The Haskell Road to Logic, Maths and Programming
by Kees Doets, Jan van Eijck
Publisher: College Publications 2004
Number of pages: 449
The purpose of this book is to teach logic and mathematical reasoning in practice, and to connect logical reasoning with computer programming. The programming language that will be our tool for this is Haskell, a member of the Lisp family.
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by Vilnis Detlovs, Karlis Podnieks - University of Latvia
From the table of contents: 1. Introduction. What Is Logic, Really?; 2. Propositional Logic; 3. Predicate Logic; 4. Completeness Theorems (Model Theory); 5. Normal Forms. Resolution Method; 6. Miscellaneous (Negation as Contradiction or Absurdity).
by Bertrand Russell - University of Massachusetts Amherst
A very accessible mathematical classic. It sets forth in elementary form the logical definition of number, the analysis of the notion of order, the modern doctrine of the infinite, and the theory of descriptions and classes as symbolic fictions.
by Edward Nelson - Princeton Univ Pr
The book based on lecture notes of a course given at Princeton University in 1980. From the contents: the impredicativity of induction, the axioms of arithmetic, order, induction by relativization, the bounded least number principle, and more.
This book provides a survey of mathematical logic and its various applications. After covering basic material of propositional logic and first-order logic, the course presents the foundations of finite model theory and descriptive complexity.