This book examines three areas in which abductive reasoning is especially important: medicine, science, and law. The reader is introduced to abduction and shown how it has evolved historically into the framework of conventional wisdom in logic. Discussions draw upon recent techniques used in artificial intelligence, particularly in the areas of multi-agent systems and plan recognition, to develop a dialogue model of explanation. Cases of causal explanations in law are analyzed using abductive reasoning, and all the components are finally brought (...) together to build a new account of abductive reasoning. By clarifying the notion of abduction as a common and significant type of reasoning in everyday argumentation, _Abductive Reasoning_ will be useful to scholars and students in many fields, including argumentation, computing and artificial intelligence, psychology and cognitive science, law, philosophy, linguistics, and speech communication and rhetoric. (shrink)

Vagueness is epistemic, according to some. Vagueness is ontological, according to others. This article deploys what I take to be a compromise position. Predicates are coined in specific contexts for specific purposes, but these limited practices do not automatically fix the extensions of predicates over the domain of all objects. The linguistic community using the predicate has rarely considered, much less decided, all questions that might arise about the predicate’s extension. To this extent, the ontological view is correct. But a (...) predicate that applies in some contexts can be reasonably extended to other contexts where it is initially vague. This process of development approximates the cognitive remedy for vagueness that the epistemic view prescribes. The process is piecemeal and inductive, akin to what von Wright described as the molding of concepts. Vagueness cannot be understood apart from the backdrop of classification, for vagueness is classification gone awry. Hence these pages explore the classification of particulars, both its clear successes and vague failures. How we classify unique particulars is the theme of Sections 2 and 3, which are primarily descriptive. Section 2 identifies a way of classifying particulars that pervades discourse of all sorts, and Section 3 illustrates its use in a field notorious for vagueness: ethics. Why a certain particular should (or should not) be classified in a certain way is a normative question, however, and it occupies Sections 4 and 5. Section 4 proposes a norm for strong arguments by analogy, and Section 5 illustrates how the norm might resolve vagueness in one kind of ethical dispute. This norm, which has a strong probabilistic component, is one way of affirming that probability is a guide to life. (shrink)

The focus of this study is cognitive choice: the selection of one cognitive option (a hypothesis, a theory, or an axiom, for instance) rather than another. The study proposes that cognitive choice should be based on the plausibilities of states posited by rival cognitive options and the utilities of these options' information outcomes. The proposal introduces a form of decision theory that is novel because comparative; it permits many choices among cognitive options to be based on merely comparative plausibilities and (...) utilities. This form of decision theory intersects with recommendations by advocates of decision theory for cognitive choice, on the one hand, and defenders of comparative evaluation of scientific hypotheses and theories, on the other. But it differs from prior decision-theoretic proposals because it requires no more than minimal precision in specifying plausibilities and utilities. And it differs from comparative proposals because none has shown how comparative evaluations can be carried out within a decision-theoretic framework. (shrink)

Current practice in logic increasingly accords recognition to abductive, presumptive or plausible arguments, in addition to deductive and inductive arguments. But there is uncertainty about what these terms exactly mean, what the differences between them are (if any), and how they relate. By examining some analyses ofthese terms and some of the history of the subject (including the views of Peirce and Cameades), this paper sets out considerations leading to a set of definitions, discusses the relationship of these three forms (...) of argument to argumentation schemes and sets out a new argumentation scheme for abductive argument. (shrink)

In their unifying theory to model uncertainty, Friedman and Halpern (1995–2003) applied plausibility measures to default reasoning satisfying certain sets of axioms. They proposed a distinctive condition for plausibility measures that characterizes “qualitative” reasoning (as contrasted with probabilistic reasoning). A similar and similarly fundamental, but more general and thus stronger condition was independently suggested in the context of “basic” entrenchment-based belief revision by Rott (1996–2003). The present paper analyzes the relation between the two approaches to formalizing basic notions of plausibility (...) as used in qualitative default reasoning. While neither approach is a special case of the other, translations can be found that elucidate their relationship. I argue that Rott’s notion of plausibility allows for a more modular set-up and has a better philosophical motivation than that of Friedman and Halpern. (shrink)

In contrast to other prominent models of belief change, models based on epistemic entrenchment have up to now been applicable only in the context of very strong packages of requirements for belief revision. This paper decomposes the axiomatization of entrenchment into independent modules. Among other things it is shown how belief revision satisfying only the 'basic' postulates of Alchourrón, Gärdenfors and Makinson can be represented in terms of entrenchment.

Using formal systems to represent and reason about uncertainty.

I use a version of the case in "sophie's choice" as an example of the strongest sort of dilemma, With all options seriously wrong, And no permissible way of choosing one of them. This is worse, I argue, Than a choice between conflicting obligations, Where the agent has an overriding obligation "to choose", And does nothing wrong, Once the choice is made, By ignoring one of his prior obligations. Here, "contra" marcus, Guilt seems inappropriate.

