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Intuition and the Axiomatic Methodby Emily Carson; Renate Huber
Springer 2006; US$ 179.00Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant's theory of intuition to be obsolete. This work explores various views of intuition and the axiomatic method, with Kant's approach. It covers logical and non-logical, and systematic issues in mathematics and physics. more...
Function Algebras on Finite Setsby Dietlinde Lau
Springer 2006; US$ 135.00Gives an introduction to the theory of function algebras. This book gives the general concepts of the Universal Algebra in order to familiarize the reader from the beginning on with the algebraic side of function algebras. It is a source on function algebras for students and researchers in mathematical logic and theoretical computer science. more...
Intensional Mathematicsby S. Shapiro
Elsevier 1985; US$ 100.75``Platonism and intuitionism are rival philosophies of Mathematics, the former holding that the subject matter of mathematics consists of abstract objects whose existence is independent of the mathematician, the latter that the subject matter consists of mental construction... both views are implicitly opposed to materialistic accounts of mathematics which take the subject matter of mathematics to consist (in a direct way) of material objects...'' FROM THE INTRODUCTION Among the aims of this book are: - The discussion of some important philosophical issues using the precision of mathematics. - The development of formal systems that contain both classical and constructive components. This allows the study of constructivity in otherwise... more...
One Hundred Years of Intuitionism (1907-2007)by Pascal Boldini; Michel Bourdeau
Springer 2008; US$ 159.00With logicism and formalism, intuitionism is one of the main foundations for mathematics proposed in the twentieth century. This book aims to review and complete the historical account of intuitionism; to present philosophical work on intuitionism; and, to give examples of technical advances and applications of intuitionism. more...
Quantification in Nonclassical Logicby Dov M. Gabbay; Dimitrij Skvortsov; Valentin Shehtman
Elsevier 2009; US$ 210.00Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and language in ancient times; they were studied by traditional informal methods until the 20th century. In the last century the tools became highly mathematical, and both modal logic and quantification found numerous applications in Computer Science. At the same time many other kinds of nonclassical logics were investigated and applied to Computer Science. Although there exist several good books in propositional modal logics, this book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years. The field is very large, so we confine ourselves... more...
Non-classical logics, model theory, and computabilityby A.I. Arruda; N. C. A. De Costa; R. Chuaqui
Elsevier Science & Technology 2000; US$ 250.00Provability, Computability and Reflection more...
Many-values logicsby J. Barkley J. Rosser; Atwell R. Turoutte
Elsevier 2000; US$ 250.00Provability, Computability and Reflection more...
Aristotle's Modal Proofsby Adriane Rini
Springer 2011; US$ 139.00Aristotle's modal syllogistic is his study of patterns of reasoning about necessity and possibility. Many scholars think the modal syllogistic is incoherent, a 'realm of darkness'. Others think it is coherent, but devise complicated formal modellings to mimic Aristotle's results. This volume provides a simple interpretation of Aristotle's modal syllogistic using standard predicate logic. Rini distinguishes between red terms, such as 'horse', 'plant' or 'man', which name things in virtue of features those things must have, and green terms, such as 'moving', which name things in virtue of their non-necessary features. By applying this distinction to the Prior Analytics, Rini shows how traditional... more...
Multiple-Valued Logicby D. Michael Miller; Mitchell A. Thornton
Morgan & Claypool Publishers 2007; US$ 40.00Multiple Valued Logic: Concepts and Representations begins with a survey of the use ofmultiple-valued logic in several modern application areas including electronic design automation algorithms and circuit design. The mathematical basis and concepts of various algebras and systems of multiple valued logic are provided including comparisons among various systems and examples of their application. The book also provides an examination of alternative representations of multiple-valued logic suitable for implementation as data structures in automated computer applications. Decision diagram structures for multiple valued applications are described in detail with particular emphasis on the recently developed quantum multiple valued decision diagram. more...
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