The Similarity of Causal Structure

2013

Scientists often use directed acyclic graphs (days) to model the qualitative structure of causal theories, allowing the parameters to be estimated from observational data. Two causal models are equivalent if there is no experiment which could distinguish one from the other. A canonical representation for causal models is presented which yields an efficient graphical criterion for deciding equivalence, and provides a theoretical basis for extracting causal structures from empirical data. This representation is then extended to the more general case of an embedded causal model, that is, a dag in which only a subset of the variables are observable. The canonical representation presented here yields an efficient algorithm for determining when two embedded causal models reflect the same dependency information. This algorithm leads to a model theoretic definition of causation in terms of statistical dependencies.

2018

We explore the relationships between causal rules and counterfactuals, as well as their relative representation capabilities, in the logical framework of the causal calculus. It will be shown that, though counterfactuals are readily definable on the basis of causal rules, the reverse reduction is achievable only up to a certain logical threshold (basic equivalence). As a result, we will argue that counterfactuals cannot distinguish causal theories that justify different claims of actual causation, which could be seen as the main source of the problem of ‘structural equivalents’ in counterfactual approaches to causation. This will lead us to a general conclusion about the primary role of causal rules in representing causation.

2022

We develop a category-theoretic criterion for determining the equivalence of causal models having different but homomorphic directed acyclic graphs over discrete variables. Following Jacobs et al. (2019), we define a causal model as a probabilistic interpretation of a causal string diagram, i.e., a functor from the ``syntactic'' category $\textsf{Syn}_G$ of graph $G$ to the category $\textsf{Stoch}$ of finite sets and stochastic matrices. The equivalence of causal models is then defined in terms of a natural transformation or isomorphism between two such functors, which we call a $Φ$-abstraction and $Φ$-equivalence, respectively. It is shown that when one model is a $Φ$-abstraction of another, the intervention calculus of the former can be consistently translated into that of the latter. We also identify the condition under which a model accommodates a $Φ$-abstraction, when transformations are deterministic.

We present a precise definition of cause and effect in terms of a fundamental notion called unresponsiveness. Our definition is based on Savage's (1954) formulation of decision theory and departs from the traditional view of causation in that our causal assertions are made relative to a set of decisions. An important consequence of this departure is that we can reason about cause locally, not requiring a causal explanation for every dependency. Such local reasoning can be beneficial because it may not be necessary to determine whether a particular dependency is causal to make a decision. Also in this paper, we examine the graphical encoding of causal relationships. We show that influence diagrams in canonical form are an accurate and efficient representation of causal relationships. In addition, we establish a correspondence between canonical form and Pearl's causal theory.

2001

Abstract Considerable evidence indicates that causal information provides a vital constraint on conceptual representation and coherence. We investigated the role of causal information as a constraint on similarity, exploiting an asymmetry between predictive causal reasoning (given the cause, predict the effect) and diagnostic causal reasoning (given the effect, diagnose the cause). This asymmetry allowed us to isolate the effects of causal understanding from the effects of sharing non-causal features.

Counterfactuals are contrary to fact conditionals of the form, If A were the case then B would be the case. In this usage, A is usually false or untrue in the world so that A is contrary to fact or counterfactual. The semantics of counterfactuals is normally developed according to the principle of similarity, and the key point is to specify the notion of relative similarity. In this paper, we focus on a specific type of counterfactuals called causal counterfactuals and study in detail its applications to the philosophy of science. We consider Causal counterfactuals such as for e.g., 'if the ignition key had been turned then the car would have started' and causal conditionals e.g., 'if the ignition key was turned then the car started'. These counterfactuals hold because of the causal relationship between the antecedent and consequent. It is the connection between counterfactuals and causation that makes them relevant to social science research. Research on counterfactuals have attracted wide attention amongst philosophers and AI community. in the recent years, much work on counterfactuals in philosophy are focussed on criteria for judging the counterfactuals to be true. In this paper, we deal with the semantics of counterfactuals and address some of the challenges being addressed in the traditional and recent work on theories of counterfactuals. Counterfactuals finds utmost importance in analyzing laws, causality and explanation.

Determining what constitutes a causal relationship between two or more concepts, and how to infer causation, are fundamental concepts in statistics and all the sciences. Causation becomes especially difficult in the social sciences where there is a myriad of different factors that are not always easily observed or measured that directly or indirectly influence the dynamic relationships between independent variables and dependent variables. This paper proposes a procedure for helping researchers explicitly understand what their underlying assumptions are, what kind of data and methodology are needed to understand a given relationship, and how to develop explicit assumptions with clear alternatives, such that researchers can then apply a process of probabilistic elimination. The procedure borrows from Pearl's concept of " causal diagrams " and concept mapping to create a repeatable, step-by-step process for systematically researching complex relationships and, more generally, complex systems. The significance of this methodology is that it can help researchers determine what is more probably accurate and what is less probably accurate in a comprehensive fashion for complex phenomena. This can help resolve many of our current and future political and policy debates by eliminating that which has no evidence in support of it, and that which has evidence against it, from the pool of what can be permitted in research and debates. By defining and streamlining a process for inferring truth in a way that is graspable by human cognition, we can begin to have more productive and effective discussions around political and policy questions.

Pacific Philosophical Quarterly, 1991

Scalable Uncertainty Management, 2008

Ascribing causality amounts to determining what elements in a sequence of reported facts can be related in a causal way, on the basis of some knowledge about the course of the world. The paper offers a comparison of a large span of formal models (based on structural equations, non-monotonic consequence relations, trajectory preference relations, identification of violated norms, graphical representations, or connectionism), using a running example taken from a corpus of car accident reports. Interestingly enough, the ...