It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlations in the sense of Reichenbach's definition of common cause. It is shown, further, that, given any quantum probability space and any set of commuting events in it which are correlated with respect to a fixed quantum state, the quantum probability space can be extended in such a way that the extension contains common causes of all the selected correlations, where common cause is again taken in the sense of Reichenbach's definition. It is argued that these results very strongly restrict the possible ways of disproving Reichenbach's Common Cause Principle.

A biochemical pathway is a sequence of chemical reactions in a biological organism. Such pathways specify mechanisms that explain how cells carry out their major functions by means of molecules and reactions that produce regular changes. Many diseases can be explained by defects in pathways, and new treatments often involve finding drugs that correct those defects. This paper presents explanation schemas and treatment strategies that characterize how thinking about pathways contributes to biomedical discovery. It discusses the significance of pathways for understanding the nature of diseases, explanations, and theories.

In this chapter, I review the main methods and techniques of complex systems science. As a

has elicited considerable criticism from the education research community, but this criticism has not focused on a key assumption of the report—its Humean, regularity conception of causality. It is argued that this conception, which also underlies other arguments for “scientifically-based research, ” is narrow and philosophically outdated, and leads to a misrepresentation of the nature and value of qualitative research for causal explanation. An alternative, realist approach to causality is presented that supports the scientific legitimacy of using qualitative research for causal investigation, reframes the arguments for experimental methods in educational research, and can support a more productive collaboration between qualitative and quantitative researchers. Amajor effort to establish “scientifically-based research” (SBR) in education has been under way for some time

In this paper, we present a short overview of di#erent theories of explanation. We argue that the goals of the user should be taken into account when deciding what is a good explanation for a given CBR system. Some general types relevant to many Case-Based Reasoning (CBR) systems are identified and we use these goals to identify some limitations in using the case as an explanation in CBR systems.

Bayesian networks are normally given one of two types of foundations: they are either treated purely formally as an abstract way of representing probability functions, or they are interpreted, with some causal interpretation given to the graph in a network and some standard interpretation of probability given to the probabilities specified in the network. In this chapter I argue that current foundations are problematic, and put forward new foundations which involve aspects of both the interpreted and the formal approaches. One standard approach is to interpret a Bayesian network objectively: the graph in a Bayesian network represents causality in the world and the specified probabilities are objective, empirical probabilities. Such an interpretation founders when the Bayesian network independence assumption (often called the causal Markov condition) fails to hold. In §2 I catalogue the occasions when the independence assumption fails, and show that such failures are pervasive. Next, in §3, I show that even where the independence assumption does hold objectively, an agent’s causal knowledge is unlikely to satisfy the assumption with respect to her subjective probabilities, and that slight differences between an agent’s subjective Bayesian network and an objective Bayesian network can lead to large differences between probability distributions determined by these networks. To overcome these difficulties I put forward logical Bayesian foundations in §5. I show that if the graph and probability specification in a Bayesian network are thought of as an agent’s background knowledge, then the agent is most rational if she adopts the probability distribution determined by the

The article first addresses the importance of cognitive modeling, in terms of its value to cognitive science (as well as other social and behavioral sciences). In particular, it emphasizes the use of cognitive architectures in this undertaking. Based on this approach, the article addresses, in detail, the idea of a multi-level approach that ranges from social to neural levels. In physical sciences, a rigorous set of theories is a hierarchy of descriptions/explanations, in which causal relationships among entities at a high level can be reduced to causal relationships among simpler entities at a more detailed level. We argue that a similar hierarchy makes possible an equally productive approach toward cognitive modeling. The levels of models that we conceive in relation to cognition include, at the highest level, sociological/anthropological models of collective human behavior, behavioral models of individual performance, cognitive models involving detailed mechanisms, representations, and processes, as well as biological/physiological models of neural circuits, brain regions, and other detailed biological processes.

Belief networks provide an important bridge between statistical modeling and expert systems. In this paper we present methods for visualizing probabilistic "evidence flows" in belief networks, thereby enabling belief networks to explain their behavior. Building on earlier research on explanation in expert systems, we present a hierarchy of explanations, ranging from simple colorings to detailed displays. Our approach complements parallel work on textual explanations in belief networks. GRAPHICAL-BELIEF, Mathsoft Inc.'s belief network software, implements the methods. 1 Introduction A fundamental reason for building a mathematical or statistical model is to foster deeper understanding of complex, real-world systems. Consequently, explanations---descriptions of the mechanisms which comprise such models---form an important part of model validation, exploration, and use. Early tests of rule-based expert system models indicated the critical need for detailed explanations in that setting (...

Philosophical theories summarized here include regularity and necessity theories from Hume to the present; manipulability theory; the theory of powerful particulars; causation as connected changes within a defined state of affairs; departures from "normal " events or from some standard for compar-ison; causation as a transfer of something between objects; and causal propagation and production. Issues found in this literature and of relevance for psychology include whether actual causal relations can be perceived or known; what sorts of things people believe can be causes; different levels of causal analysis; the distinction between the causal relation itself and cues to causal relations; causal frames or fields; internal and external causes; and understanding of causation in different realms of the world, such as the natural and artificial realms. A full theory of causal inference by laypeople should address all of these issues. The main purpose of this article is to survey philosophical theories of causation in a manner intended to be suitable for psychologists interested in causation. The article has two sec-tions: The first presents brief summaries of philosophical theo-ries of causation from Aristotle to the present. In the second, issues found in the philosophical literature are used to suggest new approaches to the study of causation in psychology. Philosophical Theories of Causation Several psychologists have written about selected philosophi-cal theories of causation (Cook & Campbell, 1979; Einhorn &

Inferring the causal structure that links n observables is usually basedupon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only single observations are present. We develop a theory how to generate causal graphs explaining similarities between single objects. To this end, we replace the notion of conditional stochastic independence in the causal Markov condition with the vanishing of conditional algorithmic mutual information anddescribe the corresponding causal inference rules. We explain why a consistent reformulation of causal inference in terms of algorithmic complexity implies a new inference principle that takes into account also the complexity of conditional probability densities, making it possible to select among Markov equivalent causal graphs. This insight provides a theoretical foundation of a heuristic principle proposed in earlier work. We also discuss how to replace Kolmogorov complexity with decidable complexity criteria. This can be seen as an algorithmic analog of replacing the empirically undecidable question of statistical independence with practical independence tests that are based on implicit or explicit assumptions on the underlying distribution. email: