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| propositional calculus exercises: Propositional and Predicate Calculus: A Model of Argument Derek Goldrei, 2005-12-27 Designed specifically for guided independent study. Features a wealth of worked examples and exercises, many with full teaching solutions, that encourage active participation in the development of the material. It focuses on core material and provides a solid foundation for further study. |
| propositional calculus exercises: Mathematical Logic René Cori, Daniel Lascar, 2000 Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. It is a major element in theoretical computer science and has undergone a huge revival with the every- growing importance of computer science. This text is based on a course to undergraduates and provides a clear and accessible introduction to mathematical logic. The concept of model provides the underlying theme, giving the text a theoretical coherence whilst still covering a wide area of logic. The foundations having been laid in Part I, this book starts with recursion theory, a topic essential for the complete scientist. Then follows Godel's incompleteness theorems and axiomatic set theory. Chapter 8 provides an introduction to model theory. There are examples throughout each section, and varied selection of exercises at the end. Answers to the exercises are given in the appendix. |
| propositional calculus exercises: Mathematical Logic: Propositional calculus, Boolean algebras, predicate calculus René Cori, Daniel Lascar, 2000 The requirement to reason logically forms the basis of all mathematics, and hence mathematical logic is one of the most fundamental topics that students will study. Assuming no prior knowledge of the topic, this book provides an accessible introduction for advanced undergraduate students. |
| propositional calculus exercises: Introduction to Mathematical Logic Alonzo Church, 2016-03-02 Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today. Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic. Church was one of the principal founders of the Association for Symbolic Logic; he founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979 At his death in 1995, Church was still regarded as the greatest mathematical logician in the world. |
| propositional calculus exercises: Beginning Logic Edward John Lemmon, 1978-01-01 One of the most careful and intensive among the introductory texts that can be used with a wide range of students. It builds remarkably sophisticated technical skills, a good sense of the nature of a formal system, and a solid and extensive background for more advanced work in logic. . . . The emphasis throughout is on natural deduction derivations, and the text's deductive systems are its greatest strength. Lemmon's unusual procedure of presenting derivations before truth tables is very effective. --Sarah Stebbins, The Journal of Symbolic Logic |
| propositional calculus exercises: A Logical Approach to Discrete Math David Gries, Fred B. Schneider, 2013-03-14 This text attempts to change the way we teach logic to beginning students. Instead of teaching logic as a subject in isolation, we regard it as a basic tool and show how to use it. We strive to give students a skill in the propo sitional and predicate calculi and then to exercise that skill thoroughly in applications that arise in computer science and discrete mathematics. We are not logicians, but programming methodologists, and this text reflects that perspective. We are among the first generation of scientists who are more interested in using logic than in studying it. With this text, we hope to empower further generations of computer scientists and math ematicians to become serious users of logic. Logic is the glue Logic is the glue that binds together methods of reasoning, in all domains. The traditional proof methods -for example, proof by assumption, con tradiction, mutual implication, and induction- have their basis in formal logic. Thus, whether proofs are to be presented formally or informally, a study of logic can provide understanding. |
| propositional calculus exercises: Logic in Computer Science Michael Huth, Mark Ryan, 2004-08-26 Recent years have seen the development of powerful tools for verifying hardware and software systems, as companies worldwide realise the need for improved means of validating their products. There is increasing demand for training in basic methods in formal reasoning so that students can gain proficiency in logic-based verification methods. The second edition of this successful textbook addresses both those requirements, by continuing to provide a clear introduction to formal reasoning which is both relevant to the needs of modern computer science and rigorous enough for practical application. Improvements to the first edition have been made throughout, with extra and expanded sections on SAT solvers, existential/universal second-order logic, micro-models, programming by contract and total correctness. The coverage of model-checking has been substantially updated. Further exercises have been added. Internet support for the book includes worked solutions for all exercises for teachers, and model solutions to some exercises for students. |
