Computational Logic and Proof Theory
Author: Georg Gottlob
Publisher:
Published: 1993
Total Pages: 376
ISBN-13:
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Computational Logic and Set Theory
Author: Jacob T. Schwartz
Publisher: Springer Science & Business Media
Published: 2011-07-16
Total Pages: 426
ISBN-13: 0857298089
DOWNLOAD EBOOK →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.
Computational Logic and Proof Theory
Author: Georg Gottlob
Publisher: Springer Science & Business Media
Published: 1997-08-13
Total Pages: 364
ISBN-13: 9783540633853
DOWNLOAD EBOOK →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.
A Computational Logic
Author: Robert S. Boyer
Publisher: Academic Press
Published: 2014-06-25
Total Pages: 414
ISBN-13: 1483277887
DOWNLOAD EBOOK →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.
Computational Logic and Proof Theory
Author: Georg Gottlob
Publisher:
Published: 2014-01-15
Total Pages: 364
ISBN-13: 9783662185575
DOWNLOAD EBOOK →Computational Logic and Proof Theory
Author: Georg Gottlob
Publisher: Springer
Published: 2014-10-08
Total Pages: 354
ISBN-13: 9783662183151
DOWNLOAD EBOOK →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.
Arithmetic, Proof Theory, and Computational Complexity
Author: Peter Clote
Publisher: Clarendon Press
Published: 1993-05-06
Total Pages: 442
ISBN-13: 9780198536901
DOWNLOAD EBOOK →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.
Computational Logic
Author: Ulrich Berger
Publisher: Springer
Published: 2012-10-29
Total Pages: 448
ISBN-13: 9783642636707
DOWNLOAD EBOOK →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).
Hybrid Logic and its Proof-Theory
Author: Torben Braüner
Publisher: Springer Science & Business Media
Published: 2010-11-17
Total Pages: 240
ISBN-13: 9400700024
DOWNLOAD EBOOK →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).
Computational Logic and Proof Theory
