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Author: Andrew M. Pitts
Publisher: Cambridge University Press
ISBN: 0521580579
Category : Computers
Languages : en
Pages : 375
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Book Description
The aim of this volume is to present modern developments in semantics and logics of computation in a way that is accessible to graduate students. The book is based on a summer school at the Isaac Newton Institute and consists of a sequence of linked lecture course by international authorities in the area. The whole set have been edited to form a coherent introduction to these topics, most of which have not been presented pedagogically before.
Author: Andrew M. Pitts
Publisher: Cambridge University Press
ISBN: 0521580579
Category : Computers
Languages : en
Pages : 375
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Book Description
The aim of this volume is to present modern developments in semantics and logics of computation in a way that is accessible to graduate students. The book is based on a summer school at the Isaac Newton Institute and consists of a sequence of linked lecture course by international authorities in the area. The whole set have been edited to form a coherent introduction to these topics, most of which have not been presented pedagogically before.
Author: Zhe Hou
Publisher: Springer Nature
ISBN: 3030878821
Category : Computers
Languages : en
Pages : 225
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Book Description
This textbook aims to help the reader develop an in-depth understanding of logical reasoning and gain knowledge of the theory of computation. The book combines theoretical teaching and practical exercises; the latter is realised in Isabelle/HOL, a modern theorem prover, and PAT, an industry-scale model checker. I also give entry-level tutorials on the two software to help the reader get started. By the end of the book, the reader should be proficient in both software. Content-wise, this book focuses on the syntax, semantics and proof theory of various logics; automata theory, formal languages, computability and complexity. The final chapter closes the gap with a discussion on the insight that links logic with computation. This book is written for a high-level undergraduate course or a Master's course. The hybrid skill set of practical theorem proving and model checking should be helpful for the future of readers should they pursue a research career or engineering in formal methods.
Author: Theodore Hailperin
Publisher: Rowman & Littlefield
ISBN: 1611460107
Category : Mathematics
Languages : en
Pages : 124
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Book Description
The present study is an extension of the topic introduced in Dr. Hailperin's Sentential Probability Logic, where the usual true-false semantics for logic is replaced with one based more on probability, and where values ranging from 0 to 1 are subject to probability axioms. Moreover, as the word "sentential" in the title of that work indicates, the language there under consideration was limited to sentences constructed from atomic (not inner logical components) sentences, by use of sentential connectives ("no," "and," "or," etc.) but not including quantifiers ("for all," "there is"). An initial introduction presents an overview of the book. In chapter one, Halperin presents a summary of results from his earlier book, some of which extends into this work. It also contains a novel treatment of the problem of combining evidence: how does one combine two items of interest for a conclusion-each of which separately impart a probability for the conclusion-so as to have a probability for the conclusion basedon taking both of the two items of interest as evidence? Chapter two enlarges the Probability Logic from the first chapter in two respects: the language now includes quantifiers ("for all," and "there is") whose variables range over atomic sentences, notentities as with standard quantifier logic. (Hence its designation: ontological neutral logic.) A set of axioms for this logic is presented. A new sentential notion-the suppositional-in essence due to Thomas Bayes, is adjoined to this logic that later becomes the basis for creating a conditional probability logic. Chapter three opens with a set of four postulates for probability on ontologically neutral quantifier language. Many properties are derived and a fundamental theorem is proved, namely, for anyprobability model (assignment of probability values to all atomic sentences of the language) there will be a unique extension of the probability values to all closed sentences of the language. The chapter concludes by showing the Borel's early denumerableprobability concept (1909) can be justified by its being, in essence, close to Hailperin's probability result applied to denumerable language. The final chapter introduces the notion of conditional-probability to a language having quantifiers of the kind
Author: Glynn Winskel
Publisher: MIT Press
ISBN: 9780262731034
Category : Computers
Languages : en
Pages : 388
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Book Description
The Formal Semantics of Programming Languages provides the basic mathematical techniques necessary for those who are beginning a study of the semantics and logics of programming languages. These techniques will allow students to invent, formalize, and justify rules with which to reason about a variety of programming languages. Although the treatment is elementary, several of the topics covered are drawn from recent research, including the vital area of concurency. The book contains many exercises ranging from simple to miniprojects.Starting with basic set theory, structural operational semantics is introduced as a way to define the meaning of programming languages along with associated proof techniques. Denotational and axiomatic semantics are illustrated on a simple language of while-programs, and fall proofs are given of the equivalence of the operational and denotational semantics and soundness and relative completeness of the axiomatic semantics. A proof of Godel's incompleteness theorem, which emphasizes the impossibility of achieving a fully complete axiomatic semantics, is included. It is supported by an appendix providing an introduction to the theory of computability based on while-programs. Following a presentation of domain theory, the semantics and methods of proof for several functional languages are treated. The simplest language is that of recursion equations with both call-by-value and call-by-name evaluation. This work is extended to lan guages with higher and recursive types, including a treatment of the eager and lazy lambda-calculi. Throughout, the relationship between denotational and operational semantics is stressed, and the proofs of the correspondence between the operation and denotational semantics are provided. The treatment of recursive types - one of the more advanced parts of the book - relies on the use of information systems to represent domains. The book concludes with a chapter on parallel programming languages, accompanied by a discussion of methods for specifying and verifying nondeterministic and parallel programs.