| propositional calculus exercises: Foundations of Logic and Mathematics Yves Nievergelt, 2012-12-06 This modem introduction to the foundations of logic, mathematics, and computer science answers frequent questions that mysteriously remain mostly unanswered in other texts: • Why is the truth table for the logical implication so unintuitive? • Why are there no recipes to design proofs? • Where do these numerous mathematical rules come from? • What are the applications of formal logic and abstract mathematics? • What issues in logic, mathematics, and computer science still remain unresolved? Answers to such questions must necessarily present both theory and significant applica tions, which explains the length of the book. The text first shows how real life provides some guidance for the selection of axioms for the basis of a logical system, for instance, Boolean, classical, intuitionistic, or minimalistic logic. From such axioms, the text then derives de tailed explanations of the elements of modem logic and mathematics: set theory, arithmetic, number theory, combinatorics, probability, and graph theory, with applications to computer science. The motivation for such detail, and for the organization of the material, lies in a continuous thread from logic and mathematics to their uses in everyday life. |
| propositional calculus exercises: Applied Logic for Computer Scientists Mauricio Ayala-Rincón, Flávio L. C. de Moura, 2017-02-04 This book provides an introduction to logic and mathematical induction which are the basis of any deductive computational framework. A strong mathematical foundation of the logical engines available in modern proof assistants, such as the PVS verification system, is essential for computer scientists, mathematicians and engineers to increment their capabilities to provide formal proofs of theorems and to certify the robustness of software and hardware systems. The authors present a concise overview of the necessary computational and mathematical aspects of ‘logic’, placing emphasis on both natural deduction and sequent calculus. Differences between constructive and classical logic are highlighted through several examples and exercises. Without neglecting classical aspects of computational logic, the authors also highlight the connections between logical deduction rules and proof commands in proof assistants, presenting simple examples of formalizations of the correctness of algebraic functions and algorithms in PVS. Applied Logic for Computer Scientists will not only benefit students of computer science and mathematics but also software, hardware, automation, electrical and mechatronic engineers who are interested in the application of formal methods and the related computational tools to provide mathematical certificates of the quality and accuracy of their products and technologies. |
| propositional calculus exercises: Logical Structures for Representation of Knowledge and Uncertainty Ellen Hisdal, 2013-04-17 It is the business of science not to create laws, but to discover them. We do not originate the constitution of our own minds, greatly as it may be in our power to modify their character. And as the laws of the human intellect do not depend upon our will, so the forms of science, of (1. 1) which they constitute the basis, are in all essential regards independent of individual choice. George Boole [10, p. llJ 1. 1 Comparison with Traditional Logic The logic of this book is a probability logic built on top of a yes-no or 2-valued logic. It is divided into two parts, part I: BP Logic, and part II: M Logic. 'BP' stands for 'Bayes Postulate'. This postulate says that in the absence of knowl edge concerning a probability distribution over a universe or space one should assume 1 a uniform distribution. 2 The M logic of part II does not make use of Bayes postulate or of any other postulates or axioms. It relies exclusively on purely deductive reasoning following from the definition of probabilities. The M logic goes an important step further than the BP logic in that it can distinguish between certain types of information supply sentences which have the same representation in the BP logic as well as in traditional first order logic, although they clearly have different meanings (see example 6. 1. 2; also comments to the Paris-Rome problem of eqs. (1. 8), (1. 9) below). |
| propositional calculus exercises: Type Theory and Formal Proof Rob Nederpelt, Herman Geuvers, 2014-11-06 Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive nature of well-structured proofs. The authors begin with untyped lambda calculus and proceed to several fundamental type systems, including the well-known and powerful Calculus of Constructions. The book also covers the essence of proof checking and proof development, and the use of dependent type theory to formalise mathematics. The only prerequisite is a basic knowledge of undergraduate mathematics. Carefully chosen examples illustrate the theory throughout. Each chapter ends with a summary of the content, some historical context, suggestions for further reading and a selection of exercises to help readers familiarise themselves with the material. |
