We consider a sequence of successively more restrictive definitions of abstraction for causal models, starting with a notion introduced by Rubenstein et al. (2017) 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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Pearl opened the door to formally defining actual causation using causal models. His approach rests on two strategies: first, capturing the widespread intuition that X = x causes Y = y iff X = x is a Necessary Element of a Sufficient Set for Y = y, and second, showing that his definition gives intuitive answers on a wide set of problem cases. This inspired dozens of variations of his definition of actual causation, the most prominent of which are due to Halpern & Pearl. Yet all of them ignore Pearl’s first strategy, and the second strategy taken by itself is unable to deliver a consensus. This paper offers a way out by going back to the first strategy: it offers six formal definitions of causal sufficiency and two interpretations of necessity. Combining the two gives twelve new definitions of actual causation. Several interesting results about these definitions and their relation to the various Halpern & Pearl definitions are presented. Afterwards the second strategy is evaluated as well. In order to maximize neutrality, the paper relies mostly on the examples and intuitions of Halpern & Pearl. One definition comes out as being superior to all others, and is therefore suggested as a new definition of actual causation.

The counterfactual tradition to defining actual causation has come a long way since Lewis started it off. However there are still important open problems that need to be solved. One of them is the (in)transitivity of causation. Endorsing transitivity was a major source of trouble for the approach taken by Lewis, which is why currently most approaches reject it. But transitivity has never lost its appeal, and there is a large literature devoted to understanding why this is so. Starting from a survey of this work, we will develop a formal analysis of transitivity and the problems it poses for causation. This analysis provides us with a sufficient condition for causation to be transitive, a sufficient condition for dependence to be necessary for causation, and several characterisations of the transitivity of dependence. Finally, we show how this analysis leads naturally to several conditions a definition of causation should satisfy, and use those to suggest a new definition of causation.

Since Pearl's seminal work on providing a formal language for causality, the subject has garnered a lot of interest among philosophers and researchers in artificial intelligence alike. One of the most debated topics in this context is the notion of actual causation, which concerns itself with specificas opposed to general -causal claims. The search for a proper formal definition of actual causation has evolved into a controversial debate, that is pervaded with ambiguities and confusion. The goal of our research is twofold. First, we wish to provide a clear way to compare competing definitions. Second, we want to improve upon these definitions so they can be applied to a more diverse range of instances, including non-deterministic ones. To achieve these goals we provide a general, abstract definition of actual causation, formulated in the context of the expressive language of CP-logic (Causal Probabilistic logic). We will then show that three recent definitions by Ned Hall (originally formulated for structural models) and a definition of our own (formulated for CP-logic directly) can be viewed and directly compared as instantiations of this abstract definition, which also allows them to deal with a broader range of examples.

Beckers & Vennekens recently proposed a definition of actual causation that is based on certain plausible principles, thereby allowing the debate on causation to shift away from its heavy focus on examples towards a more systematic analysis. This paper contributes to that analysis in two ways. First, I show that their definition is in fact a formalization of Wright’s famous NESS definition of causation combined with a counterfactual difference-making condition. This means that their definition integrates two highly influential approaches to causation that are claimed to stand in opposition to each other. Second, I modify their definition to offer a substantial improvement: I weaken their difference-making condition in such a way that it avoids their problematic analysis of cases of preemption. The resulting Counterfactual NESS definition of causation forms a natural compromise between counterfactual approaches and the NESS approach.

The ethical concerns regarding the successful development of an Artificial Intelligence have received a lot of attention lately. The idea is that even if we have good reason to believe that it is very unlikely, the mere possibility of an AI causing extreme human suffering is important enough to warrant serious consideration. Others look at this problem from the opposite perspective, namely that of the AI itself. Here the idea is that even if we have good reason to believe that it is very unlikely, the mere possibility of humanity causing extreme suffering to an AI is important enough to warrant serious consideration. This paper starts from the observation that both concerns rely on problematic philosophical assumptions. Rather than tackling these assumptions directly, it proceeds to present an argument that if one takes these assumptions seriously, then one has a moral obligation to advocate for a ban on the development of a conscious AI.

The aim of this paper is to offer the first systematic exploration and definition of equivalent causal models in the context where both models are not made up of the same variables. The idea is that two models are equivalent when they agree on all "essential" causal information that can be expressed using their common variables. I do so by focussing on the two main features of causal models, namely their structural relations and their functional relations. In particular, I define several relations of causal ancestry and several relations of causal sufficiency, and require that the most general of these relations are preserved across equivalent models.