Bøger i Trends in Logic serien

This book is the first to present a comprehensive investigation of the technical features of the metainferential logics developed in the last years, with their most relevant results and applications. It provides some new paths to define and investigate metainferential logics and offers a thorough study of the semantics and the proof-theories of this new and exciting variety of families of logics.This volume examines the hierarchies of metainferential logics and gives a general and systematic theory of them, and of the truth theories based on these logics. This book puts forward the prospects for truth-theories based on the metainferential logics of the TS/ST hierarchy and argues for its promise noting that each of these logics can be safely expanded with a transparent truth predicate. It also goes onto to explore new developments in three fields related to logics ¿ namely metainferential logics built by means of the Weak Kleene schema and combining them with logics defined through the Strong Kleene schema, proof-theoretic presentations, and those with a with a global or an absolutely global validity standard, instead of a local one. This book is of interest to scholars in formal logic.

By extending the technique of Plonka sums from algebras to logical matrices, the authors investigate the different classes of models for logics of variable inclusion and they shed new light into their formal properties.The book opens with the historical origins of logics of variable inclusion and on their philosophical motivations.

This book is for researchers in computer science, mathematical logic, and philosophical logic. It shows the state of the art in current investigations of process calculi with mainly two major paradigms at work: linear logic and modal logic. The combination of approaches and pointers for further integration also suggests a grander vision for the field.

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 spaces, compactness, separation axioms, and canonical examples; and thus this work is, with respect to topology, a continuation of the standardization of the Hand­ book. At the same time, this work significantly complements the Handbook in regard to algebraic structures. Thus the present volume is an extension of the content and role of the Handbook as a reference work. On the other hand, this volume, even as the Handbook, is a culmination of mathematical developments motivated by the renowned International Sem­ inar on Fuzzy Set Theory, also known as the Linz Seminar, held annually in Linz, Austria. Much of the material of this volume is related to the Twenti­ eth Seminar held in February 1999, material for which the Seminar played a crucial and stimulating role, especially in providing feedback, connections, and the necessary screening of ideas.

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos.

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics.

This volume clusters together issues centered upon the variety of types of intensional semantics.

This volume presents the state of the art in the algebraic investigation into substructural logics.

This book presents a detailed treatment of ordinal combinatorics of large sets tailored for independence results.

This volume clusters together issues centered upon the variety of types of intensional semantics.

This volume presents the state of the art in the algebraic investigation into substructural logics.

This book presents an English translation of a classic Russian text on duality theoryfor Heyting algebras.

This book provides a critical examination of how the choice of what to believe is represented in the standard model of belief change. It also explores sentential revision and demonstrates how local and global operations of revision by a sentence can be derived as a special case of descriptor revision.

Toward Predicate Approaches to Modality

This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. In the end, the book shows that the constructive path may branch in different directions: towards intuitionistic logic, dual intuitionistic logic and several variations of Nelson logics.

This book presents adaptive logics (ALs) as an intuitive and powerful framework to model defeasible reasoning. It offers case studies stemming from various contexts of defeasible reasoning, such as default reasoning, argumentation, and normative reasoning.