| propositional calculus exercises: Logic for Philosophy Theodore Sider, 2010-01-07 Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy. |
| propositional calculus exercises: Forall X P. D. Magnus, 2018-07-25 Forall x is an introduction to sentential logic and first-order predicate logic with identity, logical systems that significantly influenced twentieth-century analytic philosophy. After working through the material in this book, a student should be able to understand most quantified expressions that arise in their philosophical reading. This book treats symbolization, formal semantics, and proof theory for each language. The discussion of formal semantics is more direct than in many introductory texts. Although forall x does not contain proofs of soundness and completeness, it lays the groundwork for understanding why these are things that need to be proven. Throughout the book, I have tried to highlight the choices involved in developing sentential and predicate logic. Students should realize that these two are not the only possible formal languages. In translating to a formal language, we simplify and profit in clarity. The simplification comes at a cost, and different formal languages are suited to translating different parts of natural language. The book is designed to provide a semester's worth of material for an introductory college course. It would be possible to use the book only for sentential logic, by skipping chapters 4-5 and parts of chapter 6--Open Textbook Library |
| propositional calculus exercises: Logic, Mathematics, and Computer Science Yves Nievergelt, 2015-10-13 This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory. It also serves as an excellent independent study reference and resource for instructors. Adapted from Foundations of Logic and Mathematics: Applications to Science and Cryptography © 2002 Birkhӓuser, this second edition provides a modern introduction to the foundations of logic, mathematics, and computers science, developing the theory that demonstrates construction of all mathematics and theoretical computer science from logic and set theory. The focuses is on foundations, with specific statements of all the associated axioms and rules of logic and set theory, and provides complete details and derivations of formal proofs. Copious references to literature that document historical development is also provided. Answers are found to many questions that usually remain unanswered: Why is the truth table for logical implication so unintuitive? Why are there no recipes to design proofs? Where do these numerous mathematical rules come from? What issues in logic, mathematics, and computer science still remain unresolved? And the perennial question: In what ways are we going to use this material? Additionally, the selection of topics presented reflects many major accomplishments from the twentieth century and includes applications in game theory and Nash's equilibrium, Gale and Shapley's match making algorithms, Arrow's Impossibility Theorem in voting, to name a few. From the reviews of the first edition: ...All the results are proved in full detail from first principles...remarkably, the arithmetic laws on the rational numbers are proved, step after step, starting from the very definitions!...This is a valuable reference text and a useful companion for anybody wondering how basic mathematical concepts can be rigorously developed within set theory. —MATHEMATICAL REVIEWS Rigorous and modern in its theoretical aspect, attractive as a detective novel in its applied aspects, this paper book deserves the attention of both beginners and advanced students in mathematics, logic and computer sciences as well as in social sciences. —Zentralblatt MATH |
| propositional calculus exercises: Mathematical Logic for Computer Science Mordechai Ben-Ari, 2012-12-06 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. |
| propositional calculus exercises: A First Course in Logic Mark Verus Lawson, 2018-12-07 A First Course in Logic is an introduction to first-order logic suitable for first and second year mathematicians and computer scientists. There are three components to this course: propositional logic; Boolean algebras; and predicate/first-order, logic. Logic is the basis of proofs in mathematics — how do we know what we say is true? — and also of computer science — how do I know this program will do what I think it will? Surprisingly little mathematics is needed to learn and understand logic (this course doesn't involve any calculus). The real mathematical prerequisite is an ability to manipulate symbols: in other words, basic algebra. Anyone who can write programs should have this ability. |
