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Author : Georg Gottlob,Alexander Leitsch,Daniele Mundici
Publisher : Unknown
Page : 376 pages
File Size : 45,7 Mb
Release : 1993
Category : Automatic theorem proving
ISBN : UOM:39015033145890
"The Third Kurt G
Author : Georg Gottlob,Alexander Leitsch,Daniele Mundici
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 48,6 Mb
Release : 1997-08-13
Category : Computers
ISBN : 3540633855
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 : Georg Gottlob,Alexander Leitsch,Daniele Mundici
Publisher : Unknown
Page : 364 pages
File Size : 43,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662185571
Author : Jacob T. Schwartz,Domenico Cantone,Eugenio G. Omodeo
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 46,9 Mb
Release : 2011-07-16
Category : Computers
ISBN : 0857298089
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 : Torben Braüner
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 42,9 Mb
Release : 2010-11-17
Category : Philosophy
ISBN : 9789400700024
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 : Robert S. Boyer,J Strother Moore
Publisher : Academic Press
Page : 414 pages
File Size : 55,7 Mb
Release : 2014-06-25
Category : Mathematics
ISBN : 9781483277882
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 : Peter Clote,Jan Krajícek
Publisher : Clarendon Press
Page : 442 pages
File Size : 46,5 Mb
Release : 1993-05-06
Category : Mathematics
ISBN : 0198536909
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 : Georg Gottlob,Alexander Leitsch,Daniele Mundici
Publisher : Springer
Page : 354 pages
File Size : 45,6 Mb
Release : 2014-10-08
Category : Mathematics
ISBN : 3662183153
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,Stanley S. Wainer
Publisher : Cambridge University Press
Page : 480 pages
File Size : 42,9 Mb
Release : 2011-12-15
Category : Mathematics
ISBN : 9781139504164
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,Alexander Leitsch,Daniele Mundici
Publisher : Unknown
Page : 348 pages
File Size : 48,8 Mb
Release : 1997
Category : Automatic theorem proving
ISBN : 0354063855
Author : Ulrich Berger,Helmut Schwichtenberg
Publisher : Springer
Page : 448 pages
File Size : 53,5 Mb
Release : 2012-10-29
Category : Computers
ISBN : 3642636705
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 : Dieter Probst,Peter Schuster
Publisher : Walter de Gruyter GmbH & Co KG
Page : 384 pages
File Size : 42,9 Mb
Release : 2016-07-25
Category : Philosophy
ISBN : 9781501502644
A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.
Author : David J. Pym
Publisher : Springer Science & Business Media
Page : 323 pages
File Size : 47,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401700917
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 : Jean Goubault-Larrecq,I. Mackie
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 51,6 Mb
Release : 2001-11-30
Category : Computers
ISBN : 1402003684
Interest in computer applications has led to a new attitude to applied logic in which researchers tailor a logic in the same way they define a computer language. In response to this attitude, this text for undergraduate and graduate students discusses major algorithmic methodologies, and tableaux and resolution methods. The authors focus on first-order logic, the use of proof theory, and the computer application of automated searches for proofs of mathematical propositions. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Heinrich Wansing
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 52,5 Mb
Release : 2013-06-29
Category : Philosophy
ISBN : 9789401727983
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.