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An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models. |
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The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability. |
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We must restrict to mere probability not only statements of comparatively great uncertainty, like predictions about the weather, where we would cautiously ... |
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The Concept of Law is the most important and original work of legal philosophy written this century. First published in 1961, it is considered the masterpiece of H.L.A. Hart's enormous contribution to the study of jurisprudence and legal philosophy. Its elegant language and balanced arguments have sparked wide debate and unprecedented growth in the quantity and quality of scholarship in this area--much of it devoted to attacking or defending Hart's theories. Principal among Hart's critics is renowned lawyer and political philosopher (...) |
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No mathematical background is necessary to appreciate this classic of probability theory, which remains unsurpassed in its clarity, readability, and sheer charm. Its author, British logician John Venn (1834-1923), popularized the famous Venn Diagrams that are commonly used in teaching elementary mathematics. |
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Suitable for students and scholars, this title challenges the assumption that skepticism, rather than established belief, lies at the heart of scientific discovery. |
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In this paper, it is shown (1) that there are two schemes for argument from analogy that seem to be competitors but are not, (2) how one of them is based on a distinctive type of similarity premise, (3) how to analyze the notion of similarity using story schemes illustrated by some cases, (4) how arguments from precedent are based on arguments from analogy, and in many instances arguments from classification, and (5) that when similarity is defined by means of (...) |
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This paper presents a formal reconstruction of a Dutch civil legal case in Prakken’s formal model of adjudication dialogues. The object of formalisation is the argumentative speech acts exchanged during the dispute by the adversaries and the judge. The goal of this formalisation is twofold: to test whether AI & law models of legal dialogues in general, and Prakken’s model in particular, are suitable for modelling particular legal procedures; and to learn about the process of formalising an actual legal dispute. |
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Counterfactuals is David Lewis' forceful presentation of and sustained argument for a particular view about propositions which express contrary to fact conditionals, including his famous defense of realism about possible worlds and his theory of laws of nature. |
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The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference (...) |
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Much of the philosophical literature on causation has focused on the concept of actual causation, sometimes called token causation. In particular, it is this notion of actual causation that many philosophical theories of causation have attempted to capture.2 In this paper, we address the question: what purpose does this concept serve? As we shall see in the next section, one does not need this concept for purposes of prediction or rational deliberation. What then could the purpose be? We will argue (...) |
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Bruce Waller has defended a deductive reconstruction of the kinds of analogical arguments found in ethics, law, and metaphysics. This paper demonstrates the limits of such a reconstruction and argues for an alternative. non-deductive reconstruction. It will be shown that some analogical arguments do not fit Waller's deductive schema, and that such a schema does not allow for an adequate account of the strengths and weaknesses of an analogical argument. The similarities and differences between the account defended herein and the (...) |
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The logical interpretation of probability, or "objective Bayesianism'' – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a "principle of insufficient reason" inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; that it (...) |
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ON DECEMBER 10, 1991 Charles Shonubi, a Nigerian citizen but a resident of the USA, was arrested at John F. Kennedy International Airport for the importation of heroin into the United States.1 Shonubi's modus operandi was ``balloon swallowing.'' That is, heroin was mixed with another substance to form a paste and this paste was sealed in balloons which were then swallowed. The idea was that once the illegal substance was safely inside the USA, the smuggler would pass the balloons and (...) |
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H. L. A. Hart and the "Open Texture" of Language tries to clarify the writings of both Hart and Friedrich Waismann on "open texture". In Waismann's work, "open texture" referred to the potential vagueness of words under extreme (hypothetical) circumstances. Hart's use of the term was quite different, and his work has been misunderstood because those differences were underestimated. Hart should not be read as basing his argument for judicial discretion on the nature of language; primarily, he was putting forward (...) |
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Modelling reasoning with legal cases has been a central concern of AI and Law since the 1980s. The approach which represents cases as factors and dimensions has been a central part of that work. In this paper I consider how several varieties of the approach can be applied to the interesting case of Popov v Hayashi. After briefly reviewing some of the key landmarks of the approach, the case is represented in terms of factors and dimensions, and further explored using (...) |
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A Critique of Artificial Reason Hubert L. Dreyfus . HUBERT L. DREYFUS What Computers Still Can't Do Thi s One XZKQ-GSY-8KDG What. WHAT COMPUTERS STILL CAN'T DO Front Cover. |
