Elementary Logic With Applications

Elementary Logic with Applications is written for undergraduate logic and logic programming courses. Logic has been applied to a wide variety of subjects such as software engineering and hardware design, to programming and artificial intelligence. In this way, it has served to stimulate the search for clear conceptual foundations. Recently many extensions of classical logic such as temporal, modal, relevance, fuzzy and non-monotonic logics have been widely used in computer science, therefore requiring a new formulation of classic logic which can be modified to yield the effect of non-classical logics. This text aims to introduce classical logic in such a way that one can easily deviate into discussing non-classical logics. It defines a number of different types of logics and the differences between them, starting with the basic notions of the most common logic. Elementary Logic with Applications develops a theorem prover for classical logic in a way that maintains a procedural point of view and presents the reader with the real challenges facing applied logic. Dov Gabbay and Odinaldo Rodrigues have been teaching logic and computer science for many years. Dov Gabbay has written numerous other titles on the subject of logic and is a world authority on non-classical logics. Odinaldo Rodrigues is widely known for his work on logic, belief revision and argumentation. The "Elementary Logic with Applications" course is currently taught at the Department of Informatics, King's College London.

This lucid, non-intimidating presentation by a Russian scholar explores propositional logic, propositional calculus, and predicate logic. Topics include computer science and systems analysis, linguistics, and problems in the foundations of mathematics. Accessible to high school students, it also constitutes a valuable review of fundamentals for professionals. 1970 edition.

In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the re cent dramatic growth in the applications oflogic to computer science. Thus, our choice oftopics has been heavily influenced by such applications. Of course, we cover the basic traditional topics: syntax, semantics, soundnes5, completeness and compactness as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much ofour book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic especially in its application to Logic Programming and PRO LOG. We deal extensively with the mathematical foundations ofall three ofthese subjects. In addition, we include two chapters on nonclassical logics - modal and intuitionistic - that are becoming increasingly important in computer sci ence. We develop the basic material on the syntax and semantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method in troduced for classical logic. We indicate how it can easily be adapted to various other special types of modal logics. A number of more advanced topics (includ ing nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.

The ability to reason correctly is critical to most aspects of computer science and to software development in particular. This book teaches readers how to better reason about software development, to communicate reasoning, to distinguish between good and bad reasoning, and to read professional literature that presumes knowledge of elementary logic. The reader’s knowledge and understanding can be assessed through numerous examples and exercises. This book provides a reader-friendly foundation to logic and offers valuable insight into the topic, thereby serving as a helpful reference for practitioners, as well as students studying software development.

Much revised since its first appearance in 1941, Willard Van Orman Quine’s Elementary Logic, despite its brevity, is notable for its scope and rigor. It provides a single strand of simple techniques for the central business of modern logic. Basic formal concepts are explained, the paraphrasing of words into symbols is treated at some length, and a testing procedure is given for truth-function logic along with a complete proof procedure for the logic of quantifiers. Fully one third of this revised edition is new, and presents a nearly complete turnover in crucial techniques of testing and proving, some change of notation, and some updating of terminology. The study is intended primarily as a convenient encapsulation of minimum essentials, but concludes by giving brief glimpses of further matters.

Now much revised since its first appearance in 1941, this book, despite its brevity, is notable for its scope and rigor. It provides a single strand of simple techniques for the central business of modern logic. Basic formal concepts are explained, the paraphrasing of words into symbols is treated at some length, and a testing procedure is given for truth-function logic along with a complete proof procedure for the logic of quantifiers. Fully one third of this revised edition is new, and presents a nearly complete turnover in crucial techniques of testing and proving, some change of notation, and some updating of terminology. The study is intended primarily as a convenient encapsulation of minimum essentials, but concludes by giving brief glimpses of further matters.

Elementary Logic explains what logic is, how it is done, and why it can be exciting. The book covers the central part of logic that all students have to learn: propositional logic. It aims to provide a crystal-clear introduction to what is often regarded as the most technically difficult area in philosophy. The book opens with an explanation of what logic is and how it is constructed. Subsequent chapters take the reader step-by-step through all aspects of elementary logic. Throughout, ideas are explained simply and directly, with the chapters packed with overviews, illustrative examples, and summaries. Each chapter builds on previous explanation and example, with the final chapters presenting more advanced methods. After a discussion of meta-logic and logical systems, the book closes with an exploration of how paradoxes can exist in the world of logic. Elementary Logic's clarity and engagement make it ideal for any reader studying logic for the first time.

Two conferences, Logic and Its Applications in Algebra and Geometry and Combinatorial Set Theory, Excellent Classes, and Schanuel Conjecture, were held at the University of Michigan (Ann Arbor). These events brought together model theorists and set theorists working in these areas. This volume is the result of those meetings. It is suitable for graduate students and researchers working in mathematical logic.