by a directed acyclic graph for any parametric family with a uniformly consistent test of conditional independence, under the Causal Markov and Causal Faithfulness assumptions. Robins et al. [Biometrika 90 491–515], however, proved that there are no uniformly consistent estimators of Markov equivalence classes of causal structures under those assumptions. Subsequently, Kalisch and B¨uhlmann (...) [J. Mach. Learn. Res. 8 613–636] described a uniformly consistent estimator of the Markov equivalence class of a linear Gaussian causal structure under the Causal Markov and Strong Causal Faithfulness assumptions. However, the Strong Faithfulness assumption may be false with high probability in many domains. We describe a uniformly consistent estimator of both the Markov equivalence class of a linear Gaussian causal structure and the identifiable structural coefficients in the Markov equivalence class under the Causal Markov assumption and the considerably weaker k-Triangle-Faithfulness assumption. (shrink)