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Author : Georg Gottlob
Publisher :
ISBN 13 :
Total Pages : 376 pages
Book Rating : 4.3/5 (91 download)
Download or read book Computational Logic and Proof Theory written by Georg Gottlob and published by . This book was released on 1993 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Third Kurt G
Author : Georg Gottlob
Publisher : Springer Science & Business Media
ISBN 13 : 9783540633853
Total Pages : 364 pages
Book Rating : 4.6/5 (338 download)
Download or read book Computational Logic and Proof Theory written by Georg Gottlob and published by Springer Science & Business Media. This book was released on 1997-08-13 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory, KGC '97, held in Vienna, Austria, in August 1997. The volume presents 20 revised full papers selected from 38 submitted papers. Also included are seven invited contributions by leading experts in the area. The book documents interdisciplinary work done in the area of computer science and mathematical logics by combining research on provability, analysis of proofs, proof search, and complexity.
Author : Jacob T. Schwartz
Publisher : Springer Science & Business Media
ISBN 13 : 9780857298089
Total Pages : 416 pages
Book Rating : 4.2/5 (98 download)
Download or read book Computational Logic and Set Theory written by Jacob T. Schwartz and published by Springer Science & Business Media. This book was released on 2011-07-16 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Georg Gottlob
Publisher :
ISBN 13 : 9783662185575
Total Pages : 364 pages
Book Rating : 4.1/5 (855 download)
Download or read book Computational Logic and Proof Theory written by Georg Gottlob and published by . This book was released on 2014-01-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Torben Braüner
Publisher : Springer Science & Business Media
ISBN 13 : 9400700024
Total Pages : 231 pages
Book Rating : 4.4/5 (7 download)
Download or read book Hybrid Logic and its Proof-Theory written by Torben Braüner and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).
Author : Peter Clote
Publisher : Clarendon Press
ISBN 13 : 9780198536901
Total Pages : 442 pages
Book Rating : 4.5/5 (369 download)
Download or read book Arithmetic, Proof Theory, and Computational Complexity written by Peter Clote and published by Clarendon Press. This book was released on 1993-05-06 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book principally concerns the rapidly growing area of "Logical Complexity Theory", the study of bounded arithmetic, propositional proof systems, length of proof, etc and relations to computational complexity theory. Additional features of the book include (1) the transcription and translation of a recently discovered 1956 letter from K Godel to J von Neumann, asking about a polynomial time algorithm for the proof in k-symbols of predicate calculus formulas (equivalent to the P-NP question), (2) an OPEN PROBLEM LIST consisting of 7 fundamental and 39 technical questions contributed by many researchers, together with a bibliography of relevant references.
Author : Robert S. Boyer
Publisher : Academic Press
ISBN 13 : 1483277887
Total Pages : 414 pages
Book Rating : 4.4/5 (832 download)
Download or read book A Computational Logic written by Robert S. Boyer and published by Academic Press. This book was released on 2014-06-25 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: ACM Monograph Series: A Computational Logic focuses on the use of induction in proving theorems, including the use of lemmas and axioms, free variables, equalities, and generalization. The publication first elaborates on a sketch of the theory and two simple examples, a precise definition of the theory, and correctness of a tautology-checker. Topics include mechanical proofs, informal development, formal specification of the problem, well-founded relations, natural numbers, and literal atoms. The book then examines the use of type information to simplify formulas, use of axioms and lemmas as rewrite rules, and the use of definitions. Topics include nonrecursive functions, computing values, free variables in hypothesis, infinite backwards chaining, infinite looping, computing type sets, and type prescriptions. The manuscript takes a look at rewriting terms and simplifying clauses, eliminating destructors and irrelevance, using equalities, and generalization. Concerns include reasons for eliminating isolated hypotheses, precise statement of the generalization heuristic, restricting generalizations, precise use of equalities, and multiple destructors and infinite looping. The publication is a vital source of data for researchers interested in computational logic.
Author : Georg Gottlob
Publisher : Springer
ISBN 13 : 9783662183151
Total Pages : 354 pages
Book Rating : 4.1/5 (831 download)
Download or read book Computational Logic and Proof Theory written by Georg Gottlob and published by Springer. This book was released on 2014-10-08 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Third Kurt G|del Symposium, KGC'93, held in Brno, Czech Republic, August1993, is the third in a series of biennial symposia on logic, theoretical computer science, and philosophy of mathematics. The aim of this meeting wasto bring together researchers working in the fields of computational logic and proof theory. While proof theory traditionally is a discipline of mathematical logic, the central activity in computational logic can be foundin computer science. In both disciplines methods were invented which arecrucial to one another. This volume contains the proceedings of the symposium. It contains contributions by 36 authors from 10 different countries. In addition to 10 invited papers there are 26 contributed papers selected from over 50 submissions.