| propositional calculus exercises: Intelligent Computing Kohei Arai, 2022-07-06 The book, “Intelligent Computing - Proceedings of the 2022 Computing Conference”, is a comprehensive collection of chapters focusing on the core areas of computing and their further applications in the real world. Each chapter is a paper presented at the Computing Conference 2022 held on July 14–15, 2022. Computing 2022 attracted a total of 498 submissions which underwent a double-blind peer-review process. Of those 498 submissions, 179 submissions have been selected to be included in this book. The goal of this conference is to give a platform to researchers with fundamental contributions and to be a premier venue for academic and industry practitioners to share new ideas and development experiences. We hope that readers find this book interesting and valuable as it provides the state-of-the-art intelligent methods and techniques for solving real-world problems. We also expect that the conference and its publications will be a trigger for further related research and technology improvements in this important subject. |
| propositional calculus exercises: Higher Education Computer Science Jenny Carter, Michael O'Grady, Clive Rosen, 2023-05-29 The march towards on-line and blended teaching—present before the Covid-19 pandemic—has been accelerated by it, and there is no going back. Students and staff may object, but the economic drive towards “greater productivity” will inevitably result in less face-to-face (f2f) instruction. Therefore, it is incumbent for those delivering this precious, in-person resource to make maximum use of time...which raises the question, “how”? The second edition of Higher Education Computer Science offers some potential answers. It also addresses other questions, such as “why have f2f teaching at all?” “what is the purpose of f2f?” and “what is the appropriate balance between the two?” The first edition began to offer suggestions for optimising limited opportunities to get together with students. Aligned with that, this unique new volume examines how to use the technology available to maximum advantage: For example, resources such as Moocs and other on-line instructional materials can provide invaluable pedagogic support. In addition, the book addresses ‘problem-based learning,’ using robotics in the teaching of programming, and a multidisciplinary approach to data science. Although it includes a chapter on distance learning, there is greater emphasis placed on the soft, transferable skills and employability skills that are best delivered in person. Further, the work provides several examples of putting theory into practice when teaching computer science at both undergraduate and postgraduate levels. Written by experienced practitioners, each chapter tackles a particular teaching activity or topic within computing, presented in such a way that other practitioners can use. As such, this new volume will be an invaluable resource to those who want to protect and optimise in-person teaching. |
| propositional calculus exercises: Current Trends in Theoretical Computer Science Gheorghe P?un, Arto Salomaa, 2001 The scientific developments at the end of the past millennium were dominated by the huge increase and diversity of disciplines with the common label computer science. The theoretical foundations of such disciplines have become known as theoretical computer science. This book highlights some key issues of theoretical computer science as they seem to us now, at the beginning of the new millennium. The text is based on columns and tutorials published in the Bulletin of the European Association for Theoretical Computer Science in the period 1995 -- 2000. The columnists themselves selected the material they wanted for the book, and the editors had a chance to update their work. Indeed, much of the material presented here appears in a form quite different from the original. Since the presentation of most of the articles is reader-friendly and does not presuppose much knowledge of the area, the book constitutes suitable supplementary reading material for various courses in computer science. |
| propositional calculus exercises: Discrete Mathematics James L. Hein, 2003 Winner at the 46th Annual New England Book Show (2003) in the College Covers & Jackets category This introduction to discrete mathematics prepares future computer scientists, engineers, and mathematicians for success by providing extensive and concentrated coverage of logic, functions, algorithmic analysis, and algebraic structures. Discrete Mathematics, Second Edition illustrates the relationships between key concepts through its thematic organization and provides a seamless transition between subjects. Distinct for the depth with which it covers logic, this text emphasizes problem solving and the application of theory as it carefully guides the reader from basic to more complex topics. Discrete Mathematics is an ideal resource for discovering the fundamentals of discrete math. Discrete Mathematics, Second Edition is designed for an introductory course in discrete mathematics for the prospective computer scientist, applied mathematician, or engineer who wants to learn how the ideas apply to computer sciences.The choice of topics-and the breadth of coverage-reflects the desire to provide students with the foundations needed to successfully complete courses at the upper division level in undergraduate computer science courses. This book differs in several ways from current books about discrete mathematics.It presents an elementary and unified introduction to a collection of topics that has not been available in a single source.A major feature of the book is the unification of the material so that it does not fragment into a collection of seemingly unrelated ideas. |
