Lectures on the Logic of Computer Programming

This monograph deals with aspects of the computer programming process that involve techniques derived from mathematical logic.

Author: Zohar Manna

Publisher: SIAM

ISBN: 1611970385

Category: Computers

Page: 53

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This monograph deals with aspects of the computer programming process that involve techniques derived from mathematical logic. The author focuses on proving that a given program produces the intended result whenever it halts, that a given program will eventually halt, that a given program is partially correct and terminates, and that a system of rewriting rules always halts. Also, the author describes the intermediate behavior of a given program, and discusses constructing a program to meet a given specification.
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Ewa Or owska on Relational Methods in Logic and Computer Science

Comon, H. & Cortier, V. (2000). Flatness is not a weakness. In P. Clote & H. Schwichtenberg (Eds.), Proceedings of 14th Annual Conference of the Computer Science Logic, EACSL (Vol. 1862, pp. 262–276). Lecture Notes in Computer Science.

Author: Joanna Golińska-Pilarek

Publisher: Springer

ISBN: 9783319978796

Category: Philosophy

Page: 502

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This book is a tribute to Professor Ewa Orłowska, a Polish logician who was celebrating the 60th year of her scientific career in 2017. It offers a collection of contributed papers by different authors and covers the most important areas of her research. Prof. Orłowska made significant contributions to many fields of logic, such as proof theory, algebraic methods in logic and knowledge representation, and her work has been published in 3 monographs and over 100 articles in internationally acclaimed journals and conference proceedings. The book also includes Prof. Orłowska’s autobiography, bibliography and a trialogue between her and the editors of the volume, as well as contributors' biographical notes, and is suitable for scholars and students of logic who are interested in understanding more about Prof. Orłowska’s work.
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Logic and Computer Science

Meyer, A. R. [88 } Invited lecture at the 3rd IEEE Symposium on Logic in Computer Science, Edinburgh, July, 1988. Milner, R., [84] A proposal for standard ML, In : ACM Symposium on DISP and Functiona 1 Programming, 1984, pp.

Author: Steven Homer

Publisher: Springer

ISBN: 9783540471356

Category: Mathematics

Page: 170

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The courses given at the 1st C.I.M.E. Summer School of 1988 dealt with the main areas on the borderline between applied logic and theoretical computer science. These courses are recorded here in five expository papers: S. Homer: The Isomorphism Conjecture and its Generalization.- A. Nerode: Some Lectures on Intuitionistic Logic.- R.A. Platek: Making Computers Safe for the World. An Introduction to Proofs of Programs. Part I. - G.E. Sacks: Prolog Programming.- A. Scedrov: A Guide to Polymorphic Types.
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Lectures on the Curry Howard Isomorphism

The logical abstract machine: A Curry-Howard isomorphism for machine code. In A. Middledorp and T. Sato, editors, Functional and Logic Programming, volume 1722 of Lecture Notes in Computer Science, pages 300– 318. Springer-Verlag, 1999.

Author: Morten Heine Sørensen

Publisher: Elsevier

ISBN: 0080478921

Category: Mathematics

Page: 456

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The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc. But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transforms proofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq). This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features - The Curry-Howard Isomorphism treated as common theme - Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics - Thorough study of the connection between calculi and logics - Elaborate study of classical logics and control operators - Account of dialogue games for classical and intuitionistic logic - Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme. · Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics. · Elaborate study of classical logics and control operators. · Account of dialogue games for classical and intuitionistic logic. · Theoretical foundations of computer-assisted reasoning
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Logical Foundations of Computer Science

Hybrid Systems III , Lecture Notes in Computer Science 1066 ( Springer - Verlag , Berlin , 1996 ) , 76-100 . [ KJN96 ] Wolf Kohn , John James and Anil Nerode , " The Declarative Approach to the Design of Robust Control Systems ” ...

Author: Sergei Adian

Publisher: Springer Science & Business Media

ISBN: 3540630457

Category: Computers

Page: 429

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A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.
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First Order Programming Theories

SZAMALK Technical Report, Budapest Gergely, T., Üry, L. £ A uniform approach to programming logics. SZAMALK Technical Report, Budapest Goldblatt, R. [1982] Axiomatising the Logic of Computer Programming. Lecture Notes in Computer ...

