# Handbook of Mathematical Fuzzy Logic

From Mathfuzzlog

The *Handbook of Mathematical Fuzzy Logic* is a series of books collecting the state of the art in the main trends of Mathematical Fuzzy Logic. The first two volumes have been published in 2011 by College Publications (volumes 37 and 38 of Studies in Logic, subseries Mathematical Logic and Foundations), and edited by Petr Cintula, Petr Hájek and Carles Noguera.

## Volume I

- Chapter I: Introduction to Mathematical Fuzzy Logic (written by Libor Běhounek, Petr Cintula and Petr Hájek).
- Chapter II: A General Framework for Mathematical Fuzzy Logic (written by Petr Cintula and Carles Noguera).
- Chapter III: Proof Theory for Mathematical Fuzzy Logic (written by George Metcalfe).
- Chapter IV: Algebraic Semantics: Semilinear FL-algebras (written by Rostislav Horčík).
- Chapter V: Hájek's Logic BL and BL-Algebras (written by Manuela Busaniche and Franco Montagna).

(It can be bought at Amazon)

## Volume II

- Chapter VI: Lukasiewicz Logic and MV-Algebras (written by Antonio Di Nola and Ioana Leustean).
- Chapter VII: Gödel-Dummett Logics (written by Matthias Baaz and Norbert Preining).
- Chapter VIII: Fuzzy Logics with Enriched Language (written by Francesc Esteva, Lluís Godo and Enrico Marchioni).
- Chapter IX: Free Algebras and Functional Representation for Fuzzy Logics (written by Stefano Aguzzoli, Simone Bova and Brunella Gerla).
- Chapter X: Computational Complexity of Propositional Fuzzy Logics (written by Zuzana Haniková).
- Chapter XI: Arithmetical Complexity of First-Order Fuzzy Logics (written by Petr Hájek, Franco Montagna and Carles Noguera).

(It can be bought at Amazon)

## Volume III

- Chapter XII: Algebraic Semantics: The Structure of Residuated Chains (written by Thomas Vetterlein).
- Chapter XIII: Dialogue Semantic Games for Fuzzy Logics (written by Christian Fermüller).
- Chapter XIV: Ulam-Rényi Game Based Semantics for Fuzzy Logics (written by Ferdinando Cicalese and Franco Montagna).
- Chapter XV: Fuzzy Logic with Evaluated Syntax (written by Vilém Novák).
- Chapter XVI: Fuzzy Description Logics (written by Fernando Bobillo, Marco Cerami, Francesc Esteva, Àngel García-Cerdaña, Rafael Peñaloza and Umberto Straccia).
- Chapter XVII: States of MV-algebras (written by Tommaso Flaminio and Tomáš Kroupa).
- Chapter XVIII: Fuzzy Logics in Theories of Vagueness (written by Nick Smith).

(New volume edited by Petr Cintula, Christian Fermüller and Carles Noguera)