Matematisk logik

Proceedings of the BB Fest 96, a conference held at the University of Cape Town, 15-20 July 1996, on Category Theory and its Applications to Topology, Order and Algebra

Information technology has been, in recent years, under increasing commercial pressure to provide devices and systems which help/ replace the human in his daily activity. This pressure requires the use of logic as the underlying foundational workhorse of the area. New logics were developed as the need arose and new foci and balance has evolved within logic itself. One aspect of these new trends in logic is the rising impor- tance of model based reasoning. Logics have become more and more tailored to applications and their reasoning has become more and more application dependent. In fact, some years ago, I myself coined the phrase "e;direct deductive reasoning in application areas"e;, advocating the methodology of model-based reasoning in the strongest possible terms. Certainly my discipline of Labelled Deductive Systems allows to bring "e;pieces"e; of the application areas as "e;labels"e; into the logic. I therefore heartily welcome this important book to Volume 25 of the Applied Logic Series and see it as an important contribution in our overall coverage of applied logic.

This book gives a proof of Cherlin¿s conjecture for finite binary primitive permutation groups. Motivated by the part of model theory concerned with Lachlan¿s theory of finite homogeneous relational structures, this conjecture proposes a classification of those finite primitive permutation groups that have relational complexity equal to 2. The first part gives a full introduction to Cherlin¿s conjecture, including all the key ideas that have been used in the literature to prove some of its special cases. The second part completes the proof by dealing with primitive permutation groups that are almost simple with socle a group of Lie type. A great deal of material concerning properties of primitive permutation groups and almost simple groups is included, and new ideas are introduced. Addressing a hot topic which cuts across the disciplines of group theory, model theory and logic, this book will be of interest toa wide range of readers. It will be particularly useful for graduate students and researchers who need to work with simple groups of Lie type.

A significant number of works have set forth, over the past decades, the emphasis laid by seventeenth-century mathematicians and philosophers on motion and kinematic notions in geometry. These works demonstrated the crucial role attributed in this context to genetic definitions, which state the mode of generation of geometrical objects instead of their essential properties. While the growing importance of genetic definitions in sixteenth-century commentaries on Euclid's Elements has been underlined, the place, uses and status of motion in this geometrical tradition has however never been thoroughly and comprehensively studied. This book therefore undertakes to fill a gap in the history of early modern geometry and philosophy of mathematics by investigating the different treatments of motion and genetic definitions by seven major sixteenth-century commentators on Euclid's Elements, from Oronce Fine (1494-1555) to Christoph Clavius (1538-1612), including Jacques Peletier (1517-1582), John Dee (1527-1608/1609) and Henry Billingsley (d. 1606), among others. By investigating the ontological and epistemological conceptions underlying the introduction and uses of kinematic notions in their interpretation of Euclidean geometry, this study displays the richness of the conceptual framework, philosophical and mathematical, inherent to the sixteenth-century Euclidean tradition and shows how it contributed to a more generalised acceptance and promotion of kinematic approaches to geometry in the early modern period.

We look at problems of truth and knowledge from various angles. Insufficient information may prevent the direct use of certain operations, as the use of probability in legal reasoning, so we have to take detours. We may have only contradictory information from different sources, and will use and adjust past reliability of the sources to evaluate the information.Conjectures about homogenousness of the domain may also help.On a more formal level, we extend the formal semantics of counterfactual conditionals to analogical reasoning, and examine Yablo's Paradox using various concepts and examples.

This book honors J. Michael Dunn, who was a preeminent relevance logician. Dunn's careerspanned over 50 years and his research results had an impact on philosophy, mathematics and informatics. Dunn often used algebraic techniques in his research into logics such as relevance, orthomodular and substructural logics. He invented the logic R-mingle and the sequent calculus LR+; he proved crucial theorems about 2-valued first-order logic and non-classical higher-order logics - among many other results. The papers in this volume touch upon topics that Dunn was concerned with. Some authors were students or colleagues of Dunn; some other authors had not met Dunn in person, but share his research interests. None of the articles published here have appeared in print before; indeed, most of the papers were written specifically for this collection. The diversity of the themes of the articles reflects the scope of Dunn's own research in logic. It will also ensure that anybody with an interest in logic - whether a student, a logician or a scholar in another field - will find reading this book a worthwhile endeavor. The editor, Katalin Bimbó was the 14th Ph.D. student of J. Michael Dunn at Indiana University in Bloomington, IN, U.S.A.; currently, she is a professor of philosophy at the University of Alberta in Canada.