| propositional calculus exercises: The Structure of Typed Programming Languages David A. Schmidt, 1994 The text is unique in its tutorial presentation of higher-order lambda calculus and intuitionistic type theory. |
| propositional calculus exercises: Logic Nicholas J.J. Smith, 2012-04-01 Logic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an exceptionally clear introduction to classical logic, with a unique approach that emphasizes both the hows and whys of logic. Here Nicholas Smith thoroughly covers the formal tools and techniques of logic while also imparting a deeper understanding of their underlying rationales and broader philosophical significance. In addition, this is the only introduction to logic available today that presents all the major forms of proof--trees, natural deduction in all its major variants, axiomatic proofs, and sequent calculus. The book also features numerous exercises, with solutions available on an accompanying website. Logic is the ideal textbook for undergraduates and graduate students seeking a comprehensive and accessible introduction to the subject. Provides an essential introduction to classical logic Emphasizes the how and why of logic Covers both formal and philosophical issues Presents all the major forms of proof--from trees to sequent calculus Features numerous exercises, with solutions available at http://njjsmith.com/philosophy/lawsoftruth/ The ideal textbook for undergraduates and graduate students |
| propositional calculus exercises: A Spiral Workbook for Discrete Mathematics Harris Kwong, 2015-11-06 A Spiral Workbook for Discrete Mathematics covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions,relations, and elementary combinatorics, with an emphasis on motivation. The text explains and claries the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a nal polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a dierent perspective or at a higher level of complexity, in order to slowly develop the student's problem-solving and writing skills. |
| propositional calculus exercises: Models and Ultraproducts John Lane Bell, A. B. Slomson, 2006-01-01 In this text for first-year graduate students, the authors provide an elementary exposition of some of the basic concepts of model theory--focusing particularly on the ultraproduct construction and the areas in which it is most useful. The book, which assumes only that its readers are acquainted with the rudiments of set theory, starts by developing the notions of Boolean algebra, propositional calculus, and predicate calculus. Model theory proper begins in the fourth chapter, followed by an introduction to ultraproduct construction, which includes a detailed look at its theoretic properties. An overview of elementary equivalence provides algebraic descriptions of the elementary classes. Discussions of completeness follow, along with surveys of the work of Jónsson and of Morley and Vaught on homogeneous universal models, and the results of Keisler in connection with the notion of a saturated structure. Additional topics include classical results of Gödel and Skolem, and extensions of classical first-order logic in terms of generalized quantifiers and infinitary languages. Numerous exercises appear throughout the text. |
| propositional calculus exercises: Logic, Induction and Sets Thomas Forster, 2003-07-21 This is an introduction to logic and the axiomatization of set theory from a unique standpoint. Philosophical considerations, which are often ignored or treated casually, are here given careful consideration, and furthermore the author places the notion of inductively defined sets (recursive datatypes) at the center of his exposition resulting in a treatment of well established topics that is fresh and insightful. The presentation is engaging, but always great care is taken to illustrate difficult points. Understanding is also aided by the inclusion of many exercises. Little previous knowledge of logic is required of the reader, and only a background of standard undergraduate mathematics is assumed. |
| propositional calculus exercises: Computability Theory S. Barry Cooper, 2017-09-06 Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way. |