Author: Tamas Gergely

Publisher: Springer Science & Business Media

ISBN: 9783642582059

Category: Computers

Page: 353

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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.
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Logic from Computer Science

McCarty, D. C. [1984], “Realizability and recursive mathematics”, Doctoral Dissertation, Computer Science ... Makkai, M. and G. Reyes [1977), “First order categorical logic”, Lecture Notes in Mathematics 611, Springer-Verlag, Berlin.

Author: Yiannis N. Moschovakis

Publisher: Springer Science & Business Media

ISBN: 9781461228226

Category: Mathematics

Page: 608

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The volume is the outgrowth of a workshop with the same title held at MSRI in the week of November 13-17, 1989, and for those who did not get it, Logic from Computer Science is the converse of Logic in Computer Science, the full name of the highly successful annual LICS conferences. We meant to have a conference which would bring together the LICS commu nity with some of the more traditional "mathematical logicians" and where the emphasis would be on the flow of ideas from computer science to logic rather than the other way around. In a LICS talk, sometimes, the speaker presents a perfectly good theorem about (say) the A-calculus or finite model theory in terms of its potential applications rather than its (often more ob vious) intrinsic, foundational interest and intricate proof. This is not meant to be a criticism; the LICS meetings are, after all, organized by the IEEE Computer Society. We thought, for once, it would be fun to see what we would get if we asked the speakers to emphasize the relevance of their work for logic rather than computer science and to point out what is involved in the proofs. I think, mostly, it worked. In any case, the group of people represented as broad a selection of logicians as I have seen in recent years, and the quality of the talks was (in my view) exceptionally, unusually high. I learned a lot and (I think) others did too.
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Lectures on Logic and Computation

Lecture Notes in Game Theory for Computer Scientists, pp. 185–212. Cambridge University Press (2011) Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 995–1072.

Author: Nick Bezhanishvili

Publisher: Springer

ISBN: 9783642314858

Category: Computers

Page: 265

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The European Summer School in Logic, Language and Information (ESSLLI) is organized every year by the Association for Logic, Language and Information (FoLLI) in different sites around Europe. The main focus of ESSLLI is on the interface between linguistics, logic and computation. ESSLLI offers foundational, introductory and advanced courses, as well as workshops, covering a wide variety of topics within the three areas of interest: Language and Computation, Language and Logic, and Logic and Computation. During two weeks, around 50 courses and 10 workshops are offered to the attendants, each of 1.5 hours per day during a five days week, with up to seven parallel sessions. ESSLLI also includes a student session (papers and posters by students only, 1.5 hour per day during the two weeks) and four evening lectures by senior scientists in the covered areas. The 6 course notes were carefully reviewed and selected. The papers are organized in topical sections on computational complexity, multi-agant systems, natural language processing, strategies in games and formal semantics.
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Geometric Computing Science

Manes , E. G. and Arbib , M. A .: Algebraic Approaches to Program Semantics , Springer - Verlag , New York , 1986 . 20. Manna , Z : Lectures on the Logic of Computer Programming , Society for Industrial and Applied Mathematics ...

Author: Robert Hermann

Publisher: Math Science Press

ISBN: 0915692414

Category: Computers

Page: 400

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Programming Languages Implementations Logics and Programs

Proceedings of the 17th Colloqium on Trees and Algebra in Programming ( CAAP'92 ) , Rennes , France , Lecture Notes in Computer Science 581 , Springer - Verlag , Berlin , pp . 300-322 .

Author: Manuel Hermenegildo

Publisher: Springer Science & Business Media

ISBN: 354060359X

Category: Computers

Page: 476

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This book constitutes the proceedings of the Seventh International Symposium on Programming Languages: Implementations, Logics and Programs, PLILP '95, held in Utrecht, The Netherlands, in September 1995. The book presents 26 refereed full papers selected from 84 submissions; they report research on declarative programming languages and provide insights in the relation between the logic of those languages, implementation techniques, and the use of these languages in constructing real programs. In addition there are abstracts or full presentations of three invited talks as well as eight posters and demonstrations.
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