
16Causal Learning with Occam’s RazorStudia Logica 107 (5): 9911023. 2019.Occam’s razor directs us to adopt the simplest hypothesis consistent with the evidence. Learning theory provides a precise definition of the inductive simplicity of a hypothesis for a given learning problem. This definition specifies a learning method that implements an inductive version of Occam’s razor. As a case study, we apply Occam’s inductive razor to causal learning. We consider two causal learning problems: learning a causal graph structure that presents global causal connections among a…Read more

10Eric Martin and Daniel Osherson, Elements of Scientific Inquiry. Cambridge, MA: Bradford, MIT Press, 1998, cloth £23.95. ISBN: 0 262 13342 3British Journal for the Philosophy of Science 51 (2): 347352. 2000.

60Meansends epistemologyBritish Journal for the Philosophy of Science 50 (1): 131. 1999.This paper describes the cornerstones of a meansends approach to the philosophy of inductive inference. I begin with a fallibilist ideal of convergence to the truth in the long run, or in the 'limit of inquiry'. I determine which methods are optimal for attaining additional epistemic aims (notably fast and steady convergence to the truth). Meansends vindications of (a version of) Occam's Razor and the natural generalizations in a Goodmanian Riddle of Induction illustrate the power of this app…Read more

From one perspective, the fundamental notions of pointset 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 …Read more

Sequential von Neumann–Morgernstern (VM) games are a very general formalism for representing multiagent 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 gametheoretic reasoning and solution concepts such as Nash equilibrium. We discuss the application of various conce…Read more

56Minimal belief change and the pareto principleSynthese 118 (3): 329361. 1999.This paper analyzes the notion of a minimal belief change that incorporates new information. I apply the fundamental decisiontheoretic principle of Paretooptimality 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 Paretominimal revisions of theori…Read more

17The codiscovery of conservation laws and particle familiesStudies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (2): 288314. 2008.

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 consi…Read more

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 to b, then it is common belief that all other agen…Read more

73The codiscovery of conservation laws and particle familiesStudies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (2): 288314. 2008.

This paper analyzes the notion of a minimal belief change that incorporates new information. I apply the fundamental decisiontheoretic principle of Paretooptimality 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 Paretominimal revisions of theories, …Read more

The situation calculus is a logical formalism that has been extensively developed for planning. We apply the formalism in a complex multiagent 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.

66Review. Elements of scientific inquiry. E Martin, D OshersonBritish Journal for the Philosophy of Science 51 (2): 347352. 2000.

164Inferring conservation laws in particle physics: A case study in the problem of inductionBritish Journal for the Philosophy of Science 51 (4): 771806. 2000.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 precisel…Read more

43The logic of reliable and efficient inquiryJournal of Philosophical Logic 28 (4): 399438. 1999.This paper pursues a thoroughgoing instrumentalist, or meansends, 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 pr…Read more

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 nece…Read more

51Formal learning theoryStanford Encyclopedia of Philosophy. 2008.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.

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 or b. Respect for public preferences requir…Read more

Logically reliable inductive inferenceIn Michele Friend, Norma B. Goethe & Valentina Harizanov (eds.), Induction, algorithmic learning theory, and philosophy, Springer. pp. 157178. 2007.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.

78Discussion. What to believe and what to take seriously: A reply to David chart concerning the Riddle of inductionBritish Journal for the Philosophy of Science 51 (1): 151153. 2000.In his commentary on my paper, “MeansEnds Epistemology”, David Chart constructs a Riddle of Induction with the following feature: Meansends analysis, as I formulated it in the paper, selects “all emeralds are grue” as the optimal conjecture after observing a sample of all green emeralds. Chart’s construction is rigorous and correct. If we disagree, it is in the philosophical morals to be drawn from his example. Such morals are best discussed by elucidating some of the larger epistemological is…Read more

25We 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

26Philosophical 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

67Learning theory and the philosophy of sciencePhilosophy of Science 64 (2): 245267. 1997.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 learningtheoretic 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