Mundici, D: Advanced Lukasiewicz calculus and MV-algebras

In recent years, the discovery of the relationships between formulas in ?ukasiewicz 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 in?nite-valued ?ukasiewicz 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 e?ective procedures that have been re¬cently developed for the algebraic and geometric objects represented by formulas in ?ukasiewicz logic.

The book embodies the viewpoint that modern ?ukasiewicz 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 re?nable partitions of unity, and ?rst-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.e¬cent results, well beyond the traditional domain of algebraic logic: among others, a comprehensive account is given of many e?ective procedures that have been re¬cently developed for the algebraic and geometric objects represented by formulas in ?ukasiewicz logic.

The book embodies the viewpoint that modern ?ukasiewicz 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 algebr