Author : Helmut Schwichtenberg
Publisher : Cambridge University Press
ISBN 13 : 1139504169
Total Pages : 480 pages
Book Rating : 4.1/5 (395 download)
Download or read book Proofs and Computations written by Helmut Schwichtenberg and published by Cambridge University Press. This book was released on 2011-12-15 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.
Author : Georg Gottlieb
Publisher :
ISBN 13 : 9780354063852
Total Pages : 348 pages
Book Rating : 4.0/5 (638 download)
Download or read book Computational Logic and Proof Theory written by Georg Gottlieb and published by . This book was released on 1997 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David J. Pym
Publisher : Springer Science & Business Media
ISBN 13 : 9401700915
Total Pages : 323 pages
Book Rating : 4.4/5 (17 download)
Download or read book The Semantics and Proof Theory of the Logic of Bunched Implications written by David J. Pym and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Heinrich Wansing
Publisher : Springer Science & Business Media
ISBN 13 : 9401727988
Total Pages : 317 pages
Book Rating : 4.4/5 (17 download)
Download or read book Proof Theory of Modal Logic written by Heinrich Wansing and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.
Author : Alexandre Rademaker
Publisher : Springer Science & Business Media
ISBN 13 : 1447140028
Total Pages : 106 pages
Book Rating : 4.4/5 (471 download)
Download or read book A Proof Theory for Description Logics written by Alexandre Rademaker and published by Springer Science & Business Media. This book was released on 2012-05-17 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Description Logics (DLs) is a family of formalisms used to represent knowledge of a domain. They are equipped with a formal logic-based semantics. Knowledge representation systems based on description logics provide various inference capabilities that deduce implicit knowledge from the explicitly represented knowledge. A Proof Theory for Description Logics introduces Sequent Calculi and Natural Deduction for some DLs (ALC, ALCQ). Cut-elimination and Normalization are proved for the calculi. The author argues that such systems can improve the extraction of computational content from DLs proofs for explanation purposes.
Author : Ulrich Berger
Publisher : Springer
ISBN 13 : 9783642636707
Total Pages : 448 pages
Book Rating : 4.6/5 (367 download)
Download or read book Computational Logic written by Ulrich Berger and published by Springer. This book was released on 2012-10-29 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent developments in computer science clearly show the need for a better theoretical foundation for some central issues. Methods and results from mathematical logic, in particular proof theory and model theory, are of great help here and will be used much more in future than previously. This book provides an excellent introduction to the interplay of mathematical logic and computer science. It contains extensively reworked versions of the lectures given at the 1997 Marktoberdorf Summer School by leading researchers in the field. Topics covered include: proof theory and specification of computation (J.-Y. Girard, D. Miller), complexity of proofs and programs (S. R. Buss, S. S. Wainer), computational content of proofs (H. Schwichtenberg), constructive type theory (P. Aczel, H. Barendregt, R. L. Constable), computational mathematics, (U. Martin), rewriting logic (J. Meseguer), and game semantics (S. Abramski).
Author : Leonard Bolc
Publisher : Routledge
ISBN 13 : 1000507319
Total Pages : 207 pages
Book Rating : 4.0/5 (5 download)
Download or read book Time & Logic written by Leonard Bolc and published by Routledge. This book was released on 2019-10-24 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1995 Time and Logic examines understanding and application of temporal logic, presented in computational terms. The emphasis in the book is on presenting a broad range of approaches to computational applications. The techniques used will also be applicable in many cases to formalisms beyond temporal logic alone, and it is hoped that adaptation to many different logics of program will be facilitated. Throughout, the authors have kept implementation-orientated solutions in mind. The book begins with an introduction to the basic ideas of temporal logic. Successive chapters examine particular aspects of the temporal theoretical computing domain, relating their applications to familiar areas of research, such as stochastic process theory, automata theory, established proof systems, model checking, relational logic and classical predicate logic. This is an essential addition to the library of all theoretical computer scientists. It is an authoritative work which will meet the needs both of those familiar with the field and newcomers to it.
Author : Mauricio Ayala-Rincón
Publisher : Springer
ISBN 13 : 3319516531
Total Pages : 150 pages
Book Rating : 4.3/5 (195 download)
Download or read book Applied Logic for Computer Scientists written by Mauricio Ayala-Rincón and published by Springer. This book was released on 2017-02-04 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Peter M. Schuster
Publisher : Springer Nature
ISBN 13 : 3030302296
Total Pages : 391 pages
Book Rating : 4.0/5 (33 download)
Download or read book Well-Quasi Orders in Computation, Logic, Language and Reasoning written by Peter M. Schuster and published by Springer Nature. This book was released on 2020-01-01 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.
