Mathematical Logic

e-books in Mathematical Logic category

Actual Causality
by Joseph Y. Halpern - The MIT Press , 2016
In this book, Joseph Halpern explores actual causality, and such related notions as degree of responsibility, degree of blame, and causal explanation. The goal is to arrive at a definition of causality that matches our natural language usage.
(5975 views)

Topics in Logic and Foundations
by Stephen G. Simpson - The Pennsylvania State University , 2005
This is a set of lecture notes from a 15-week graduate course at the Pennsylvania State University. The course covered some topics which are important in contemporary mathematical logic and foundations but usually omitted from introductory courses.
(5654 views)

A Friendly Introduction to Mathematical Logic
by Christopher C. Leary, Lars Kristiansen - Milne Library Publishing , 2015
In this book, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study.
(9201 views)

What is Mathematics: Gödel's Theorem and Around
by Karlis Podnieks - University of Latvia , 2013
Textbook for students in mathematical logic and foundations of mathematics. Contents: Platonism, intuition and the nature of mathematics; Axiomatic Set Theory; First Order Arithmetic; Hilbert's Tenth Problem; Incompleteness Theorems; Godel's Theorem.
(8140 views)

Introduction to Mathematical Logic
by Vilnis Detlovs, Karlis Podnieks - University of Latvia , 2014
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).
(11584 views)

Logic for Computer Science
- Wikibooks , 2010
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.
(10664 views)

Natural Topology
by Frank Waaldijk - arXiv , 2012
We give a theoretical and applicable framework for dealing with real-world phenomena. Joining pointwise and pointfree notions in BISH, natural topology gives a faithful idea of important concepts and results in intuitionism.
(9687 views)

Logic for Computer Scientists
by Uli Furbach - Wikibooks , 2010
This book is intended for computer scientists and it assumes only some basic mathematical notions like relations and orderings. The aim was to create an interactive script where logics can be experienced by interaction and experimentation.
(10658 views)

Logics of Time and Computation
by Robert Goldblatt - Center for the Study of Language , 1992
Sets out the basic theory of normal modal and temporal propositional logics, applies this theory to logics of discrete, dense, and continuous time, to the temporal logic of henceforth, next, and until, and to the dynamic logic of regular programs.
(11376 views)

Intuitionistic Logic
by Nick Bezhanishvili, Dick de Jongh - Universiteit van Amsterdam , 2010
In this course we give an introduction to intuitionistic logic. We concentrate on the propositional calculus mostly, make some minor excursions to the predicate calculus and to the use of intuitionistic logic in intuitionistic formal systems.
(14382 views)

Lectures on Linear Logic
by A. S. Troelstra - CSLI , 1992
This text deals with logical formalism, cut-elimination, the embedding of intuitionistic logic in classical linear logic, proofnets for the multiplicative fragment and the algorithmic interpretation of cut-elimination in proofnets.
(13046 views)

A Second Course in Logic
by Christopher Gauker - University of Cincinnati , 2013
This book is for anyone who has had a solid introductory logic course and wants more. Topics covered include soundness and completeness for first-order logic, Tarski's theorem on the undefinability of truth, Godel's incompleteness theorems, etc.
(12942 views)

Notes on the Science of Logic
by Nuel Belnap - University of Pittsburgh , 2009
This course assumes you know how to use truth functions and quantifiers as tools. Our task here is to study these very tools. Contents: logic of truth functional connectives; first order logic of extensional predicates, operators, and quantifiers.
(11500 views)

The Art of Logic
by Nuel Belnap - University of Pittsburgh , 2009
Contents: Grammar; The art of the logic of truth-functional connectives; Quantifier proofs; A modicum of set theory; Symbolizing English quantifiers; Quantifier semantics - interpretation and counterexample; Theories; Definitions.
(14158 views)

An Introduction to Mathematical Logic
by Wolfram Pohlers, Thomas Glass , 1992
This text treats pure logic and in this connection introduces to basic proof-theoretic techniques. Fundamentals of model theory and those of recursion theory are dealt with. Furthermore, some extensions of first order logic are treated.
(13281 views)

