Mathematics : Logic

Towards the end of the nineteenth century, Frege gave us the abstraction principles and the general notion of functions. Self-application of functions was at the heart of Russell's paradox. This led Russell to introduce type theory in order to avoid the paradox. Since, the twentieth century has seen an amazing number of theories concerned with types and functions and many applications. Progress in computer science also meant more and more emphasis on the use of logic, types and functions to study the syntax, semantics, design and implementation of programming languages and theorem provers, and the correctness of proofs and programs. The authors of this book have themselves been leading the way by providing various extensions of type theory which have been shown to bring many advantages. This book gathers much of their influential work and is highly recommended for anyone interested in type theory. The main emphasis is on: The first part of the book is historical, yet at the same time, places historical systems (like Russell's RTT) in the modern setting. The second part deals with modern type theory as it developed since the 1940s, and with the role of propositions as types (or pro more...

Price: $195.00

Methods of dimensionality reduction provide a way to understand and visualize the structure of complex data sets. This book describes the methods to reduce the dimensionality of numerical databases. For each method, the description starts from intuitive ideas, develops the mathematical details, and ends by outlining the algorithmic implementation. more...

Price: $79.95

Fuzzy set and logic theory suggest that all natural language linguistic expressions are imprecise and must be assessed as a matter of degree. But in general membership degree is an imprecise notion which requires that Type 2 membership degrees be considered in most applications related to human decision making schemas. Even if the membership functions are restricted to be Type1, their combinations generate an interval – valued Type 2 membership. This is part of the general result that Classical equivalences breakdown in Fuzzy theory. Thus all classical formulas must be reassessed with an upper and lower expression that are generated by the breakdown of classical formulas. Key features: - Ontological grounding - Epistemological justification - Measurement of Membership - Breakdown of equivalences - FDCF is not equivalent to FCCF - Fuzzy Beliefs - Meta-Linguistic axioms more...

Price: $180.00

This title represents an integrated discussion of all major topics in the area of paraconsistent logic, highlighting philosophical and historical aspects, major developments and real-world applications. more...

Price: $189.95

This photocopy master book, which has proven extremely popular over the years, provides a range of 30+ problem solving activities using strategies such as: Developing logical thinking; Using number concepts to develop logical thinking; Logical reasoning; Developing visual imagery; and Pattern perception using number. more...

Price: $7.45