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First-Order Dynamic Logic

First-Order Dynamic Logic
Author: D. Harel
Publisher:
Total Pages: 152
Release: 2014-01-15
Genre:
ISBN: 9783662174500

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First-Order Dynamic Logic

First-Order Dynamic Logic
Author: David Harel
Publisher: Lecture Notes in Computer Science
Total Pages: 156
Release: 1979
Genre: Computers
ISBN:

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Dynamic Logic

Dynamic Logic
Author: David Harel
Publisher: MIT Press
Total Pages: 492
Release: 2000-09-29
Genre: Computers
ISBN: 9780262263023

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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.


Extensions of First-Order Logic

Extensions of First-Order Logic
Author: Maria Manzano
Publisher: Cambridge University Press
Total Pages: 414
Release: 1996-03-29
Genre: Computers
ISBN: 9780521354356

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An introduction to many-sorted logic as an extension of first-order logic.


Deductive Software Verification – The KeY Book

Deductive Software Verification – The KeY Book
Author: Wolfgang Ahrendt
Publisher: Springer
Total Pages: 714
Release: 2016-12-19
Genre: Computers
ISBN: 3319498126

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Static analysis of software with deductive methods is a highly dynamic field of research on the verge of becoming a mainstream technology in software engineering. It consists of a large portfolio of - mostly fully automated - analyses: formal verification, test generation, security analysis, visualization, and debugging. All of them are realized in the state-of-art deductive verification framework KeY. This book is the definitive guide to KeY that lets you explore the full potential of deductive software verification in practice. It contains the complete theory behind KeY for active researchers who want to understand it in depth or use it in their own work. But the book also features fully self-contained chapters on the Java Modeling Language and on Using KeY that require nothing else than familiarity with Java. All other chapters are accessible for graduate students (M.Sc. level and beyond). The KeY framework is free and open software, downloadable from the book companion website which contains also all code examples mentioned in this book.


FIRST-ORDER DYNAMIC LOGIC

FIRST-ORDER DYNAMIC LOGIC
Author: David Harel
Publisher:
Total Pages: 133
Release: 1979
Genre:
ISBN:

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First-Order Programming Theories

First-Order Programming Theories
Author: Tamas Gergely
Publisher: Springer Science & Business Media
Total Pages: 342
Release: 2012-12-06
Genre: Computers
ISBN: 3642582052

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This work presents a purely classical first-order logical approach to the field of study in theoretical computer science sometimes referred to as the theory of programs, or programming theory. This field essentially attempts to provide a precise mathematical basis for the common activities involved in reasoning about computer programs and programming languages, and it also attempts to find practical applications in the areas of program specification, verification and programming language design. Many different approaches with different mathematical frameworks have been proposed as a basis for programming theory. They differ in the mathe matical machinery they use to define and investigate programs and program properties and they also differ in the concepts they deal with to understand the programming paradigm. Different approaches use different tools and viewpoints to characterize the data environment of programs. Most of the approaches are related to mathe matical logic and they provide their own logic. These logics, however, are very eclectic since they use special entities to reflect a special world of programs, and also, they are usually incomparable with each other. This Babel's mess irritated us and we decided to peel off the eclectic com ponents and try to answer all the questions by using classical first-order logic.


First-Order Logic

First-Order Logic
Author: Raymond R. Smullyan
Publisher: Springer Science & Business Media
Total Pages: 167
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642867189

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Except for this preface, this study is completely self-contained. It is intended to serve both as an introduction to Quantification Theory and as an exposition of new results and techniques in "analytic" or "cut-free" methods. We use the term "analytic" to apply to any proof procedure which obeys the subformula principle (we think of such a procedure as "analysing" the formula into its successive components). Gentzen cut-free systems are perhaps the best known example of ana lytic proof procedures. Natural deduction systems, though not usually analytic, can be made so (as we demonstrated in [3]). In this study, we emphasize the tableau point of view, since we are struck by its simplicity and mathematical elegance. Chapter I is completely introductory. We begin with preliminary material on trees (necessary for the tableau method), and then treat the basic syntactic and semantic fundamentals of propositional logic. We use the term "Boolean valuation" to mean any assignment of truth values to all formulas which satisfies the usual truth-table conditions for the logical connectives. Given an assignment of truth-values to all propositional variables, the truth-values of all other formulas under this assignment is usually defined by an inductive procedure. We indicate in Chapter I how this inductive definition can be made explicit-to this end we find useful the notion of a formation tree (which we discuss earlier).


First Order Logic

First Order Logic
Author: Fouad Sabry
Publisher: One Billion Knowledgeable
Total Pages: 163
Release: 2023-06-25
Genre: Computers
ISBN:

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What Is First Order Logic First-order logic is a collection of formal systems that are utilized in the fields of mathematics, philosophy, linguistics, and computer science. Other names for first-order logic include predicate logic, quantificational logic, and first-order predicate calculus. In first-order logic, quantified variables take precedence over non-logical objects, and the use of sentences that contain variables is permitted. As a result, rather than making assertions like "Socrates is a man," one can make statements of the form "there exists x such that x is Socrates and x is a man," where "there exists" is a quantifier and "x" is a variable. This is in contrast to propositional logic, which does not make use of quantifiers or relations; propositional logic serves as the basis for first-order logic in this sense. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: First-order logic Chapter 2: Axiom Chapter 3: Propositional calculus Chapter 4: Peano axioms Chapter 5: Universal quantification Chapter 6: Conjunctive normal form Chapter 7: Consistency Chapter 8: Zermelo–Fraenkel set theory Chapter 9: Interpretation (logic) Chapter 10: Quantifier rank (II) Answering the public top questions about first order logic. (III) Real world examples for the usage of first order logic in many fields. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of first order logic.