Algebraic and Proof-theoretic Aspects of Non-classical Logics

Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the third volume of the FoLLI LNAI subline. The 17 revised papers of this Festschrift volume - published in honour of Daniele Mundici on the occasion of his 60th birthday - include invited extended versions of the most interesting contributions to the International Conference on the Algebraic and Logical Foundations of Many-Valued Reasoning, held in Gargnano, Italy, in March 2006.

Daniele Mundici is widely acknowledged as a leading scientist in many-valued logic and ordered algebraic structures. In the last decades, his work has unveiled profound connections between logic and such diverse fields of research as functional analysis, probability and measure theory, the geometry of toric varieties, piecewise linear geometry, and error-correcting codes. Several prominent logicians, mathematicians, and computer scientists attending the conference have contributed to this wide-ranging collection with papers all variously related to Daniele's work.

Inhalt
Many-Valued Non-deterministic Semantics for First-Order Logics of Formal (In)consistency.- Note on Conditional Constructivity.- Symmetric MV-Algebras.- Implicit Operations in MV-Algebras and the Connectives of ?ukasiewicz Logic.- The Algebras of ?ukasiewicz Many-Valued Logic: A Historical Overview.- Reversibility and Irreversibility in Quantum Computation and in Quantum Computational Logics.- CantorBernstein Property for MV-Algebras.- A Note on Representing and Interpreting MV-Algebras.- Towards the Generalization of Mundici's ? Functor to IMTL Algebras: The Linearly Ordered Case.- Verification by Parallelization of Parametric Code.- Finitely Presented Abelian Lattice-Ordered Groups.- On Fuzzy Theories with Crisp Sentences.- Proof Transformations and Structural Invariance.- Rényi-Ulam Game Semantics for Product Logic and for the Logic of Cancellative Hoops.- Notes on Strong Completeness in ?ukasiewicz, Product and BL Logics and in Their First-Order Extensions.- The Automorphism Group of Falsum-Free Product Logic.- Probability Theory on IF Events.