The aim of this book is to give self-contained proofs of all basic
results concerning the infinite-valued proposition al calculus of
Lukasiewicz and its algebras, Chang's MV -algebras. This book is for
self-study: with the possible exception of Chapter 9 on advanced topics,
the only prere- quisite for the reader is some acquaintance with
classical propositional logic, and elementary algebra and topology. In
this book it is not our aim to give an account of Lukasiewicz's
motivations for adding new truth values: readers interested in this
topic will find appropriate references in Chapter 10. Also, we shall not
explain why Lukasiewicz infinite-valued propositionallogic is a ba- sic
ingredient of any logical treatment of imprecise notions: Hajek's book
in this series on Trends in Logic contains the most authorita- tive
explanations. However, in order to show that MV-algebras stand to
infinite-valued logic as boolean algebras stand to two-valued logic, we
shall devote Chapter 5 to Ulam's game of Twenty Questions with
lies/errors, as a natural context where infinite-valued propositions,
con- nectives and inferences are used. While several other semantics for
infinite-valued logic are known in the literature-notably Giles' game-
theoretic semantics based on subjective probabilities-still the transi-
tion from two-valued to many-valued propositonallogic can hardly be
modelled by anything simpler than the transformation of the familiar
game of Twenty Questions into Ulam game with lies/errors.
