Mathematics : Logic

Presents a set of problem solving techniques for thinking about the puzzles and questions of mathematics. Each of the eight techniques is accompanied by practice questions to consolidate the skill. The book also contains 100 additional problems for students to attempt as their problem solving skills increase. more...

Price: $8.90

Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. - ;Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be. calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming. Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and. computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in Logic,. Mathematics, Philosophy, and Computer Science. - ;Mathematical Logic is crisply written and is a pleasure to read. ..Chiswell and Hodges' book is at the very top of the re more...

Price: $70.00

Presents chapters from selected logicians. This work provides an overview of open problems and perspectives in such fields as non-standard inferences in description logics, logic of provability, logical dynamics, and computability theory. It contains contributions concerning the role of logic. more...

Price: $195.00

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: $189.00

Preface, Cristopher Moore and David Griffeath. Self-Organized Construction in Sparse Random Arrays of Conway's Game of Life, Nicholas M. Gotts. Synthesis of Complex Life Objects from Gliders, Mark D. Niemiec. A Two-Dimensional Cellular Automaton Crystal with Irrational Density, David Griffeath and Dean Hickerson. Still Life Theory, Matthew Cook. Replicators and Larger-than-Life Examples, Kellie Michele Evans. Growth Phenomena in Cellular Automata, Janko Gravner. Constructive Molecular Dynamics Lattice Gases: Three-Dimensional Molecular Self-Assembly, Martin Nilsson, Steen Rasmussen, Bernd Mayer, and David Whitten. Simulating Digital Logic with the Reversible Aggregation Model of Crystal Growth, Raissa D'Souza, George E. Homsy, and Norman H. Margolus. Universal Cellular Automata Based on the Collisions of Soft Spheres, Norman H. Margolus. Emerging Markets and Persistent Inequality in a Nonlinear Voting Model, Nienke A. Oomes. Cellular Automata for Imaging, Art, and Video, Joy V. Hughes. Continuous-Valued Cellular Automata in Two Dimensions, Rudy Rucker. Phase Transition via Cellular Automata, Gadi Moran. Index more...

Price: $53.32