Author: David J. Pym
Publisher: Springer Science & Business Media
ISBN: 9401700915
Category : Mathematics
Languages : en
Pages : 323
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Book Description
This is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: • Resources as a basis for semantics; • Proof-search as a basis for reasoning; and • The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts.
Author: Eric Pacuit
Publisher: Springer
ISBN: 3319671499
Category : Philosophy
Languages : en
Pages : 165
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Book Description
This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic (the so-called non-normal modal logics). In addition, the book discusses a broad range of topics, including standard modal logic results (i.e., completeness, decidability and definability); bisimulations for neighborhood models and other model-theoretic constructions; comparisons with other semantics for modal logic (e.g., relational models, topological models, plausibility models); neighborhood semantics for first-order modal logic, applications in game theory (coalitional logic and game logic); applications in epistemic logic (logics of evidence and belief); and non-normal modal logics with dynamic modalities. The book can be used as the primary text for seminars on philosophical logic focused on non-normal modal logics; as a supplemental text for courses on modal logic, logic in AI, or philosophical logic (either at the undergraduate or graduate level); or as the primary source for researchers interested in learning about the uses of neighborhood semantics in philosophical logic and game theory.
Author: Simon Gay
Publisher: Cambridge University Press
ISBN: 052151374X
Category : Computers
Languages : en
Pages : 497
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Book Description
Explores quantum computation from the perspective of the branch of theoretical computer science known as semantics.
Author: Mordechai Ben-Ari
Publisher: Springer Science & Business Media
ISBN: 1447103351
Category : Computers
Languages : en
Pages : 311
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Book Description
This is a mathematics textbook with theorems and proofs. 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. In order to provide a balanced treatment of logic, tableaux are related to deductive proof systems. The book presents various logical systems and contains exercises. Still further, Prolog source code is available on an accompanying Web site. The author is an Associate Professor at the Department of Science Teaching, Weizmann Institute of Science.
Author: Sergei Artemov
Publisher: Cambridge University Press
ISBN: 1108424910
Category : Mathematics
Languages : en
Pages : 271
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Book Description
Develops a new logic paradigm which emphasizes evidence tracking, including theory, connections to other fields, and sample applications.
Author: M. Nivat
Publisher: CUP Archive
ISBN: 9780521267939
Category : Computers
Languages : en
Pages : 664
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Book Description
This book, which contains contributions from leading researchers in France, USA and Great Britain, gives detailed accounts of a variety of methods for describing the semantics of programming languages, i.e. for attaching to programs mathematical objects that encompass their meaning. Consideration is given to both denotational semantics, where the meaning of a program is regarded as a function from inputs to outputs, and operational semantics, where the meaning includes the sequence of states or terms generated internally during the computation. The major problems considered include equivalence relations between operational and denotational semantics, rules for obtaining optimal computations (especially for nondeterministic programs), equivalence of programs, meaning-preserving transformations of programs and program proving by assertions. Such problems are discussed for a variety of programming languages and formalisms, and a wealth of mathematical tools is described.
