Gaussian scale-space is one of the best understood multi-resolution techniques available to the computer vision and image analysis community. It is the purpose of this book to guide the reader through some of its main aspects. During an intensive weekend in May 1996 a workshop on Gaussian scale-space theory was held in Copenhagen, which was attended by many of the leading experts in the field. The bulk of this book originates from this workshop. Presently there exist only two books on the subject. In contrast to Lindeberg's monograph (Lindeberg, 1994e) this book collects contributions from...

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named fuzzy inference' can be naturally understood as logical deduction.
There are two main groups of intended readers. First, logicians: they can see that fuzzy logic is indeed a branch of...

Proof theory and category theory were first drawn together by Lambek some 30 years ago but, until now, the most fundamental notions of category theory (as opposed to their embodiments in logic) have not been explained systematically in terms of proof theory. Here it is shown that these notions, in particular the notion of adjunction, can be formulated in such as way as to be characterised by composition elimination. Among the benefits of these composition-free formulations are syntactical and simple model-theoretical, geometrical decision procedures for the commuting of diagrams of arrows....

The aim of this book is to give self-contained proofs of all basic results concerning the infinite-valued proposition al calculus of Lukasiewicz and its algebras, Chang's MV -algebras. This book is for self-study: with the possible exception of Chapter 9 on advanced topics, the only prere quisite for the reader is some acquaintance with classical propositional logic, and elementary algebra and topology. In this book it is not our aim to give an account of Lukasiewicz's motivations for adding new truth values: readers interested in this topic will find appropriate references in Chapter 10....

The history of triangular norms started with the paper "Statistical metrics" Menger 1942]. The main idea of Karl Menger was to construct metric spaces where probability distributions rather than numbers are used in order to de- scribe the distance between two elements of the space in question. Triangular norms (t-norms for short) naturally came into the picture in the course of the generalization of the classical triangle inequality to this more general set- ting. The original set of axioms for t-norms was considerably weaker, including among others also the functions which are known today...

This is this, this ain't something else, this is this -Robert De Niro, Deerhunter his book may to some extent be viewed as the continuation of my T Doctoral thesis Epistemology, Methodology and Reliability. The dissertation was, first of all, a methodological study of the reliable performance of the AGM-axioms (Alchourr6n, Gardenfors and Makin- son) of belief revision. Second of all the dissertation included the first steps toward an epistemology for the limiting convergence of knowledge for scientific inquiry methods of both discovery and assessment. The idea of methodological reliability as...

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named fuzzy inference' can be naturally understood as logical deduction.
There are two main groups of intended readers. First, logicians: they can see that fuzzy logic is indeed a branch of...

Godel's modal ontological argument is the centrepiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and the Prawitz/Takahashi completeness proof is given. Then modal machinery is added, semantically and through tableau rules, to produce a modified version of Montague/Gallin intensional logic. Extensionality, rigidity, equality, identity, and definite descriptions are investigated. Finally, various ontological proofs for the existence of God are discussed informally, and the Godel argument is fully...

Substructural logics are by now one of the most prominent branches of the research field usually labelled as "nonclassical logics" - and perhaps of logic tout court. Over the last few decades a vast amount of research papers and even some books have been devoted to this subject. The aim of the present book is to give a comprehensive account of the "state of the art" of substructural logics, focusing both on their proof theory (especially on sequent calculi and their generalizations) and on their semantics (both algebraic and relational).
Readership: This textbook is...

The approach to probability theory followed in this book (which differs radically from the usual one, based on a measure-theoretic framework) characterizes probability as a linear operator rather than as a measure, and is based on the concept of coherence, which can be framed in the most general view of conditional probability. It is a flexible' and unifying tool suited for handling, e.g., partial probability assessments (not requiring that the set of all possible outcomes' be endowed with a previously given algebraic structure, such as a Boolean algebra), and conditional independence, in a...