Kategoria BISAC: Mathematics >> Logic

This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language – and specifically, the ability to institute conventions for the truth conditions of sentences.

This philosophical stance leads to an alternative way of practicing mathematics: instead of “building” objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory.

Semantic conventionalism is...

This volume contains English translations of Gödel's chapters on logicism and the antinomies and on the calculi of pure logic, as well as outlines for a chapter on metamathematics. It also comprises most of his reading notes. 

This book is a testimony to Gödel's understanding of the situation of foundational research in mathematics after his great discovery, the incompleteness theorem of 1931. It is also a source for his views on his logical predecessors, from Leibniz, Frege, and Russell to his own times. Gödel's "own book on foundations," as he called it, is essential...

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...

Parameterized complexity theory is a recent branch of computational complexity theory that provides a framework for a refined analysis of hard algorithmic problems. The central notion of the theory, fixed-parameter tractability, has led to the development of various new algorithmic techniques and a whole new theory of intractability.

This book is a state-of-the-art introduction to both algorithmic techniques for fixed-parameter tractability and the structural theory of parameterized complexity classes, and it presents detailed proofs of recent advanced results that have not appeared...

Formal methods are a robust approach for problem solving. It is based on logic and algebraic methods where problems can be formulated in a way that can help to find an appropriate solution. This book shows the basic concepts of formal methods and highlights modern modifications and enhancements to provide a more robust and efficient problem solving tool.

Applications are presented from different disciplines such as engineering where the operation of chemical plants is synthesized using formal methods. Computational biology becomes easier and systematic using formal methods. Also,...

Formal methods are a robust approach for problem solving. It is based on logic and algebraic methods where problems can be formulated in a way that can help to find an appropriate solution. This book shows the basic concepts of formal methods and highlights modern modifications and enhancements to provide a more robust and efficient problem solving tool.

Applications are presented from different disciplines such as engineering where the operation of chemical plants is synthesized using formal methods. Computational biology becomes easier and systematic using formal methods. Also,...