4 found
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  1. Causal Models and the Logic of Counterfactuals.Jonathan Vandenburgh - manuscript
    Causal models provide a framework for making counterfactual predictions, making them useful for evaluating the truth conditions of counterfactual sentences. However, current causal models for counterfactual semantics face limitations compared to the alternative similarity-based approach: they only apply to a limited subset of counterfactuals and the connection to counterfactual logic is not straightforward. This paper argues that these limitations arise from the theory of interventions where intervening on variables requires changing structural equations rather than the values of variables. Using an (...)
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  2. Causal Models and the Relevant Alternatives Theory of Knowledge.Jonathan Vandenburgh - manuscript
    One approach to knowledge, termed the relevant alternatives theory, stipulates that a belief amounts to knowledge if one can eliminate all relevant alternatives to the belief in the epistemic situation. This paper uses causal graphical models to formalize the relevant alternatives approach to knowledge. On this theory, an epistemic situation is encoded through the causal relationships between propositions, which determine which alternatives are relevant and irrelevant. This formalization entails that statistical evidence is not sufficient for knowledge, provides a simple way (...)
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    Learning as Hypothesis Testing: Learning Conditional and Probabilistic Information.Jonathan Vandenburgh - manuscript
    Complex constraints like conditionals ('If A, then B') and probabilistic constraints ('The probability that A is p') pose problems for Bayesian theories of learning. Since these propositions do not express constraints on outcomes, agents cannot simply conditionalize on the new information. Furthermore, a natural extension of conditionalization, relative information minimization, leads to many counterintuitive predictions, evidenced by the sundowners problem and the Judy Benjamin problem. Building on the notion of a `paradigm shift' and empirical research in psychology and economics, I (...)
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  4. Triviality Results, Conditional Probability, and Restrictor Conditionals.Jonathan Vandenburgh - manuscript
    Conditional probability is often used to represent the probability of the conditional. However, triviality results suggest that the thesis that the probability of the conditional always equals conditional probability leads to untenable conclusions. In this paper, I offer an interpretation of this thesis in a possible worlds framework, arguing that the triviality results make assumptions at odds with the use of conditional probability. I argue that these assumptions come from a theory called the operator theory and that the rival restrictor (...)
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