Halpern and Pearl ([2005a], [2005b]) use the framework of structural equation models to define a notion of explanation that is based on actual causation. But while Halpern and Pearl’s definition of actual causation has been met with ample, often constructive, criticism, their subsequent definition of explanation has not faced similar scrutiny. It only underwent a slight reformulation by Halpern ([2016]). In this article, I will show that Halpern and Pearl’s definition of explanation is, despite many promising features, still problematic, even (...) if we presuppose adequately defined causal concepts. I will propose some changes to Halpern and Pearl’s definition and argue that those changes are able to resolve the revealed problems while maintaining all the benefits of their approach. (shrink)

While structural equations modeling is increasingly used in philosophical theorizing about causation, it remains unclear what it takes for a particular structural equations model to be correct. To the extent that this issue has been addressed, the consensus appears to be that it takes a certain family of causal counterfactuals being true. I argue that this account faces difficulties in securing the independent manipulability of the structural determination relations represented in a correct structural equations model. I then offer an alternate (...) understanding of structural determination, and I demonstrate that this theory guarantees that structural determination relations are independently manipulable. The account provides a straightforward way of understanding hypothetical interventions, as well as a criterion for distinguishing hypothetical changes in the values of variables which constitute interventions from those which do not. It additionally affords a semantics for causal counterfactual conditionals which is able to yield a clean solution to a problem case for the standard ‘closest possible world’ semantics. (shrink)

We present a probabilistic extension to active path analyses of token causation (Halpern & Pearl 2001, forthcoming; Hitchcock 2001). The extension uses the generalized notion of intervention presented in (Korb et al. 2004): we allow an intervention to set any probability distribution over the intervention variables, not just a single value. The resulting account can handle a wide range of examples. We do not claim the account is complete --- only that it fills an obvious gap in previous active-path approaches. (...) It still succumbs to recent counterexamples by Hiddleston (2005), because it does not explicitly consider causal processes. We claim three benefits: a detailed comparison of three active-path approaches, a probabilistic extension for each, and an algorithmic formulation. (shrink)

Roughly put, explanatory circles — if any exist — would be propositions such that (i) each explains the next, and (ii) the last explains the first. In this paper, I give two arguments for the view that there are explanatory circles. The first argument appeals to general relativistic worlds in which time is circular. The second argument appeals to special science theories that describe feedback loops. In addition, I show that three standard arguments against explanatory circles are unsuccessful.

Causal reasoning and game-theoretic reasoning are fundamental topics in artificial intelligence, among many other disciplines: this paper is concerned with their intersection. Despite their importance, a formal framework that supports both these forms of reasoning has, until now, been lacking. We offer a solution in the form of (structural) causal games, which can be seen as extending Pearl's causal hierarchy to the game-theoretic domain, or as extending Koller and Milch's multi-agent influence diagrams to the causal domain. We then consider three (...) key questions: i) How can the (causal) dependencies in games - either between variables, or between strategies - be modelled in a uniform, principled manner? ii) How may causal queries be computed in causal games, and what assumptions does this require? iii) How do causal games compare to existing formalisms? To address question i), we introduce mechanised games, which encode dependencies between agents' decision rules and the distributions governing the game. In response to question ii), we present definitions of predictions, interventions, and counterfactuals, and discuss the assumptions required for each. Regarding question iii), we describe correspondences between causal games and other formalisms, and explain how causal games can be used to answer queries that other causal or game-theoretic models do not support. Finally, we highlight possible applications of causal games, aided by an extensive open-source Python library. (shrink)

It is often assumed that theorizing in terms of natural properties is more objectively valuable than theorizing in terms of non-natural properties. But this assumption faces an explanatory challenge: explain the greater objective value of theorizing in terms of natural properties. In this paper, I answer that challenge by proposing and exploring three different accounts of the objective value of naturalness. Two appeal to constitutive natures: it is part of the constitutive nature of explanation, or of objective value, that theorizing (...) in terms of natural properties is more objectively valuable. The third appeals to the theoretical role that naturalness plays. (shrink)

Cancer biology features the ascription of normal functions to parts of cancers. At least some ascriptions of function in cancer biology track local normality of parts within the global abnormality of the aberration to which those parts belong. That is, cancer biologists identify as functions activities that, in some sense, parts of cancers are supposed to perform, despite cancers themselves having no purpose. The present paper provides a theory to accommodate these normal function ascriptions—I call it the Modeling Account of (...) Normal Function (MA). MA comprises two claims. First, normal functions are activities whose performance by the function-bearing part contributes to the self-maintenance of the whole system and, thereby, results in the continued presence of that part. Second, MA holds that models of system-level activities that are (partly) constitutive of self-maintenance are improved by including a representation of the relevant function-bearing part and by making reference to the activity/activities that part performs which contribute(s) to those system-level activities. I contrast MA with two other accounts that seek to explicate the ascription of normal functions in biology, namely, the organizational account and the selected effects account. Both struggle to extend to cancer biology. However, I offer ecumenical readings which allow them to recover some ascriptions of normal function to parts of cancers. So, though I contend that MA excels in this respect, the purpose of this paper is served if it provides materials for bridging the gap between cancer biology, philosophy of cancer, and the literature on function. (shrink)

Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence, a fast-growing research area that is so far lacking in firm theoretical foundations. In this article, an expanded version of a paper originally presented at the 37th Conference on Uncertainty in Artificial Intelligence, we attempt to fill this gap. Building on work in logic, probability, and causality, we establish the central role of (...) necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We propose a novel formulation of these concepts, and demonstrate its advantages over leading alternatives. We present a sound and complete algorithm for computing explanatory factors with respect to a given context and set of agentive preferences, allowing users to identify necessary and sufficient conditions for desired outcomes at minimal cost. Experiments on real and simulated data confirm our method’s competitive performance against state of the art XAI tools on a diverse array of tasks. (shrink)

