Beginning Logic
by E. J. Lemmon
from Hackett Pub Co Inc
The aim of this book is to provide an exposition of elementary formal logic. The course, which is primarily intended for first-year students who have no previous knowledge of the subject, forms a working basis for more advanced reading and is presented in such a way as to be intelligible to the layman. The nature of logic is examined with the gradual introduction of worked samples showing how to distinguish the sound statement from the unsound. Arguments whose soundness cannot be proved by propositional calculus are discussed, and it is shown how formalization can reveal the logical form of arguments. The final section of the book deals with the application of the predicate calculus as applied in various other fields of logic.
Elements of Deductive Inference: An Introduction to Symbolic Logic
by Joseph Bessie
from Wadsworth Publishing
The text covers elementary logic, from statement logic through relational logic with identity and function symbols. The authors acquaint students with formal techniques at a level appropriate for undergraduates, but extends far enough and deep enough into the subject that it is suitable for a brief first-year graduate course. The text covers full and brief truth tables, and presents the method of truth (consistency) trees and natural deduction for the whole of elementary logic. The text's organization allows instructors to cover just statement logic, or statement logic combined with various extensions into predicate logic: monadic logic with or without identity, or the preceding plus relational logic with or without identity and with or without function symbols. At each stage, the instructor may elect to pursue truth trees and/or natural deduction. A final chapter provides a perspective for further study and applications of logic. The text may be used with or without the accompanying software.
Propositional and Predicate Calculus: A Model of Argument
by Derek Goldrei
from Springer
At the heart of the justification for the reasoning used in modern mathematics lies the completeness theorem for predicate calculus. This unique textbook covers two entirely different ways of looking at such reasoning. Topics include:
- the representation of mathematical statements by formulas in a formal language;
- the interpretation of formulas as true or false in a mathematical structure;
- logical consequence of one formula from others;
- formal proof;
- the soundness and completeness theorems connecting logical consequence and formal proof;
- the axiomatization of some mathematical theories using a formal language;
- the compactness theorem and an introduction to model theory.
This book is designed for self-study by students, as well as for taught courses, using principles successfully developed by the Open University and used across the world. It includes exercises embedded within the text with full solutions to many of these. In addition there are a number of exercises without answers so that students studying under the guidance of a tutor may be assessed on the basis of what has been taught.
Some experience of axiom-based mathematics is required but no previous experience of logic. Propositional and Predicate Calculus gives students the basis for further study of mathematical logic and the use of formal languages in other subjects.
Derek Goldrei is Senior Lecturer and Staff Tutor at the Open University and part-time Lecturer in Mathematics at Mansfield College, Oxford, UK.
Mathematical Logic for Computer Science
by Mordechai Ben-Ari
from Springer
Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. To provide a balanced treatment of logic, tableaux are related to deductive proof systems.
The logical systems presented are:
- Propositional calculus (including binary decision diagrams);
- Predicate calculus;
- Resolution;
- Hoare logic;
- Z;
- Temporal logic.
Answers to exercises (for instructors only) as well as Prolog source code for algorithms may be found via the Springer London web site: http://www.springer.com/978-1-85233-319-5
Mordechai Ben-Ari is an associate professor in the Department of Science Teaching of the Weizmann Institute of Science. He is the author of numerous textbooks on concurrency, programming languages and logic, and has developed software tools for teaching concurrency. In 2004, Ben-Ari received the ACM/SIGCSE Award for Outstanding Contributions to Computer Science Education.
A categorical view of weakest liberal preconditions (Research report RC. International Business Machine Inc. Research Division)
A logical-form and knowledge-base design for natural language generation (ISI reprint series. University of Southern California. Information Sciences Institute)
Model-theoretic methods in methodology of propositional calculi
Digital formulation and computational methods for some aspects of the functional calculus of symbolic logic (Technical memorandum / Johns Hopkins University, Operations Research Office)
Can fair choice be added to Dijkstra's calculus (SRC reports)
Single axioms for the classical equivalential calculus (University of Auckland. Dept. of Mathematics. Report series)
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