The book was planned and written as a single, sustained argument. But earlier versions of a few parts of it have appeared separately. The object of this book is both to establish the existence of the paradoxes, and also to describe a non-Pascalian concept of probability in terms of which one can analyse the structure of forensic proof without giving rise to such typical signs of theoretical misfit. Neither the complementational principle for negation nor the multiplicative principle for conjunction applies (...) to the central core of any forensic proof in the Anglo-American legal system. There are four parts included in this book. Accordingly, these parts have been written in such a way that they may be read in different orders by different kinds of reader. (shrink)

The purpose of this paper is to improve on the logical and measure-theoretic foundations for the notion of probability in the law of evidence, which were given in my contributions Åqvist [ (1990) Logical analysis of epistemic modality: an explication of the Bolding–Ekelöf degrees of evidential strength. In: Klami HT (ed) Rätt och Sanning (Law and Truth. A symposium on legal proof-theory in Uppsala May 1989). Iustus Förlag, Uppsala, pp 43–54; (1992) Towards a logical theory of legal evidence: semantic analysis (...) of the Bolding–Ekelöf degrees of evidential strength. In: Martino AA (ed) Expert systems in law. Elsevier Science Publishers BV, Amsterdam, North-Holland, pp 67–86]. The present approach agrees with the one adopted in those contributions in taking its main task to be that of providing a semantic analysis, or explication, of the so called Bolding–Ekelöf degrees of evidential strength (“proof-strength”) as applied to the establishment of matters of fact in law-courts. However, it differs from the one advocated in our earlier work on the subject in explicitly appealing to what is known as “Pro-et-Contra Argumentation”, after the famous Norwegian philosopher Arne Naess. It tries to bring out the logical form of that interesting kind of reasoning, at least in the context of the law of evidence. The formal techniques used here will be seen to be largely inspired by the important work done by Patrick Suppes, notably Suppes [(1957) Introduction to logic. van Nostrand, Princeton and (1972) Finite equal-interval measurement structures. Theoria 38:45–63]. (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)

Gives the first published adaptation of the Lindenbaum/Henkin method of maximal consistent sets for establishing the completeness of modal propositional logics with respect to the relational models of Kripke.

We consider an infinite hierarchy of systems of Alethic Modal Logic with so-called Levels of Perfection, and add to them suitable definitions of such interesting deontic categories as those of supererogation, offence, conditional obligation and conditional permission. We then state three problems concerning the proper characterization of the resulting logic(s) for our defined notions, and discuss two of these problems in some detail.