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A detailed treatment regarding the diverse properties and uses of evidence and the judgmental tasks they entail. Examines various processes by which evidence may be developed or discovered. Considers the construction of arguments made in defense of the relevance and credibility of individual items and masses of evidence as well as the task of assessing the inferential force of evidence. Includes over 100 numerical examples to illustrate the workings of diverse probabilistic expressions for the inferential force of evidence and the (...) |
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In What Science Knows, the Australian philosopher and mathematician James Franklin explains in captivating and straightforward prose how science works its magic. It offers a semipopular introduction to an objective Bayesian/logical probabilist account of scientific reasoning, arguing that inductive reasoning is logically justified (though actually existing science sometimes falls short). Its account of mathematics is Aristotelian realist. |
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Degrees of belief; Dempster's rule of combination; Simple and separable support functions; The weights of evidence; Compatible frames of discernment; Support functions; The discernment of evidence; Quasi support functions; Consonance; Statistical evidence; The dual nature of probable reasoning. |
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How were reliable predictions made before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? The book examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. Also included are the problem of induction before Hume, design arguments for (...) |
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Causal theories of mental content attempt to explain how thoughts can be about things. They attempt to explain how one can think about, for example, dogs. These theories begin with the idea that there are mental representations and that thoughts are meaningful in virtue of a causal connection between a mental representation and some part of the world that is represented. In other words, the point of departure for these theories is that thoughts of dogs are about dogs because dogs (...) |
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There has been much discussion recently about the scope and limits of purely symbolic models of the mind and about the proper role of connectionism in cognitive modeling. This paper describes the symbol grounding problem : How can the semantic interpretation of a formal symbol system be made intrinsic to the system, rather than just parasitic on the meanings in our heads? How can the meanings of the meaningless symbol tokens, manipulated solely on the basis of their shapes, be grounded (...) |
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It has long been known that people’s causal judgments can have an impact on their moral judgments. To take a simple example, if people conclude that a behavior caused the death of ten innocent children, they will therefore be inclined to regard the behavior itself as morally wrong. So far, none of this should come as any surprise. But recent experimental work points to the existence of a second, and more surprising, aspect of the relationship between causal judgment and moral (...) |
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This article reviews eight proposed strategies for solving the Symbol Grounding Problem (SGP), which was given its classic formulation in Harnad (1990). After a concise introduction, we provide an analysis of the requirement that must be satisfied by any hypothesis seeking to solve the SGP, the zero semantical commitment condition. We then use it to assess the eight strategies, which are organised into three main approaches: representationalism, semi-representationalism and non-representationalism. The conclusion is that all the strategies are semantically committed and (...) |
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Probabilistic inference from frequencies, such as "Most Quakers are pacifists; Nixon is a Quaker, so probably Nixon is a pacifist" suffer from the problem that an individual is typically a member of many "reference classes" (such as Quakers, Republicans, Californians, etc) in which the frequency of the target attribute varies. How to choose the best class or combine the information? The article argues that the problem can be solved by the feature selection methods used in contemporary Big Data science: the (...) |
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There has been a long history of discussion on the usefulness of formal methods in legal settings.1 Some of the recent debate has focussed on foundational issues in statistics, in particular, how the reference-class problem affects legal decisions based on certain types of statistical evidence.2 Here we examine aspects of this debate, stressing why the reference-class problem presents serious difficulties for the kinds of statistical inferences under consideration and the relevance of this for the use of statistics in the courtroom. (...) |
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To move beyond vague platitudes about the importance of context in legal reasoning or natural language understanding, one must take account of ideas from artificial intelligence on how to represent context formally. Work on topics like prior probabilities, the theory-ladenness of observation, encyclopedic knowledge for disambiguation in language translation and pathology test diagnosis has produced a body of knowledge on how to represent context in artificial intelligence applications. |
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Received by the IRE, October 24, 1960. The author's work summarized here—which was done at the MIT Lincoln Laboratory, a center for research operated by MIT at Lexington, Mass., with the joint Support of the U. S. Army, Navy, and Air Force under Air Force Contract AF 19-5200; and at the Res. Lab. of Electronics, MIT, Cambridge, Mass., which is supported in part by the U. S. Army Signal Corps, the Air Force Office of Scientific Research, and the ONR—is based (...) |
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