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  1. Kevin T. Kelly, Conor Mayo Wilson, Hanti Lin & Oliver Schulte, Participants:.
    Philosophy of science, statistics, and machine learning all recommend the selection of simple theories or models on the basis of empirical data, where simplicity has something to do with minimizing independent entities, principles, causes, or equational coefficients. This intuitive preference for simplicity is called Ockham's razor, after the fourteenth century theologian and logician William of Ockham. But in spite of its intuitive appeal, how could Ockham's razor help one find the true theory? For, in an updated version of Plato's Meno (...)
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  2. Oliver Schulte, Epistemology, Reliable Inquiry and Topology.
    From one perspective, the fundamental notions of point-set topology have to do with sequences (of points or of numbers) and their limits. A broad class of epistemological questions also appear to be concerned with sequences and their limits. For example, problems of empirical underdetermination–which of a collection of alternative theories is true–have to do with logical properties of sequences of evidence. Underdetermination by evidence is the central problem of Plato’s Meno [Glymour and Kelly 1992], of one of Sextus Empiricus’ many (...)
     
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  3. Oliver Schulte, Iterated Backward Inference: An Algorithm for Proper Rationalizability.
    An important approach to game theory is to examine the consequences of beliefs that agents may have about each other. This paper investigates respect for public preferences. Consider an agent A who believes that B strictly prefers an option a to an option b. Then A respects B’s preference if A assigns probability 1 to the choice of a given that B chooses a or b. Respect for public preferences requires that if it is common belief that B prefers a (...)
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  4. Oliver Schulte, Knowledge and Planning in an Action-Based Multi-Agent Framework: A Case Study.
    The situation calculus is a logical formalism that has been extensively developed for planning. We apply the formalism in a complex multi-agent domain, modelled on the game of Clue. We find that the situation calculus, with suitable extensions, supplies a unified representation of (1) the interaction protocol, or structure of the game, (2) the dynamics of the knowledge and common knowledge of the agents, and (3) principles of strategic planning.
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  5. Oliver Schulte, Logically Reliable Inductive Inference.
    This paper aims to be a friendly introduction to formal learning theory. I introduce key concepts at a slow pace, comparing and contrasting with other approaches to inductive inference such as con…rmation theory. A number of examples are discussed, some in detail, such as Goodman’s Riddle of Induction. I outline some important results of formal learning theory that are of philosophical interest. Finally, I discuss recent developments in this approach to inductive inference.
     
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  6. Oliver Schulte, Minimal Belief Change and Pareto-Optimality.
    This paper analyzes the notion of a minimal belief change that incorporates new information. I apply the fundamental decisiontheoretic principle of Pareto-optimality to derive a notion of minimal belief change, for two different representations of belief: First, for beliefs represented by a theory –a deductively closed set of sentences or propositions–and second for beliefs represented by an axiomatic base for a theory. Three postulates exactly characterize Pareto-minimal revisions of theories, yielding a weaker set of constraints than the standard AGM postulates. (...)
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  7. Oliver Schulte, Mind Change Efficient Learning.
    This paper studies efficient learning with respect to mind changes. Our starting point is the idea that a learner that is efficient with respect to mind changes minimizes mind changes not only globally in the entire learning problem, but also locally in subproblems after receiving some evidence. Formalizing this idea leads to the notion of uniform mind change optimality. We characterize the structure of language classes that can be identified with at most α mind changes by some learner (not necessarily (...)
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  8. Oliver Schulte, Means-Ends Rationality and Categorical Imperatives in Empirical Inquiry.
    Kant taught us that there are two kinds of norms: Categorical imperatives that one ought to follow regardless of one's personal aims and circumstances, and hypothetical imperatives that direct us to employ the means towards our chosen ends. Kant's distinction separates two approaches to normative epistemology. On the one hand, we have principles of "inductive rationality", typically supported by considerations such as intuitive plausibility, conformity with exemplary practice, and internal consistency. On the other hand, we may assess rules for forming (...)
     
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  9. Oliver Schulte, Respect for Public Preferences and Iterated Backward Inference.
    An important approach to game theory is to examine the consequences of beliefs that rational agents may have about each other. This paper considers respect for public preferences. Consider an agent A who believes that B strictly prefers an option a to an option b. Then A respects B’s preference if A considers the choice of a “infinitely more likely” than the choice of B; equivalently, if A assigns probability 1 to the choice of a given that B chooses a (...)
     