| propositional calculus exercises: The Calculus of Computation Aaron R. Bradley, Zohar Manna, 2007-09-18 Computational logic is a fast-growing field with applications in artificial intelligence, constraint solving, and the design and verification of software and hardware systems. Written with graduate and advanced undergraduate students in mind, this textbook introduces computational logic from the foundations of first-order logic to state-of-the-art decision procedures for arithmetic, data structures, and combination theories. This textbook also presents a logical approach to engineering correct software. The increasing ubiquity of computers makes implementing correct systems more important than ever. Verification exercises develop the reader's facility in specifying and verifying software using logic. The treatment of verification concludes with an introduction to the static analysis of software, an important component of modern verification systems. For readers interested in learning more about computational logic, decision procedures, verification, and other areas of formal methods, the final chapter outlines courses of further study. |
| propositional calculus exercises: A Mathematical Introduction to Logic Herbert B. Enderton, 2001-01-23 A Mathematical Introduction to Logic |
| propositional calculus exercises: An Algebraic Approach to Non-Classical Logics Lev D. Beklemishev, 2000-04-01 An Algebraic Approach to Non-Classical Logics |
| propositional calculus exercises: Logical Options John L. Bell, David DeVidi, Graham Solomon, 2001-03-30 Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some classical first-order logic and would like to learn about other logics important to their philosophical work. |
| propositional calculus exercises: Modal Logic for Philosophers James W. Garson, 2006-08-14 This 2006 book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications. |
| propositional calculus exercises: Propositional Logic Howard Pospesel, 1974 |
| propositional calculus exercises: Dynamic Logic David Harel, Dexter Kozen, Jerzy Tiuryn, 2000-09-29 This book provides the first comprehensive introduction to Dynamic Logic. Among the many approaches to formal reasoning about programs, Dynamic Logic enjoys the singular advantage of being strongly related to classical logic. Its variants constitute natural generalizations and extensions of classical formalisms. For example, Propositional Dynamic Logic (PDL) can be described as a blend of three complementary classical ingredients: propositional calculus, modal logic, and the algebra of regular events. In First-Order Dynamic Logic (DL), the propositional calculus is replaced by classical first-order predicate calculus. Dynamic Logic is a system of remarkable unity that is theoretically rich as well as of practical value. It can be used for formalizing correctness specifications and proving rigorously that those specifications are met by a particular program. Other uses include determining the equivalence of programs, comparing the expressive power of various programming constructs, and synthesizing programs from specifications. This book provides the first comprehensive introduction to Dynamic Logic. It is divided into three parts. The first part reviews the appropriate fundamental concepts of logic and computability theory and can stand alone as an introduction to these topics. The second part discusses PDL and its variants, and the third part discusses DL and its variants. Examples are provided throughout, and exercises and a short historical section are included at the end of each chapter. |
| propositional calculus exercises: Mathematical Structures for Computer Science Judith L. Gersting, 2014-03-01 Judith Gerstings Mathematical Structures for Computer Science has long been acclaimed for its clear presentation of essential concepts and its exceptional range of applications relevant to computer science majors. Now with this new edition, it is the first discrete mathematics textbook revised to meet the proposed new ACM/IEEE standards for the course. |
| propositional calculus exercises: Introduction to Logic Harry J. Gensler, 2012-08-06 Introduction to Logic combines likely the broadest scope of any logic textbook available with clear, concise writing and interesting examples and arguments. Its key features, all retained in the Second Edition, include: • simpler ways to test arguments than those available in competing textbooks, including the star test for syllogisms • a wide scope of materials, making it suitable for introductory logic courses (as the primary text) or intermediate classes (as the primary or supplementary book) • engaging and easy-to-understand examples and arguments, drawn from everyday life as well as from the great philosophers • a suitability for self-study and for preparation for standardized tests, like the LSAT • a reasonable price (a third of the cost of many competitors) • exercises that correspond to the LogiCola program, which may be downloaded for free from the web. This Second Edition also: • arranges chapters in a more useful way for students, starting with the easiest material and then gradually increasing in difficulty • provides an even broader scope with new chapters on the history of logic, deviant logic, and the philosophy of logic • expands the section on informal fallacies • includes a more exhaustive index and a new appendix on suggested further readings • updates the LogiCola instructional program, which is now more visually attractive as well as easier to download, install, update, and use. |
