Chapter 1. Introduction; Francesc Esteva, Lluís Godo, Siegfried Gottwald and Franco Montagna.- Chapter 2. Petr Hájek: a scientific biography; Zuzana Haniková.- Part I. Foundational aspects of Mathematical Fuzzy Logic.- Chapter 3. The logic of fuzzy set theory: a historical approach; Siegfried Gottwald.- Chapter 4. Set theory and arithmetic in fuzzy logic; Libor Bĕhounek and Zuzana Haniková.- Chapter 5. Bridges Between Contextual Linguistic Models of Vagueness and T-Norm Based Fuzzy Logic; Christian G. Fermüller and Christoph Roschger.- Part II. Semantics and consequence relation in Many-Valued Logic.- Chapter 6. Consequence and degrees of truth in many-valued logic; Josep Maria Font.- Chapter 7. The differential semantics of Łukasiewicz syntactic consequence; Daniele Mundici.- Chapter 8. Two principles in many-valued logic; Stefano Aguzzoli and Vincenzo Marra.- Part III. Algebra for Many-Valued Logic.- Chapter 9. How do `-groups and po-groups appear in algebraic and quantum structures?; Anatolij Dvurĕcenskij.- Chapter 10. Semi-linear Varieties of Lattice-Ordered Algebras; Antonio Ledda, Francesco Paoli and Constantine Tsinakis.- Part IV. More recent trends.- Chapter 11. On possibilistic modal logics defined over MTL-chains; Félix Bou, Francesc Esteva and Lluís Godo.- Chapter 12. The quest for the basic fuzzy logic; Petr Cintula, Rostislav Horˇcík and Carles Noguera.- A Bibliography of Petr Hájek.
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