Advances In Applied Logics

This book contains contributions from several international authors to topics of current interest, such as AI, intelligent systems, and logic applications in different branches of knowledge. Foundational aspects of the various techniques are also covered, notably non-classical formalisms. The tome is intended for researchers, undergraduate and graduate students, and lay readers. The book is dedicated to researcher Seiki Akama on his sixtieth birthday. Akama is one of the critical scientists who dedicated himself to understanding the use of alternative logic in the various issues of AI, ranging from its foundations to concrete applications and philosophical reflections.

Intensional logic has emerged, since the 1960' s, as a powerful theoretical and practical tool in such diverse disciplines as computer science, artificial intelligence, linguistics, philosophy and even the foundations of mathematics. The present volume is a collection of carefully chosen papers, giving the reader a taste of the frontline state of research in intensional logics today. Most papers are representative of new ideas and/or new research themes. The collection would benefit the researcher as well as the student. This book is a most welcome addition to our series. The Editors CONTENTS PREFACE IX JOHAN VAN BENTHEM AND NATASHA ALECHINA Modal Quantification over Structured Domains PATRICK BLACKBURN AND WILFRIED MEYER-VIOL Modal Logic and Model-Theoretic Syntax 29 RUY J. G. B. DE QUEIROZ AND DOV M. GABBAY The Functional Interpretation of Modal Necessity 61 VLADIMIR V. RYBAKOV Logics of Schemes for First-Order Theories and Poly-Modal Propositional Logic 93 JERRY SELIGMAN The Logic of Correct Description 107 DIMITER VAKARELOV Modal Logics of Arrows 137 HEINRICH WANSING A Full-Circle Theorem for Simple Tense Logic 173 MICHAEL ZAKHARYASCHEV Canonical Formulas for Modal and Superintuitionistic Logics: A Short Outline 195 EDWARD N. ZALTA 249 The Modal Object Calculus and its Interpretation NAME INDEX 281 SUBJECT INDEX 285 PREFACE Intensional logic has many faces. In this preface we identify some prominent ones without aiming at completeness.

"This book defines the role of advanced natural language processing within natural language processing, and alongside other disciplines such as linguistics, computer science, and cognitive science"--Provided by publisher.

How do we design a self-organizing system? Is it possible to validate and control non-deterministic dynamics? What is the right balance between the emergent patterns that bring robustness, adaptability and scalability, and the traditional need for verification and validation of the outcomes? The last several decades have seen much progress from original ideas of “emergent functionality” and “design for emergence”, to sophisticated mathematical formalisms of “guided self-organization”. And yet the main challenge remains, attracting the best scientific and engineering expertise to this elusive problem. This book presents state-of-the-practice of successfully engineered self-organizing systems, and examines ways to balance design and self-organization in the context of applications. As demonstrated in this second edition of Advances in Applied Self-Organizing Systems, finding this balance helps to deal with practical challenges as diverse as navigation of microscopic robots within blood vessels, self-monitoring aerospace vehicles, collective and modular robotics adapted for autonomous reconnaissance and surveillance, self-managing grids and multiprocessor scheduling, data visualization and self-modifying digital and analog circuitry, intrusion detection in computer networks, reconstruction of hydro-physical fields, traffic management, immunocomputing and nature-inspired computation. Many algorithms proposed and discussed in this volume are biologically inspired, and the reader will also gain an insight into cellular automata, genetic algorithms, artificial immune systems, snake-like locomotion, ant foraging, birds flocking, neuromorphic circuits, amongst others. Demonstrating the practical relevance and applicability of self-organization, Advances in Applied Self-Organizing Systems will be an invaluable tool for advanced students and researchers in a wide range of fields.

In the twentieth century, logic finally found a number of important applications and various new areas of research originated then, especially after the development of computing and the progress of the correlated domains of knowledge (artificial intelligence, robotics, automata, logical programming, hyper-computation, etc.). This happened not only in the field of classical logics, but also in the general field of non-classical logics. This reveals an interesting trait of the history of logic: despite its theoretical character, it constitutes, at present, an extraordinarily important tool in all domains of knowledge, in the same way as philosophy, mathematics, natural science, the humanities and technology. Moreover, certain new logics were inspired by the needs of specific areas of knowledge, and various new techniques and methods have been created, in part influenced and guided by logical views.

Time is a fascinating subject and has long since captured mankind's imagination, from the ancients to modern man, both adult and child alike. It has been studied across a wide range of disciplines, from the natural sciences to philosophy and logic. Today, thirty plus years since Prior's work in laying out foundations for temporal logic, and two decades on from Pnueli's seminal work applying of temporal logic in specification and verification of computer programs, temporal logic has a strong and thriving international research community within the broad disciplines of computer science and artificial intelligence. Areas of activity include, but are certainly not restricted to: Pure Temporal Logic, e. g. temporal systems, proof theory, model theory, expressiveness and complexity issues, algebraic properties, application of game theory; Specification and Verification, e. g. of reactive systems, ofreal-time components, of user interaction, of hardware systems, techniques and tools for verification, execution and prototyping methods; Temporal Databases, e. g. temporal representation, temporal query ing, granularity of time, update mechanisms, active temporal data bases, hypothetical reasoning; Temporal Aspects in AI, e. g. modelling temporal phenomena, in terval temporal calculi, temporal nonmonotonicity, interaction of temporal reasoning with action/knowledge/belief logics, temporal planning; Tense and Aspect in Natural Language, e. g. models, ontologies, temporal quantifiers, connectives, prepositions, processing tempo ral statements; Temporal Theorem Proving, e. g. translation methods, clausal and non-clausal resolution, tableaux, automata-theoretic approaches, tools and practical systems.

The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium “Advances in Proof Theory”, which was held in Bern in December 2013. ​Proof theory came into being in the twenties of the last century, when it was inaugurated by David Hilbert in order to secure the foundations of mathematics. It was substantially influenced by Gödel's famous incompleteness theorems of 1930 and Gentzen's new consistency proof for the axiom system of first order number theory in 1936. Today, proof theory is a well-established branch of mathematical and philosophical logic and one of the pillars of the foundations of mathematics. Proof theory explores constructive and computational aspects of mathematical reasoning; it is particularly suitable for dealing with various questions in computer science.