The investigation of probabilistic causality has been plagued by a variety of misconceptions and misunderstandings. One has been the thought that the aim of the probabilistic account of causality is the reduction of causal claims to probabilistic claims. Nancy Cartwright (1979) has clearly rebutted that idea. Another ill-conceived idea continues to haunt the debate, namely the idea that contextual unanimity can do the work of objective homogeneity. It cannot. We argue that only objective homogeneity in combination with a causal interpretation (...) of Bayesian networks can provide the desired criterion of probabilistic causality. (shrink)

There is general consensus that explainable artificial intelligence is valuable, but there is significant divergence when we try to articulate why, exactly, it is desirable. This question must be distinguished from two other kinds of questions asked in the XAI literature that are sometimes asked and addressed simultaneously. The first and most obvious is the ‘how’ question—some version of: ‘how do we develop technical strategies to achieve XAI?’ Another question is specifying what kind of explanation is worth having in the (...) first place. As difficult and important as the challenges are in answering these questions, they are distinct from a third question: why do we want XAI at all? There is vast literature on this question as well, but I wish to explore a different kind of answer. The most obvious way to answer this question is by describing a desirable outcome that would likely be achieved with the right kind of explanation, which would make the explanation valuable instrumentally. That is, XAI is desirable to attain some other value, such as fairness, trust, accountability, or governance. This family of arguments is obviously important, but I argue that explanations are also intrinsically valuable, because unexplainable systems can be dehumanizing. I argue that there are at least three independently valid versions of this kind of argument: an argument from participation, from knowledge, and from actualization. Each of these arguments that XAI is intrinsically valuable is independently compelling, in addition to the more obvious instrumental benefits of XAI. (shrink)

Explanations are backed by many different relations: causation, grounding, and arguably others too. But why are these different relations capable of backing explanations? In virtue of what are they explanatory? In this paper, I propose and defend a monistic account of explanation-backing relations. On my account, there is a single relation which backs all cases of explanation, and which explains why those other relations are explanation-backing.

Manipulablity theories of causation, according to which causes are to be regarded as handles or devices for manipulating effects, have considerable intuitive appeal and are popular among social scientists and statisticians. This article surveys several prominent versions of such theories advocated by philosophers, and the many difficulties they face. Philosophical statements of the manipulationist approach are generally reductionist in aspiration and assign a central role to human action. These contrast with recent discussions employing a broadly manipulationist framework for understanding causation, (...) such as those due to the computer scientist Judea Pearl and others, which are non-reductionist and rely instead on the notion of an intervention. This is simply an appropriately exogenous causal process; it has no essential connection with human action. This interventionist framework manages to avoid at least some of these difficulties faced by traditional philosophical versions of the manipulability theory and helps to clarify the content of causal claims. (shrink)

Explainable artificial intelligence (XAI) aims to help people understand black box algorithms, particularly of their outputs. But what are these explanations and when is one explanation better than another? The manipulationist definition of explanation from the philosophy of science offers good answers to these questions, holding that an explanation consists of a generalization that shows what happens in counterfactual cases. Furthermore, when it comes to explanatory depth this account holds that a generalization that has more abstract variables, is broader in (...) scope and/or more accurate is better. By applying these definitions and contrasting them with alternative definitions in the XAI literature I hope to help clarify what a good explanation is for AI. (shrink)

The present paper aims to complement causal model approaches to causal explanation by Woodward [15], Halpern and Pearl [5], and Strevens [14]. It centres on a strengthened Ramsey Test of conditionals: α ≫ γ iff, after sus- pending judgment about α and γ, an agent can infer γ from the supposition of α. It has been shown by Andreas and Gu ̈nther [1] that such a conditional can be used as starting point of an analysis of ‘because’ in natural language. (...) In what follows, we shall refine this analysis so as to yield a fully fledged account of causal explanation. (shrink)

This paper develops axiomatic foundations for a probabilistic-interventionist theory of causal strength. Transferring methods from Bayesian confirmation theory, I proceed in three steps: I develop a framework for defining and comparing measures of causal strength; I argue that no single measure can satisfy all natural constraints; I prove two representation theorems for popular measures of causal strength: Pearl's causal effect measure and Eells' difference measure. In other words, I demonstrate these two measures can be derived from a set of plausible (...) adequacy conditions. The paper concludes by sketching future research avenues. (shrink)

A central goal of research in explainable artificial intelligence (XAI) is to facilitate human understanding. However, understanding is an elusive concept that is difficult to target. In this paper, we argue that a useful way to conceptualize understanding within the realm of XAI is via certain human abilities. We present four criteria for a useful conceptualization of understanding in XAI and show that these are fulfilled by an abilities-based approach: First, thinking about understanding in terms of specific abilities is motivated (...) by research from numerous disciplines involved in XAI. Second, an abilities-based approach is highly versatile and can capture different forms of understanding important in XAI application contexts. Third, abilities can be operationalized for empirical studies. Fourth, abilities can be used to clarify the link between explainability, understanding, and societal desiderata concerning AI, like fairness and trustworthiness. Conceptualizing understanding as abilities can therefore support interdisciplinary collaboration among XAI researchers, provide practical benefit across diverse XAI application contexts, facilitate the development and evaluation of explainability approaches, and contribute to satisfying the societal desiderata of different stakeholders concerning AI systems. (shrink)