Computational Logic And Set Theory

Author: Jacob T. Schwartz
Publisher: Springer Science & Business Media
ISBN: 9780857298089
Size: 43.62 MB
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This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory. Topics and features: describes in depth how a specific first-order theory can be exploited to model and carry out reasoning in branches of computer science and mathematics; presents an unique system for automated proof verification in large-scale software systems; integrates important proof-engineering issues, reflecting the goals of large-scale verifiers; includes an appendix showing formalized proofs of ordinals, of various properties of the transitive closure operation, of finite and transfinite induction principles, and of Zorn’s lemma.

An Introduction To The Technique Of Formative Processes In Set Theory

Author: Domenico Cantone
Publisher: Springer
ISBN: 3319747789
Size: 41.12 MB
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This book presents an intuitive picture-oriented approach to the formative processes technique and to its applications. In the first part the authors introduce basic set-theoretic terminology and properties, the decision problem in set theory, and formative processes. The second part of the book is devoted to applications of the technique of formative processes to decision problems. All chapters contain exercises and the book is appropriate for researchers and graduate students in the area of computer science logic.

From Linear Operators To Computational Biology

Author: Martin Davis
Publisher: Springer Science & Business Media
ISBN: 1447142829
Size: 10.75 MB
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In his rich and varied career as a mathematician, computer scientist, and educator, Jacob T. Schwartz wrote seminal works in analysis, mathematical economics, programming languages, algorithmics, and computational geometry. In this volume of essays, his friends, students, and collaborators at the Courant Institute of Mathematical Sciences present recent results in some of the fields that Schwartz explored: quantum theory, the theory and practice of programming, program correctness and decision procedures, dextrous manipulation in Robotics, motion planning, and genomics. In addition to presenting recent results in these fields, these essays illuminate the astonishingly productive trajectory of a brilliant and original scientist and thinker.

Mathematical Logic For Computer Science

Author: Mordechai Ben-Ari
Publisher: Springer Science & Business Media
ISBN: 1447141296
Size: 57.93 MB
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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 students of computer science. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and easy to understand. The uniform use of tableaux-based techniques facilitates learning advanced logical systems based on what the student has learned from elementary systems. The logical systems presented are: propositional logic, first-order logic, resolution and its application to logic programming, Hoare logic for the verification of sequential programs, and linear temporal logic for the verification of concurrent programs. The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking.

Handbook Of Logic And Language

Author: Johan F.A.K. van Benthem
Publisher: Elsevier
ISBN: 9780444537270
Size: 52.63 MB
Format: PDF
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The logical study of language is becoming more interdisciplinary, playing a role in fields such as computer science, artificial intelligence, cognitive science and game theory. This new edition, written by the leading experts in the field, presents an overview of the latest developments at the interface of logic and linguistics as well as a historical perspective. It is divided into three parts covering Frameworks, General Topics and Descriptive Themes. Completely revised and updated - includes over 25% new material Discusses the interface between logic and language Many of the authors are creators or active developers of the theories

Applied Logic For Computer Scientists

Author: Mauricio Ayala-Rincón
Publisher: Springer
ISBN: 3319516531
Size: 49.26 MB
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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.

Meaning Logic And Ludics

Author: Alain Lecomte
Publisher: World Scientific
ISBN: 1908978244
Size: 35.94 MB
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This book presents several recent advances in natural language semantics and explores the boundaries between syntax and semantics over the last two decades. It is based on some of the most recent theories in logic, such as linear logic and ludics, first created by Jean-Yves Girard, and it also provides some sharp analyses of computational semantical representations, explaining advanced theories in theoretical computer sciences, such as the lambda–mu and Lambek–Grishin calculi which were applied by Philippe de Groote and Michael Moortgat. The author also looks at Aarne Ranta's ‘proof as meaning’ approach, which was first based on Martin–Löf's Type Theory. Meaning, Logic and Ludics surveys the many solutions which have been proposed for the syntax–semantics interface, taking into account the specifications of linguistic signs (continuous or discontinuous) and the fundamental mechanisms developed by linguists and notable Generativists. This pioneering publication also presents ludics (in a chapter co-authored with Myriam Quatrini), a framework which allows us to characterize meaning as an invariant with regard to interaction between processes. It is an excellent book for advanced students, and academics alike, in the field of computational linguistics. Contents:Truth-Conditional Meaning:Compositional Approaches and BindingDerivationalismLogic:Deductive SystemsCurry–Howard CorrespondenceProof Theory Applied to Linguistics:Using the Lambek Calculus and Its VariantsGrammatical ReasoningA Type-Theoretical Version of Minimalist GrammarsGrammars in Deductive FormsContinuations and ContextsProofs as MeaningsLudics:Interaction and DialogueThe Future in Conclusion Readership: Graduates, postdoctorates, academics in the computation linguistics/logic/mathematics/bioinformatics and computational biology/genetics fields. Keywords:Natural Language;Semantics;Logic for Language;Ludics and Applications;Continuation Theory;Proof Theory and Natural Language;Linear Logic and ApplicationsKey Features:The first didactic presentation of LudicsThe first applications of Ludics to this topicThe first didactic presentation of the use of continuationsOffers well-supported philosophical viewpoint on topicsReviews:“This book presents a large part of the ongoing research on linguistics and proof theory, as developed by the author and also by some other researchers. The very interesting content, previously unavailable in book form, is made intuitive and pleasant to read. Linguists, who are familiar with the questions but not their formal treatment, will enjoy the book, especially the linguistically oriented explanations on logical systems. Logicians, and especially proof theorists, will be convinced of the relevance of their domain to natural language semantics, and at the same time, they will be offered a gentle introduction to some active topics in linguistic research.”Mathematical Reviews