## About this book

### Introduction

*Non-Classical Logics and their Applications to Fuzzy Subsets* is the first major work devoted to a careful study of various relations between non-classical logics and fuzzy sets. This volume is indispensable for all those who are interested in a deeper understanding of the mathematical foundations of fuzzy set theory, particularly in intuitionistic logic, Lukasiewicz logic, monoidal logic, fuzzy logic and topos-like categories. The tutorial nature of the longer chapters, the comprehensive bibliography and index make it suitable as a valuable and important reference for graduate students as well as research workers in the field of non-classical logics.

The book is arranged in three parts: Part A presents the most recent developments in the theory of Heyting algebras, MV-algebras, quantales and GL-monoids. Part B gives a coherent and current account of topos-like categories for fuzzy set theory based on Heyting algebra valued sets, quantal sets of M-valued sets. Part C addresses general aspects of non-classical logics including epistemological problems as well as recursive properties of fuzzy logic.

### Keywords

Heyting algebra algebra logic proof set theory ultraproduct

### Editors and affiliations

- Ulrich Höhle
- Erich Peter Klement

- 1.Fachbereich MathematikBergische UniversitätWuppertalGermany
- 2.Institut für MathematikJohannes Kepler UniversitätLinzAustria

### Bibliographic information