William M Farmer - Böcker

This unique textbook, in contrast to a standard logic text, provides the reader with a logic that actually can be used in practice to express and reason about mathematical ideas.The book is an introduction to simple type theory, a classical higher-order version of predicate logic that extends first-order logic. It presents a practice-oriented logic called Alonzo that is based on Alonzo Church's formulation of simple type theory known as Church's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions. The book illustrates, using Alonzo, how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge.Topics and features:Offers the first book-length introduction to simple type theory as a predicate logicProvides the reader with a logic that is close to mathematical practicePresents the tools needed to build libraries of mathematical knowledgeEmploys two semantics, one for mathematics and one for logicEmphasizes the model-theoretic view of predicate logicIncludes several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooksAimed at students of computing and mathematics at the graduate or upper-undergraduate level, this book is also well-suited for mathematicians, computing professionals, engineers, and scientists who need a practical logic for expressing and reasoning about mathematical ideas.William M. Farmer is a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada.

This unique textbook, in contrast to a standard logic text, provides the reader with a logic that can be used in practice to express and reason about mathematical ideas.  The book is an introduction to simple type theory, a classical higher-order version of predicate logic that extends first-order logic.  It presents a practice-oriented logic called Alonzo that is based on Alonzo Church's formulation of simple type theory known as Church's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions.  The book illustrates using Alonzo how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge.  For this second edition, more than 400 additions, corrections, and improvements have been made, including a new chapter on inductive sets and types.Topics and features:·       Offers the first book-length introduction to simple type theory as a predicate logic·       Provides the reader with a logic that is close to mathematical practice·       Includes a module system for building libraries of mathematical knowledge·       Employs two semantics, one for mathematics and one for logic·       Emphasizes the model-theoretic view of predicate logic·       Presents several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooksAimed at students of mathematics and computing at the graduate or upper-undergraduate level, this book is well suited for mathematicians, computing professionals, engineers, and scientists who need a practical logic for expressing and reasoning about mathematical ideas.William M. Farmer is a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada.

?This book constitutes the refereed proceedings of the 11th International Conference on Intelligent Computer Mathematics, CICM 2018, held in Hagenberg, Austria, in August 2018.

This book constitutes the refereed proceedings of the 5th International Conference on Mathematical Knowledge Management, MKM 2006, held in Wokingham, UK, August 2006. The book presents 22 revised full papers. Coverage extends to the mathematical knowledge management at the intersection of mathematics, computer science, library science, and scientific publishing. The papers are organized in topical sections on proof representations, proof processing, knowledge extraction, knowledge representation, as well as systems and tools.