[PDF] Deduction Systems eBook

Author : Rolf Socher-Ambrosius
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 39,6 MB
Release : 2012-12-06
Category : Computers
ISBN : 1461222664

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The idea of mechanizing deductive reasoning can be traced all the way back to Leibniz, who proposed the development of a rational calculus for this purpose. But it was not until the appearance of Frege's 1879 Begriffsschrift-"not only the direct ancestor of contemporary systems of mathematical logic, but also the ancestor of all formal languages, including computer programming languages" ([Dav83])-that the fundamental concepts of modern mathematical logic were developed. Whitehead and Russell showed in their Principia Mathematica that the entirety of classical mathematics can be developed within the framework of a formal calculus, and in 1930, Skolem, Herbrand, and Godel demonstrated that the first-order predicate calculus (which is such a calculus) is complete, i. e. , that every valid formula in the language of the predicate calculus is derivable from its axioms. Skolem, Herbrand, and GOdel further proved that in order to mechanize reasoning within the predicate calculus, it suffices to Herbrand consider only interpretations of formulae over their associated universes. We will see that the upshot of this discovery is that the validity of a formula in the predicate calculus can be deduced from the structure of its constituents, so that a machine might perform the logical inferences required to determine its validity. With the advent of computers in the 1950s there developed an interest in automatic theorem proving.

Author : Andrzej Indrzejczak
Publisher : Springer Science & Business Media
Page : 515 pages
File Size : 33,53 MB
Release : 2010-07-03
Category : Philosophy
ISBN : 9048187850

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This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.

Author : Daniel Bonevac
Publisher : Wiley-Blackwell
Page : 528 pages
File Size : 44,54 MB
Release : 2002-11-22
Category : Philosophy
ISBN : 9780631227106

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Deduction is an efficient and elegant presentation of classical first-order logic. It presents a truth tree system based on the work of Jeffrey, as well as a natural deduction system inspired by that of Kalish and Montague. Efficient and elegant presentation of classical first-order logic. Presents a truth tree system based on the work of Jeffrey, as well as a natural deduction system inspired by that of Kalish and Montague. Contains detailed, yet accessible chapters on extensions and revisions of classical logic: modal logic, many-valued logic, fuzzy logic, intuitionistic logic, counterfactuals, deontic logic, common sense reasoning, and quantified modal logic. Includes problem sets, designed to lead students gradually from easier to more difficult problems. Further information and select answers to problems available here: http://bonevac.info/deduction/About_the_Book.html

Author : Ruy J. G. B. de Queiroz
Publisher : World Scientific
Page : 299 pages
File Size : 11,18 MB
Release : 2012
Category : Computers
ISBN : 9814360953

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This comprehensive book provides an adequate framework to establish various calculi of logical inference. Being an ?enriched? system of natural deduction, it helps to formulate logical calculi in an operational manner. By uncovering a certain harmony between a functional calculus on the labels and a logical calculus on the formulas, it allows mathematical foundations for systems of logic presentation designed to handle meta-level features at the object-level via a labelling mechanism, such as the D Gabbay's Labelled Deductive Systems. The book truly demonstrates that introducing ?labels? is useful to understand the proof-calculus itself, and also to clarify its connections with model-theoretic interpretations.

Author : Wolfgang Bibel
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 16,32 MB
Release : 2013-03-09
Category : Philosophy
ISBN : 940170435X

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1. BASIC CONCEPTS OF INTERACTIVE THEOREM PROVING Interactive Theorem Proving ultimately aims at the construction of powerful reasoning tools that let us (computer scientists) prove things we cannot prove without the tools, and the tools cannot prove without us. Interaction typi cally is needed, for example, to direct and control the reasoning, to speculate or generalize strategic lemmas, and sometimes simply because the conjec ture to be proved does not hold. In software verification, for example, correct versions of specifications and programs typically are obtained only after a number of failed proof attempts and subsequent error corrections. Different interactive theorem provers may actually look quite different: They may support different logics (first-or higher-order, logics of programs, type theory etc.), may be generic or special-purpose tools, or may be tar geted to different applications. Nevertheless, they share common concepts and paradigms (e.g. architectural design, tactics, tactical reasoning etc.). The aim of this chapter is to describe the common concepts, design principles, and basic requirements of interactive theorem provers, and to explore the band width of variations. Having a 'person in the loop', strongly influences the design of the proof tool: proofs must remain comprehensible, - proof rules must be high-level and human-oriented, - persistent proof presentation and visualization becomes very important.

Author : W. V. QUINE
Publisher : Harvard University Press
Page : 144 pages
File Size : 27,38 MB
Release : 2009-06-30
Category : Philosophy
ISBN : 0674042492

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Now much revised since its first appearance in 1941, this book, despite its brevity, is notable for its scope and rigor. It provides a single strand of simple techniques for the central business of modern logic. Basic formal concepts are explained, the paraphrasing of words into symbols is treated at some length, and a testing procedure is given for truth-function logic along with a complete proof procedure for the logic of quantifiers. Fully one third of this revised edition is new, and presents a nearly complete turnover in crucial techniques of testing and proving, some change of notation, and some updating of terminology. The study is intended primarily as a convenient encapsulation of minimum essentials, but concludes by giving brief glimpses of further matters.

Author : Mark Jago
Publisher : Oxford University Press
Page : 369 pages
File Size : 16,78 MB
Release : 2018
Category : Philosophy
ISBN : 0198823819

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Mark Jago offers a new metaphysical account of truth. He argues that to be true is to be made true by the existence of a suitable worldly entity. Truth arises as a relation between a proposition - the content of our sayings, thoughts, beliefs, and so on - and an entity (or entities) in the world.

Author : Glenford J. Myers
Publisher : John Wiley & Sons
Page : 254 pages
File Size : 34,14 MB
Release : 2004-07-22
Category : Reference
ISBN : 047167835X

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This long-awaited revision of a bestseller provides a practical discussion of the nature and aims of software testing. You'll find the latest methodologies for the design of effective test cases, including information on psychological and economic principles, managerial aspects, test tools, high-order testing, code inspections, and debugging. Accessible, comprehensive, and always practical, this edition provides the key information you need to test successfully, whether a novice or a working programmer. Buy your copy today and end up with fewer bugs tomorrow.