| propositional calculus exercises: Systems of Formal Logic L.H. Hackstaff, 2012-12-06 The present work constitutes an effort to approach the subject of symbol ic logic at the elementary to intermediate level in a novel way. The book is a study of a number of systems, their methods, their rela tions, their differences. In pursuit of this goal, a chapter explaining basic concepts of modern logic together with the truth-table techniques of definition and proof is first set out. In Chapter 2 a kind of ur-Iogic is built up and deductions are made on the basis of its axioms and rules. This axiom system, resembling a propositional system of Hilbert and Ber nays, is called P +, since it is a positive logic, i. e. , a logic devoid of nega tion. This system serves as a basis upon which a variety of further sys tems are constructed, including, among others, a full classical proposi tional calculus, an intuitionistic system, a minimum propositional calcu lus, a system equivalent to that of F. B. Fitch (Chapters 3 and 6). These are developed as axiomatic systems. By means of adding independent axioms to the basic system P +, the notions of independence both for primitive functors and for axiom sets are discussed, the axiom sets for a number of such systems, e. g. , Frege's propositional calculus, being shown to be non-independent. Equivalence and non-equivalence of systems are discussed in the same context. The deduction theorem is proved in Chapter 3 for all the axiomatic propositional calculi in the book. |
| propositional calculus exercises: Algebraic and Logic Programming Helene Kirchner, Wolfgang Wechler, 1990-09-20 This volume consists of papers presented at the Second International Conference on Algebraic and Logic Programming in Nancy, France, October 1-3, 1990. |
| propositional calculus exercises: Library of Congress Subject Headings Library of Congress, Library of Congress. Subject Cataloging Division, 1975 |
| propositional calculus exercises: Handbook of Test Problems in Local and Global Optimization Christodoulos A. Floudas, Panos M. Pardalos, Claire Adjiman, William R. Esposito, Zeynep H. Gümüs, Stephen T. Harding, John L. Klepeis, Clifford A. Meyer, Carl A. Schweiger, 2013-03-09 Significant research activities have taken place in the areas of local and global optimization in the last two decades. Many new theoretical, computational, algorithmic, and software contributions have resulted. It has been realized that despite these numerous contributions, there does not exist a systematic forum for thorough experimental computational testing and· evaluation of the proposed optimization algorithms and their implementations. Well-designed nonconvex optimization test problems are of major impor tance for academic and industrial researchers interested in algorithmic and software development. It is remarkable that eventhough nonconvex models dominate all the important application areas in engineering and applied sci ences, there is only a limited dass of reported representative test problems. This book reflects our long term efforts in designing a benchmark database and it is motivated primarily from the need for nonconvex optimization test problems. The present collection of benchmarks indudes test problems from literature studies and a large dass of applications that arise in several branches of engineering and applied science. |
| propositional calculus exercises: Mathematical Logic A. Lightstone, 2012-12-06 Before his death in March, 1976, A. H. Lightstone delivered the manu script for this book to Plenum Press. Because he died before the editorial work on the manuscript was completed, I agreed (in the fall of 1976) to serve as a surrogate author and to see the project through to completion. I have changed the manuscript as little as possible, altering certain passages to correct oversights. But the alterations are minor; this is Lightstone's book. H. B. Enderton vii Preface This is a treatment of the predicate calculus in a form that serves as a foundation for nonstandard analysis. Classically, the predicates and variables of the predicate calculus are kept distinct, inasmuch as no variable is also a predicate; moreover, each predicate is assigned an order, a unique natural number that indicates the length of each tuple to which the predicate can be prefixed. These restrictions are dropped here, in order to develop a flexible, expressive language capable of exploiting the potential of nonstandard analysis. To assist the reader in grasping the basic ideas of logic, we begin in Part I by presenting the propositional calculus and statement systems. This provides a relatively simple setting in which to grapple with the some times foreign ideas of mathematical logic. These ideas are repeated in Part II, where the predicate calculus and semantical systems are studied. |
What's the difference between predicate and propositional logic?