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  10. Oliver Schulte, Representing Von Neumann–Morgenstern Games in the Situation Calculus.
    Sequential von Neumann–Morgernstern (VM) games are a very general formalism for representing multi-agent interactions and planning problems in a variety of types of environments. We show that sequential VM games with countably many actions and continuous utility functions have a sound and complete axiomatization in the situation calculus. This axiomatization allows us to represent game-theoretic reasoning and solution concepts such as Nash equilibrium. We discuss the application of various concepts from VM game theory to the theory of planning and multi-agent (...)
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  11. Oliver Schulte, Formal Learning Theory. Stanford Encyclopedia of Philosophy.
    Formal learning theory is the mathematical embodiment of a normative epistemology. It deals with the question of how an agent should use observations about her environment to arrive at correct and informative conclusions. Philosophers such as Putnam, Glymour and Kelly have developed learning theory as a normative framework for scientific reasoning and inductive inference.
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  12. Oliver Schulte (2008). The Co-Discovery of Conservation Laws and Particle Families. Studies in History and Philosophy of Science Part B 39 (2):288-314.
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  13. Oliver Schulte (2000). Eric Martin and Daniel Osherson Elements of Scientific Inquiry. British Journal for the Philosophy of Science 51 (2):347-352.
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  14. Oliver Schulte (2000). Inferring Conservation Laws in Particle Physics: A Case Study in the Problem of Induction. British Journal for the Philosophy of Science 51 (4):771-806.
    This paper develops a means–end analysis of an inductive problem that arises in particle physics: how to infer from observed reactions conservation principles that govern all reactions among elementary particles. I show that there is a reliable inference procedure that is guaranteed to arrive at an empirically adequate set of conservation principles as more and more evidence is obtained. An interesting feature of reliable procedures for finding conservation principles is that in certain precisely defined circumstances they must introduce hidden particles. (...)
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  15. Oliver Schulte (1999). Minimal Belief Change and the Pareto Principle. Synthese 118 (3):329-361.
    This paper analyzes the notion of a minimal belief change that incorporates new information. I apply the fundamental decision-theoretic principle of Pareto-optimality to derive a notion of minimal belief change, for two different representations of belief: First, for beliefs represented by a theory – a deductively closed set of sentences or propositions – and second for beliefs represented by an axiomatic base for a theory. Three postulates exactly characterize Pareto-minimal revisions of theories, yielding a weaker set of constraints than the (...)
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  16. Oliver Schulte (1999). The Logic of Reliable and Efficient Inquiry. Journal of Philosophical Logic 28 (4):399-438.
    This paper pursues a thorough-going instrumentalist, or means-ends, approach to the theory of inductive inference. I consider three epistemic aims: convergence to a correct theory, fast convergence to a correct theory and steady convergence to a correct theory (avoiding retractions). For each of these, two questions arise: (1) What is the structure of inductive problems in which these aims are feasible? (2) When feasible, what are the inference methods that attain them? Formal learning theory provides the tools for a complete (...)
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  17. Kevin T. Kelly & Oliver Schulte, Church's Thesis and Hume's Problem.
    We argue that uncomputability and classical scepticism are both reflections of inductive underdetermination, so that Church's thesis and Hume's problem ought to receive equal emphasis in a balanced approach to the philosophy of induction. As an illustration of such an approach, we investigate how uncomputable the predictions of a hypothesis can be if the hypothesis is to be reliably investigated by a computable scientific method.
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  18. Kevin T. Kelly, Oliver Schulte & Vincent Hendricks, Reliable Belief Revision.
    Philosophical logicians proposing theories of rational belief revision have had little to say about whether their proposals assist or impede the agent's ability to reliably arrive at the truth as his beliefs change through time. On the other hand, reliability is the central concern of formal learning theory. In this paper we investigate the belief revision theory of Alchourron, Gardenfors and Makinson from a learning theoretic point of view.
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  19. Kevin T. Kelly, Oliver Schulte & Cory Juhl (1997). Learning Theory and the Philosophy of Science. Philosophy of Science 64 (2):245-267.
    This paper places formal learning theory in a broader philosophical context and provides a glimpse of what the philosophy of induction looks like from a learning-theoretic point of view. Formal learning theory is compared with other standard approaches to the philosophy of induction. Thereafter, we present some results and examples indicating its unique character and philosophical interest, with special attention to its unified perspective on inductive uncertainty and uncomputability.
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  20. Cristina Bicchieri & Oliver Schulte (1996). Common Reasoning About Admissibility. Erkenntnis 45 (2-3):299 - 325.
    We analyze common reasoning about admissibility in the strategic and extensive form of a game. We define a notion of sequential proper admissibility in the extensive form, and show that, in finite extensive games with perfect recall, the strategies that are consistent with common reasoning about sequential proper admissibility in the extensive form are exactly those that are consistent with common reasoning about admissibility in the strategic form representation of the game. Thus in such games the solution given by common (...)
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  21. Oliver Schulte (1996). Common Reasoning About Admissibility. Erkenntnis 45 (2/3):299 - 325.
    We analyze common reasoning about admissibility in the strategic and extensive form of a game. We define a notion of sequential proper admissibility in the extensive form, and show that, in finite extensive games with perfect recall, the strategies that are consistent with common reasoning about sequential proper admissibility in the extensive form are exactly those that are consistent with common reasoning about admissibility in the strategic form representation of the game. Thus in such games the solution given by common (...)
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  22. Kevin T. Kelly & Oliver Schulte (1995). The Computable Testability of Theories Making Uncomputable Predictions. Erkenntnis 43 (1):29 - 66.
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