Logics of Variable Inclusion
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Beschreibung
This monograph shows that, through a recourse to the concepts and methods of abstract algebraic logic, the algebraic theory of regular varieties and the concept of analyticity in formal logic can profitably interact. By extending the technique of Plonka sums from algebras to logical matrices, the authors investigate the different classes of models for logics of variable inclusion and they shed new light into their formal properties.
The book opens with the historical origins of logics of variable inclusion and on their philosophical motivations. It includes the basics of the algebraic theory of regular varieties and the construction of Plonka sums over semilattice direct systems of algebra. The core of the book is devoted to an abstract definition of logics of left and right variable inclusion, respectively, and the authors study their semantics using the construction of Plonka sums of matrix models. The authors also cover Paraconsistent Weak Kleene logic and survey its abstract algebraic logical properties. This book is of interest to scholars of formal logic.
This monograph shows that, through a recourse to the concepts and methods of abstract algebraic logic, the algebraic theory of regular varieties and the concept of analyticity in formal logic can profitably interact. By extending the technique of Plonka sums from algebras to logical matrices, the authors investigate the different classes of models for logics of variable inclusion and they shed new light into their formal properties.
The book opens with the historical origins of logics of variable inclusion and on their philosophical motivations. It includes the basics of the algebraic theory of regular varieties and the construction of Plonka sums over semilattice direct systems of algebra. The core of the book is devoted to an abstract definition of logics of left and right variable inclusion, respectively, and the authors study their semantics using the construction of Plonka sums of matrix models. The authors also cover Paraconsistent Weak Kleene logic and survey its abstract algebraic logical properties. This book is of interest to scholars of formal logic.
Is the first monograph ever on logics of variable inclusion Highly relevant to logicians, philosophers and algebraists alike Puts together two separate research streams, in logic and algebra respectively
Autor*in
Stefano Bonzio
Themen in »Logics of Variable Inclusion«
Many-valued Logics Logics of Variable Inclusion Significance Logics Kleene Logics Nonclassical Logics Regular Varieties Plonka Sums Bisemilattices Abstract Algebraic Logic Universal Algebra Analyticity, Consequence, and Meaninglessness Płonka Sums and Regular Varieties Dualities for Regular Varieties Logics of Left Variable Inclusion Logics of Right Variable Inclusion
Stimmen zu »Logics of Variable Inclusion«
“Logics of Variable Inclusion is a valid, rigorous, and comprehensive study in algebraic logic of the employment of Płonka sums in formal semantics, an essential reference for the future developments in the field.” (Nicolò Zamperini, Studia Logica, Vol. 111 (3), 2023)
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