Propositional logic is an axiomatization of Boolean logic. As such predicate logic includes propositional logic. Both systems are known to be consistent, e.g. by exhibiting models in …
definition - Interpretations and models in propositional logic ...
A formula of propositional logic is true under an interpretation iff the interpretation assigns the truth value $\text T$ to that formula. If a formula is true under an interpretation, then that …
Propositional logic vs predicate logic: examples? - Mathematics …
The main similarity is that the tautologies and contradictions of propositional logic stay true in first-order logic. $\endgroup$ – MathNerd Commented Feb 24, 2016 at 17:12
How to demystify the axioms of propositional logic?
Laws like Pierce's law CCCpqpp come as a bit more difficult to explain intuitively, though here goes. First let's observe that the implicational propositional calculus can get axiomatized using …
Is a propositional function a proposition in propositional logic ...
Jul 7, 2024 · In mathematical logic, a proposition is defined as a declarative sentence that is either true or false, but not both. Two examples are '1 + 1 = 2' and 'Paris is the capital of France'. I …
discrete mathematics - Is it "propositional function" or simply ...
May 27, 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
logic - What is the difference between propositional constants ...
Sep 28, 2023 · Propositional constants represent some particular proposition, while propositional variables range over the set of all atomic propositions. Schemata, however, range over all …
How to translate "When" in propositional logic?
Oct 28, 2020 · I'm looking to understand how to represent "When" in a propositional logic. For example: 1: "I buy food when I get paid." Would the order of this matter, …
What is the logical operator for but? - Mathematics Stack Exchange
An alternative way of conveying the same information would be to say "I am fine and he has flu.".. Often, the word but is used in English to mean and, especially when there is some contrast or …
Is my translation of unless into propositional logic correct?
May 28, 2016 · I have the following sentences: I won't go the library unless I need a book p: I will go the library q: I need a book I replaced unless with if not as follows: I won't go the library if I …
What's the difference between predicate and propositional logic?
Propositional logic is an axiomatization of Boolean logic. As such predicate logic includes propositional logic. Both systems are known to be consistent, e.g. by exhibiting models in …
definition - Interpretations and models in propositional logic ...
A formula of propositional logic is true under an interpretation iff the interpretation assigns the truth value $\text T$ to that formula. If a formula is true under an interpretation, then that …
Propositional logic vs predicate logic: examples? - Mathematics …
The main similarity is that the tautologies and contradictions of propositional logic stay true in first-order logic. $\endgroup$ – MathNerd Commented Feb 24, 2016 at 17:12
How to demystify the axioms of propositional logic?
Laws like Pierce's law CCCpqpp come as a bit more difficult to explain intuitively, though here goes. First let's observe that the implicational propositional calculus can get axiomatized using …
Is a propositional function a proposition in propositional logic ...
Jul 7, 2024 · In mathematical logic, a proposition is defined as a declarative sentence that is either true or false, but not both. Two examples are '1 + 1 = 2' and 'Paris is the capital of France'. I …
discrete mathematics - Is it "propositional function" or simply ...
May 27, 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
logic - What is the difference between propositional constants ...
Sep 28, 2023 · Propositional constants represent some particular proposition, while propositional variables range over the set of all atomic propositions. Schemata, however, range over all …
How to translate "When" in propositional logic?
Oct 28, 2020 · I'm looking to understand how to represent "When" in a propositional logic. For example: 1: "I buy food when I get paid." Would the order of this matter, …
What is the logical operator for but? - Mathematics Stack Exchange
An alternative way of conveying the same information would be to say "I am fine and he has flu.".. Often, the word but is used in English to mean and, especially when there is some contrast or …
Is my translation of unless into propositional logic correct?
May 28, 2016 · I have the following sentences: I won't go the library unless I need a book p: I will go the library q: I need a book I replaced unless with if not as follows: I won't go the library if I …
