This book is a revised version of my dissertation 'DiaLaw - on legal th justification and dialog games' that I defended on June 5 1998 at the Universiteit Maastricht. The chapters 1, 4 & 5 (now: 1, 5 & 6) of my dissertation have remained largely unaltered. In chapter 2 I added explicitly the distinction between constructing legal justification and reconstructing it, and tried to elucidate the differences (and similarities) between the product and process of justification. Chapter 3 is divided into two chapters: one on the general characteristics of DiaLaw (now: chapter 3), and the other on...

Simplicity theory is an extension of stability theory to a wider class of structures, containing, among others, the random graph, pseudo-finite fields, and fields with a generic automorphism. Following Kim's proof of forking symmetry' which implies a good behaviour of model-theoretic independence, this area of model theory has been a field of intense study. It has necessitated the development of some important new tools, most notably the model-theoretic treatment of hyperimaginaries (classes modulo type-definable equivalence relations). It thus provides a general notion of independence (and...

Functional Equations andInequalities provides an extensive studyofsome of the most important topics of current interest in functional equations and inequalities. Subjects dealt with include: a Pythagorean functional equation, a functional definition oftrigonometric functions, the functional equation ofthe square root spiral, a conditional Cauchy functional equation, an iterative functional equation, the Hille-type functional equation, the polynomial-like iterative functional equation, distribution ofzeros and inequalities for zeros of algebraic polynomials, a qualitative study ofLobachevsky's...

Projective geometry is a very classical part of mathematics and one might think that the subject is completely explored and that there is nothing new to be added. But it seems that there exists no book on projective geometry which provides a systematic treatment of morphisms. We intend to fill this gap. It is in this sense that the present monograph can be called modern. The reason why morphisms have not been studied much earlier is probably the fact that they are in general partial maps between the point sets G and G, noted ' 9: G -- G', i.e. maps 9: D -4 G' whose domain Dom 9: = D is a...

Nevanlinna theory (or value distribution theory) in complex analysis is so beautiful that one would naturally be interested in determining how such a theory would look in the non Archimedean analysis and Diophantine approximations. There are two "main theorems" and defect relations that occupy a central place in N evanlinna theory. They generate a lot of applications in studying uniqueness of meromorphic functions, global solutions of differential equations, dynamics, and so on. In this book, we will introduce non-Archimedean analogues of Nevanlinna theory and its applications. In value...

The first formulations of linear boundary value problems for analytic functions were due to Riemann (1857). In particular, such problems exhibit as boundary conditions relations among values of the unknown analytic functions which have to be evaluated at different points of the boundary. Singular integral equations with a shift are connected with such boundary value problems in a natural way. Subsequent to Riemann's work, D. Hilbert (1905), C. Haseman (1907) and T. Carleman (1932) also considered problems of this type. About 50 years ago, Soviet mathematicians began a systematic study of...

Finsler geometry is the most natural generalization of Riemannian geo metry. It started in 1918 when P. Finsler 1] wrote his thesis on curves and surfaces in what he called generalized metric spaces. Studying the geometry of those spaces (which where named Finsler spaces or Finsler manifolds) became an area of active research. Many important results on the subject have been brought together in several monographs (cf., H. Rund 3], G. Asanov 1], M. Matsumoto 6], A. Bejancu 8], P. L. Antonelli, R. S. Ingar den and M. Matsumoto 1], M. Abate and G. Patrizio 1] and R. Miron 3]) . However,...

'0 {oc; paxuc;, O 't XVll a1(pft (Hippokrates) That life is short needs no proof when we are engaged in ambitious projects. When I began this book, almost forty years ago, I did not forsee that its completion would take such a long time, although I was well aware that some of Hegel's texts stubbornly resist a thorough deciphering of their meaning and argumenta tion. Having written a dissertation on the young Hegel's moral, political, and religious philosophy (Lejeune Hegel et la vision morale du monde, 1960'), I was asked to teach ethics, social philosophy, and philosophy of law at various...

Gauss diagram invariants are isotopy invariants of oriented knots in- manifolds which are the product of a (not necessarily orientable) surface with an oriented line. The invariants are defined in a combinatorial way using knot diagrams, and they take values in free abelian groups generated by the first homology group of the surface or by the set of free homotopy classes of loops in the surface. There are three main results: 1. The construction of invariants of finite type for arbitrary knots in non orientable 3-manifolds. These invariants can distinguish homotopic knots with homeomorphic...

Fixed point theory in probabilistic metric spaces can be considered as a part of Probabilistic Analysis, which is a very dynamic area of mathematical research. A primary aim of this monograph is to stimulate interest among scientists and students in this fascinating field. The text is self-contained for a reader with a modest knowledge of the metric fixed point theory.
Several themes run through this book. The first is the theory of triangular norms (t-norms), which is closely related to fixed point theory in probabilistic metric spaces. Its recent development has had a strong influence...