Advanced Łukasiewicz calculus and MV-algebras - Mundici, Daniele 1946- (Trends in Logic, 2011)
In recent years, the discovery of the relationships between formulas in Lukasiewicz logic and rational polyhedra, Chang MV-algebras and lattice-ordered abelian roups, MV-algebraic states and coherent de Finetti's assessments of continuous events, has changed the study and practice of many-valued logic. This book is intended as an up-to-date monograph on innite-valued Lukasiewicz logic and MV-algebras. Each chapter features a combination of classical and re¬cent results, well beyond the traditional domain of algebraic logic: among others, a comprehensive account is given of many effective procedures that have been recently developed for the algebraic and geometric objects represented by formulas in Lukasiewicz logic. The book embodies the viewpoint that modern Lukasiewicz logic and MV-algebras provide a benchmark for the study of several deep mathematical prob¬lems, such as Rényi conditionals of continuously valued events, the many-valued generalization of Carathéodory algebraic probability theory, morphisms and invari¬ant measures of rational polyhedra, bases and Schauder bases as jointly renable partitions of unity, and first-order logic with [0,1]-valued identity on Hilbert space. Complete versions are given of a compact body of recent results and techniques, proving virtually everything that is used throughout, so that the book can be used both for individual study and as a source of reference for the more advanced reader.