Algebraic Foundations of Many-Valued ReasoningThis unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as a simple proof of the completeness theorem and of the equivalence between Chang's MV algebras and Abelian lattice-ordered groups with unit - a necessary prerequisite for the incorporation of a genuine addition operation into fuzzy logic. Readers interested in fuzzy control are provided with a rich deductive system in which one can define fuzzy partitions, just as Boolean partitions can be defined and computed in classical logic. Detailed bibliographic remarks at the end of each chapter and an extensive bibliography lead the reader on to further specialised topics. |
Contents
1 | |
4 | |
Free MValgebras | 51 |
Latticetheoretical properties | 111 |
Varieties of MValgebras | 157 |
Advanced topics | 179 |
Other editions - View all
Algebraic Foundations of Many-Valued Reasoning R.L. Cignoli,Itala M. d'Ottaviano,Daniele Mundici No preview available - 2010 |
Algebraic Foundations of Many-Valued Reasoning R.L. Cignoli,Itala M. d'Ottaviano,Daniele Mundici No preview available - 2012 |
Common terms and phrases
a₁ abelian group b₁ BELLUCE boolean algebra boolean product C*-algebras Chang's Chapter coincides complete MV-algebra completeness theorem Cont(X Corollary defined Definition denote desired conclusion direct product distributive lattices element em+1 equation holds equivalence class finite number following conditions formula free MV-algebras functor given Hausdorff space Hence homomorphism hyperarchimedean hypothesis ideal of L(A immediate consequence induction infinite-valued calculus integer intersection isomorphism l-group lattice lattice-ordered Lemma Lindenbaum algebra linear Łukasiewicz logic Many-valued logics Mathematics maximal ideal McNaughton functions monoid MUNDICI MV-chain MV-equations MV-term n-dimensional simplexes natural order NOLA nonempty notation obtain one-one operations ordered abelian group prime ideal proper ideal properties Proposition propositional calculus prove Rad(A real numbers Schauder semisimple sequence stonean ideal strong unit subalgebra subdirect product subset Suppose surjective tautology tautology problem theory toric varieties trivial Ulam game vectors vertices whence ΕΙ