Symbolic Logic: A Second Course
by Gary Hardegree - UMass Amherst , 2003
Contents: Summary; Translations in Function Logic; Derivations in Function Logic; Translations in Identity Logic; Extra Material on Identity Logic; Derivations in Identity Logic; Translations in Description Logic; Derivations in Description Logic.
(14372 views)

Symbolic Logic: A First Course
by Gary Hardegree - Mcgraw-Hill College , 1999
Contents: Basic Concepts of Logic; Truth-Functional Connectives; Validity in Sentential Logic; Translations in Sentential Logic; Derivations in Sentential Logic; Translations in Monadic Predicate Logic; Translations in Polyadic Predicate Logic; etc.
(17366 views)

Algebraic Logic
by H. Andreka, I. Nemeti, I. Sain , 2003
Part I of the book studies algebras which are relevant to logic. Part II deals with the methodology of solving logic problems by (i) translating them to algebra, (ii) solving the algebraic problem, and (iii) translating the result back to logic.
(17890 views)

The Principles Of Mathematics
by Bertrand Russell - W. W. Norton & Company
Russell's classic sets forth his landmark thesis that mathematics and logic are identical -- that what is called mathematics is simply later deductions from logical premises. His ideas have had a profound influence on the foundations of mathematics.
(14464 views)

A Concise Introduction to Mathematical Logic
by Wolfgang Rautenberg - Springer , 2009
A well-written introduction to the beautiful and coherent subject. It contains classical material such as logical calculi, beginnings of model theory, and Goedel's incompleteness theorems, as well as some topics motivated by applications.
(14601 views)

Introduction to Mathematical Logic: A problem solving course
by Arnold W. Miller - arXiv , 1996
This is a set of questions written for a course in Mathematical Logic. Topics covered are: propositional logic; axioms of ZFC; wellorderings and equivalents of AC; ordinal and cardinal arithmetic; first order logic, and the compactness theorem; etc.
(14447 views)

The Algebra of Logic
by Louis Couturat - Project Gutenberg , 2004
Mathematical Logic is a necessary preliminary to logical Mathematics. The present work is concerned with the 'calculus ratiocinator' aspect, and shows, in an admirably succinct form, the beauty of the calculus of logic regarded as an algebra.
(13068 views)

The Haskell Road to Logic, Maths and Programming
by Kees Doets, Jan van Eijck - College Publications , 2004
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.
(20320 views)

Formal Logic
- Wikibooks , 2009
An undergraduate college level textbook covering first order predicate logic with identity but omitting metalogical proofs. The first rules of formal logic were written over 2300 years ago by Aristotle and are still vital.
(15041 views)

Introduction to Mathematical Philosophy
by Bertrand Russell - University of Massachusetts Amherst , 2009
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.
(15430 views)

Mathematical Logic
by Stephen G. Simpson - Pennsylvania State University , 2013
Lecture notes for all mathematics graduate students. The text covers propositional calculus, predicate calculus, proof systems, extensions of the predicate calculus, theories, definability, interpretability, arithmetization and incompleteness.
(16871 views)

Logic For Everyone
by Robert A. Herrmann , 2006
This is Robert Herrmann's elementary book in mathematical logic that includes all basic material in the predicate and propositional calculus presented in a unique manner. Neither proof requires specialized mathematical procedures.
(16651 views)

forall x: An Introduction to Formal Logic
by P.D. Magnus , 2008
An introduction to sentential logic and first-order predicate logic with identity, logical systems that influenced twentieth-century analytic philosophy. The book should help students understand quantified expressions in their philosophical reading.
(18432 views)

Predicative Arithmetic
by Edward Nelson - Princeton Univ Pr , 1987
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.
(18250 views)

A Problem Course in Mathematical Logic
by Stefan Bilaniuk , 2003
An introduction to mathematical logic for undergraduates. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is to learn the material by solving the problems.
(21875 views)