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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.
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.
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