This edited volume collects essays on the four-valued logic known as Belnap-Dunn logic, or first-degree entailment logic (FDE). It also looks at various formal systems closely related to it. These include the strong Kleene logic and the Logic of Paradox. Inside, readers will find reprints of seminal papers written by the fathers of the field: Nuel Belnap and Michael Dunn. In addition, the collection also features a well-known but previously unpublished manuscript of Dunn, an interview with Belnap, and a new essay by Dunn.Besides the original, monumental papers, the book also includes research by leading scholars. They consider the extraordinary importance of Belnap-Dunn logic from several perspectives. They look at how, philosophically, it has served as a basic system of inconsistency-tolerant reasoning, as the core of underlying logics for theories based on dialetheism, and, more recently, for theories based on Buddhist philosophy. Coverage also explores its contributions tocomputer science, such as knowledge representation and information processing.This mix of seminal papers and insightful analysis by top scholars offers readers a comprehensive outlook on Belnap-Dunn logic and its related expansions, which have been agenda setting for the debate on philosophical logic as well as philosophy of logic. The book will also enhance further discussion on the philosophical issues related to nonclassical logics in general.

This is the revised edition of a well-established monograph on the identification of a canonical model in which the Continuum Hypothesis is false. Written by an expert in the field, it is directed to researchers and advanced graduate students in Mathematical Logic and Set Theory. The second edition is updated to take into account some of the developments in the decade since the first edition appeared, this includes a revised discussion of ¿-logic and related matters.

The field of "e;intelligent interfaces and systems"e; has seen a fast growth last decade. An impressive number of papers, conference tutorials, and volumes were devoted to the topic. Ten years ago, intelligent systems constituted a rather exotic topic and many were skeptic that such systems amount to more than a nice name. Nowadays, intelligent systems represent a powerful tool in many applications, in all industrial fields. Their development evolved on both the horizontal dimension, with a constantly increasing number of applications, and on the vertical dimension, by including more capabilities going from sensoric to neurofuzzy systems, intelligent agents, speech and image understanding, and decision making in complex environments. The domain constituted by the intelligent systems is now too large to be covered in a single volume. Consequently, the Editors considered a balance between several selected sub-fields, to insure the unity of the volume, yet allowing a large enough horizon and a consistent understanding of the entire field, including real-life applications. The volume represents a comprehensive coverage of the field, including fundamental aspects, software-, sensors-, and hardware-related issues. Moreover, the contributors to this volume offer, beyond a systematic overview of intelligent interfaces and systems, deep, practical knowledge in building and using intelligent systems in various applications. A special emphasis is on specific aspects and requirements in applications. In addition, the second Editor proposes two chapters addressing the management of projects dealing with intelligent systems.

Fuzzy theory is an interesting name for a method that has been highly effective in a wide variety of significant, real-world applications. A few examples make this readily apparent. As the result of a faulty design the method of computer-programmed trading, the biggest stock market crash in history was triggered by a small fraction of a percent change in the interest rate in a Western European country. A fuzzy theory ap- proach would have weighed a number of relevant variables and the ranges of values for each of these variables. Another example, which is rather simple but pervasive, is that of an electronic thermostat that turns on heat or air conditioning at a specific temperature setting. In fact, actual comfort level involves other variables such as humidity and the location of the sun with respect to windows in a home, among others. Because of its great applied significance, fuzzy theory has generated widespread activity internationally. In fact, institutions devoted to research in this area have come into being. As the above examples suggest, Fuzzy Systems Theory is of fundamen- tal importance for the analysis and design of a wide variety of dynamic systems. This clearly manifests the fundamental importance of time con- siderations in the Fuzzy Systems design approach in dynamic systems. This textbook by Prof. Dr. Jernej Virant provides what is evidently a uniquely significant and comprehensive treatment of this subject on the international scene.