We propose a generalization of expected utility that we call generalized EU (GEU), where a decision maker’s beliefs are represented by plausibility measures and the decision maker’s tastes are represented by general (i.e., not necessarily real-valued) utility functions. We show that every agent, “rational” or not, can be modeled as a GEU maximizer. We then show that we can customize GEU by selectively imposing just the constraints we want. In particular, we show how each of Savage’s postulates corresponds to constraints (...) on GEU. (shrink)

Who is right? In Risk and Rationality, Kristin Shrader-Frechette argues that neither charges of irresponsible endangerment nor countercharges of scientific illiteracy frame the issues properly.

This volume recreates the received notion of reflective equilibrium. It reconfigures reflective equilibrium as both a cognitive ideal and a method for approximating this ideal. The ideal of reflective equilibrium is restructured using the concept of discursive strata, which are formed by sentences and differentiated by function. Sentences that perform the same kind of linguistic function constitute a stratum. The book shows how moral discourse can be analyzed into phenomenal, instrumental, and teleological strata, and the ideal of reflective equilibrium reworked (...) in these terms. In addition, the work strengthens the method of reflective equilibrium by harnessing the resources of decision theory and inductive logic. It launches a comparative version of decision theory and employs this framework as a guide to moral theory choice. It also recruits quantitative inductive logic to inform a standard of inductive cogency. When used in tandem with comparative decision theory, this standard can aid in the effort to turn the undesirable condition of reflective disequilibrium into reflective equilibrium. (shrink)

Legal scholarship exploring the nature of evidence and the process of juridical proof has had a complex relationship with formal modeling. As evident in so many fields of knowledge, algorithmic approaches to evidence have the theoretical potential to increase the accuracy of fact finding, a tremendously important goal of the legal system. The hope that knowledge could be formalized within the evidentiary realm generated a spate of articles attempting to put probability theory to this purpose. This literature was both insightful (...) and frustrating. Much light was shed on the legal system, but it also quickly became evident that the tools of probability theory were in many ways ill-constructed for the task. Fundamental incompatibilities between the structure of legal decision making and the extant formal tools were identified, and it became evident that many of the purported explanations of legal phenomena were internally inconsistent. As a consequence, interest in this type of formal modeling declined, and attention was directed toward different kinds of explanations of the phenomena. Perhaps under the influence of a recent trend toward various types of formal modeling in legal scholarship, a recent burst of articles, rather than attempting to explain the macro structure of trials, which was the previous object of interest, attempts to quantify the probative value of various items of evidence in ways consistent with the formal features of various probability theories, and then to study decision making from that perspective. For example, the value of evidence is often purported to be its likelihood ratio, that is, the probability of discovering or receiving the evidence given a hypothesis (e.g., the defendant did it) divided by the probability of discovering or receiving the evidence given the negation of the hypothesis (the defendant didn't do it). Alternatively, the value of evidence is purported (more contextually) to be the information gain it provides, defined as the increase in probability it provides for a hypothesis above the probability of the hypothesis based on the other available evidence. Both conceptions then assume that all of the various probability assessments conform or ought to conform to the dictates of Bayes' theorem (that maintains consistency among such assessments); empirical studies are then done testing the extent to which this is so and proposing how the law can increase the probability that it is so. The general criticisms of using Bayes' theorem as a formal model of juridical proof are well known and were integral to the last wave of interest in formal modeling of the evidentiary process. This paper thus for the most part puts aside that more general issue, and focuses specifically on mathematical modeling of the value of particular items of evidence. The paper demonstrates that formal modeling has only limited value in explaining the value of legal evidence, much more limited than those constructing and discussing the models assume, and thus that the conclusions they draw about the value of evidence are unwarranted. This is done through a discussion of four recent examples that attempt to quantify evidence relating to, respectively, carpet fibers, infidelity, DNA random-match evidence, and character evidence used to impeach a witness. This article thus makes two contributions. First, and most importantly, it is another demonstration of the complex relationship between algorithmic tools and legal decision making. Second, at a minimum it points out serious pitfalls for analytical or empirical studies of juridical proof. (shrink)

Some decisions result in cognitive consequences such as information gained and information lost. The focus of this study, however, is decisions with consequences that are partly or completely noncognitive. These decisions are typically referred to as ‘real-life decisions’. According to a common complaint, the challenges of real-life decision making cannot be met by decision theory. This complaint has at least two principal motives. One is the maximizing objection that to require agents to determine the optimal act under real-world constraints is (...) unrealistic. The other is the precision objection that the numeric requirements for applying decision theory are overly demanding for real-life decisions. Responses to both objections are aired in the History section of this chapter. The maximizing objection is addressed with reference to work by Weirich and Pollock, while the precision objection is countered via a proposal by Kyburg and another by Gärdenfors and Sahlin. However, the Current Research section urges a different response to the precision objection by introducing a comparative version of decision theory. Drawing on Chu and Halpern’s notion of generalized expected utility, this version of decision theory permits many choices to be based on merely comparative plausibilities and utilities. Finally, the Further Research section undertakes an open-ended exploration of three of the assumptions upon which this form of decision theory (and many others) is based: transitivity, independence, and plausibilistic decision rules. (shrink)