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The study of scientific discovery—where do new ideas come from?—has long been denigrated by philosophers as irrelevant to analyzing the growth of scientific knowledge. In particular, little is known about how cognitive theories are discovered, and neither the classical accounts of discovery as either probabilistic induction (e.g., Reichenbach, 1938) or lucky guesses (e.g., Popper, 1959), nor the stock anecdotes about sudden “eureka ” moments deepen the insight into discovery. A heuristics approach is taken in this review, where heuristics are understood as strategies of discovery less general than a supposed unique logic of discovery but more general than lucky guesses. This article deals with how scientists’ tools shape theories of mind, in particular with how methods of statistical inference have turned into metaphors of mind. The tools-to-theories heuristic explains the emergence of a broad range of cognitive theories, from the cognitive revolution of the 1960s up to the present, and it can be used to detect both limitations and new lines of development in current cognitive theories that investigate the mind as an “intuitive statistician.” Scientific inquiry can be viewed as “an ocean, continuous everywhere and without a break or division ” (Leibniz, 1690/1951, p. 73). Hans Reichenbach (1938) nonetheless divided this ocean into two great seas, the context of discovery and the context of justification. Philosophers, logicians,

Findings in recent research on the `conjunction fallacy ' have been taken as evidence that our minds are not designed to work by the rules of probability. This conclusion springs from the idea that norms should be content-blind Ð in the present case, the assumption that sound reasoning requires following the conjunction rule of probability theory. But content-blind norms overlook some of the intelligent ways in which humans deal with uncertainty, for instance, when drawing semantic and pragmatic inferences. In a series of studies, we ®rst show that people infer nonmathematical meanings of the polysemous term `probability' in the classic Linda conjunction problem. We then demonstrate that one can design contexts in which people infer mathematical meanings of the term and are therefore more likely to conform to the conjunction rule. Finally, we report evidence that the term `frequency ' narrows the spectrum of possible interpretations of `probability ' down to its mathematical meanings, and that this fact Ð rather than the presence or absence of `extensional cues ' Ð accounts for the low proportion of violations of the conjunction rule when people are asked for

The principle of maximumentropy is a general method to assign values to probability distributions on the basis of partial information. This principle, introduced by Jaynes in 1957, forms an extension of the classical principle of insufficient reason. It has been further generalized, both in mathematical formulation and in intended scope, into the principle of maximum relative entropy or of minimum information. It has been claimed that these principles are singled out as unique methods of statistical inference that agree with certain compelling consistency requirements. This paper reviews these consistency arguments and the surrounding controversy. It is shown that the uniqueness proofs are flawed, or rest on unreasonably strong assumptions. A more general class of 1 inference rules, maximizing the so-called R'enyi entropies, is exhibited which also fulfill the reasonable part of the consistency assumptions. 1 Introduction In any application of probability theory to the pro...

Function tags are a context-sensitive annotation applied to words and phrases of natural language text, marking their syntactic or semantic role within a larger utterance. As researchers improve results on various other problems in pure natural language processing (e.g part-of-speech tagging, parsing), those who work in the more applied NLP elds (e.g. question-answering, temporal analysis) are seeking more powerful sorts of linguistic annotation as input for their own systems. Hence, function tags. In the rst part of the thesis, I present the problem of function tagging: why it is an interesting problem, who has worked on similar thing, and what exactly I intend to do. I brie y review the function tags of the Penn treebank, and explain the speci c metrics by which I will evaluate my work. In the second part of the thesis, I introduce the many features that I will use to train a function tagging system, and then I present some systems that make use of them: one using feature trees, one using decision trees (brie y), and one using perceptron models. For each system, I give a brief historical perspective, an

The development of techniques for autonomous navigation in real-world environments constitutes one of the major trends in the current research on robotics. An important problem in autonomous navigation is the need to cope with the large amount of uncertainty that is inherent of natural environments. Fuzzy logic has features that make it an adequate tool to address this problem. In this paper, we review some of the possible uses of fuzzy logic in the field of autonomous navigation. We focus on four issues: how to design robust behaviorproducing modules; how to coordinate the activity of several such modules; how to use data from the sensors; and how to integrate high-level reasoning and low-level execution. For each issue, we review some of the proposals in the literature, and discuss the pros and cons of fuzzy logic solutions.

Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for first-order sentences. Given first-order sentences ' and `, we consider the structures with domain f1; : : : ; Ng that satisfy `, and compute the fraction of them in which ' is true. We then consider what happens to this fraction as N gets large. This extends the work on 0-1 laws that considers the limiting probability of first-order sentences, by considering asymptotic conditional probabilities. As shown by Liogon'kii[31] and Grove, Halpern, and Koller [22], in the general case, asymptotic conditional probabilities do not always exist, and most questions relating to this issue are highly undecidable. These results, however, all depend on the assumption that ` can use a nonunary predicate symbol. Liogon'kii [31] shows that if we condition on formulas ` involving unary predicate symbols only (but no equality or constant symbols), then the asymptotic conditional probability does exist and can be effectively computed. This is the case even if we place no corresponding restrictions on '. We extend this result here to the case where ` involves equality and constants. We show that the complexity of computing the limit depends on various factors, such as the depth of quantifier nesting, or whether the vocabulary is finite or infinite. We completely characterize the complexity of the problem in the different cases, and show related results for the associated approximation problem.

Introduction This tutorial provides a very brief introduction to the formulation, tting, and checking of hierarchical or multilevel models from the Bayesian point of view. Hierarchical models (HMs) arise frequently in ve main kinds of applications: 1 HMs are common in elds such as health and education, in which data|both outcomes and predictors|are often gathered in a nested or hierarchical fashion, e.g., patients within hospitals, or students within classrooms within schools. HMs are thus also ideally suited to the wide range of applications in government and business in which single- or multi-stage cluster samples are routinely drawn, and oer a unied approach to the analysis of random-eects (variance-components) and mixed models. 2 Introduction (continued) 2 A dierent kind

Causal reasoning can be understood qualitatively in terms of explanatory coherence or quantitatively in terms of probability theory. Comparison of these approaches can be done by looking at computational models, using my explanatory coherence networks and Pearl’s probabilistic ones. The explanatory coherence program ECHO can be given a probabilistic interpretation, but there are many conceptual and computational problems that make it difficult to replace coherence networks by probabilistic ones. On the other hand, ECHO provides a psychologically plausible and computationally efficient model of some kinds of probabilistic causal reasoning. Hence coherence theory need not give way to probability theory as the basis for epistemology and decision making.

A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization.