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 aim of this book is to give self-contained proofs of all basic results concerning the infinite-valued proposition al calculus of Lukasiewicz and i...
The main aim of this monograph is to provide a structured study of the algebraic method in metalogic. In contrast to traditional algebraic logic, where the focus is on the algebraic forms of specific deductive systems, abstract algebraic logic is concerned with the process of algebraization itself. This book presents in a systematic way recent ideas in abstract algebraic logic centered around the notion of the Leibniz operator. The stress is put on the taxonomy of deductive systems. Isolating a list of plausible properties of the Leibniz operator serves as a basis for distinguishing certain...
The main aim of this monograph is to provide a structured study of the algebraic method in metalogic. In contrast to traditional algebraic logic, wher...
Fuzzy logic in narrow sense is a promising new chapter of formal logic whose basic ideas were formulated by Lotfi Zadeh (see Zadeh 1975]a). The aim of this theory is to formalize the "approximate reasoning" we use in everyday life, the object of investigation being the human aptitude to manage vague properties (as, for example, "beautiful," "small," "plausible," "believable," etc. ) that by their own nature can be satisfied to a degree different from 0 (false) and I (true). It is worth noting that the traditional deductive framework in many-valued logic is different from the one adopted in...
Fuzzy logic in narrow sense is a promising new chapter of formal logic whose basic ideas were formulated by Lotfi Zadeh (see Zadeh 1975]a). The aim o...
This volume summarizes recent developments in the topological and algebraic structures in fuzzy sets and may be rightly viewed as a continuation of the stan dardization of the mathematics of fuzzy sets established in the "Handbook," namely the Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Volume 3 of The Handbooks of Fuzzy Sets Series (Kluwer Academic Publish ers, 1999). Many of the topological chapters of the present work are not only based upon the foundations and notation for topology laid down in the Hand book, but also upon Handbook developments in convergence, uniform...
This volume summarizes recent developments in the topological and algebraic structures in fuzzy sets and may be rightly viewed as a continuation of th...
In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica. The volume features a series of papers by distinguished scholars reflecting both the aim and scope of this journal for symbolic logic.
In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Poli...
This volume covers recent developments in Lukasiewicz Logic and their algebras (Chang MV-algebras), with particular reference to (de Finetti) coherent evaluation of continuously valued events, (Renyi) conditionals, and related algorithms.
This volume covers recent developments in Lukasiewicz Logic and their algebras (Chang MV-algebras), with particular reference to (de Finetti) coherent...
The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of (basic) truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice (a lattice of truth values with two ordering relations) constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, a trilattice...
The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of (basic) truth va...
This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz s work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science.
The range of contributions includes material on the extension of natural deduction with higher-order rules, as opposed...
This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented a...
This book is dedicated to Dov Gabbay, one of the most outstanding and most productive researchers in the area of logic, language and reasoning. He has exerted a profound influence in the major fields of logic, linguistics and computer science. Most of the chapters included, therefore, build on his work and present results or summarize areas where Dov has made major contributions. In particular his work on Labelled Deductive Systems is addressed in most of the contributions. The chapters on computational linguistics address logical and deductive aspects of linguistic problems. The papers by...
This book is dedicated to Dov Gabbay, one of the most outstanding and most productive researchers in the area of logic, language and reasoning. He has...
The present volume has its origin in a meeting of philosophers, linguists and cognitive scientists that was held at Umea University, Sweden, September 24-26, 1993. The meeting was organized by the Department of Philosophy in cooperation with the Department of Linguistics, and it was called UmLLI-93, the Umea Colloquium on Dynamic Approaches in Logic, Language and Information. The papers published here are considerably expanded and revised versions of talks presented by invited speakers at this colloquium. The papers included here fall into three broad categories. In the first part of the...
The present volume has its origin in a meeting of philosophers, linguists and cognitive scientists that was held at Umea University, Sweden, September...
