Table Of Content

Logic for Computer Science and Artificial Intelligence Logic for Computer Science and Artificial Intelligence Ricardo Caferra First published 2011 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd John Wiley & Sons, Inc. 27-37 St George’s Road 111 River Street London SW19 4EU Hoboken, NJ 07030 UK USA www.iste.co.uk www.wiley.com © ISTE Ltd 2011 The rights of Ricardo Caferra to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. ____________________________________________________________________________________ Library of Congress Cataloging-in-Publication Data Caferra, Ricardo, 1945- Logic for computer science and artificial intelligence / Ricardo Caferra. p. cm. Includes bibliographical references and index. ISBN 978-1-84821-301-2 1. Computer logic. 2. Artificial intelligence. I. Title. QA76.9.L63C34 2011 006.3--dc23 2011014705 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-84821-301-2 Printed and bound in Great Britain by CPI Antony Rowe, Chippenham and Eastbourne. Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Chapter1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. Logic,foundationsofcomputerscience,andapplications oflogictocomputerscience . . . . . . . . . . . . . . . . . . . . . . . 1 1.2. Ontheutilityoflogicforcomputerengineers. . . . . . . . . . . . . . 3 Chapter2.AFewThoughtsBeforetheFormalization . . . . . . . . . . . 7 2.1. Whatislogic? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1. Logicandparadoxes . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.2. Paradoxesandsettheory . . . . . . . . . . . . . . . . . . . . . . 9 2.1.2.1. Theanswer . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.3. Paradoxesinarithmeticandsettheory . . . . . . . . . . . . . . 13 2.1.3.1. Thehaltingproblem. . . . . . . . . . . . . . . . . . . . . . 13 2.1.4. Onformalismsandwell-knownnotions. . . . . . . . . . . . . . 15 2.1.4.1. Some“well-known”notionsthatcouldturnout tobedifficulttoanalyze . . . . . . . . . . . . . . . . . . . 19 2.1.5. Backtothedefinitionoflogic . . . . . . . . . . . . . . . . . . . 23 2.1.5.1. Somedefinitionsoflogicforall . . . . . . . . . . . . . . . 24 2.1.5.2. Afewmoretechnicaldefinitions. . . . . . . . . . . . . . . 24 2.1.5.3. Theoryandmeta-theory(languageand meta-language) . . . . . . . . . . . . . . . . . . . . . . . . 30 2.1.6. Afewthoughtsaboutlogicandcomputerscience . . . . . . . . 30 2.2. Somehistoriclandmarks . . . . . . . . . . . . . . . . . . . . . . . . . 32 Chapter3.PropositionalLogic . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.1. Syntaxandsemantics . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.1.1. Languageandmeta-language . . . . . . . . . . . . . . . . . . . 43 vi LogicforComputerScienceandArtificialIntelligence 3.1.2. Transformationrulesforcnfanddnf . . . . . . . . . . . . . . . 49 3.2. Themethodofsemantictableaux. . . . . . . . . . . . . . . . . . . . . 54 3.2.1. Aslightlydifferentformalism: signedtableaux . . . . . . . . . 58 3.3. Formalsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.3.1. Acapitalnotion: thenotionofproof . . . . . . . . . . . . . . . 64 3.3.2. Whatdowelearnfromthewaywedomathematics? . . . . . . 72 3.4. AformalsystemforPL(PC) . . . . . . . . . . . . . . . . . . . . . . . 78 3.4.1. Somepropertiesofformalsystems . . . . . . . . . . . . . . . . 84 3.4.2. AnotherformalsystemforPL(PC) . . . . . . . . . . . . . . . . 86 3.4.3. Anotherformalsystem . . . . . . . . . . . . . . . . . . . . . . . 86 3.5. ThemethodofDavisandPutnam . . . . . . . . . . . . . . . . . . . . 92 3.5.1. TheDavis–PutnammethodandtheSATproblem . . . . . . . . 95 3.6. SemantictreesinPL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.7. TheresolutionmethodinPL . . . . . . . . . . . . . . . . . . . . . . . 101 3.8. Problems,strategies,andstatements . . . . . . . . . . . . . . . . . . . 109 3.8.1. Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 3.9. Hornclauses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.10.Algebraicpointofviewofpropositionallogic . . . . . . . . . . . . . 114 Chapter4.First-orderTerms . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.1. Matchingandunification . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.1.1. Amotivationforsearchingforamatchingalgorithm . . . . . . 121 4.1.2. Aclassificationoftrees . . . . . . . . . . . . . . . . . . . . . . . 123 4.2. First-orderterms,substitutions,unification . . . . . . . . . . . . . . . 125 Chapter5.First-OrderLogic(FOL)orPredicateLogic(PL1,PC1) . . . 131 5.1. Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.2. Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 5.2.1. Thenotionsoftruthandsatisfaction. . . . . . . . . . . . . . . . 139 5.2.2. Avariant: multi-sortedstructures . . . . . . . . . . . . . . . . . 150 5.2.2.1. Expressivepower,sortreduction. . . . . . . . . . . . . . . 150 5.2.3. Theoriesandtheirmodels . . . . . . . . . . . . . . . . . . . . . 152 5.2.3.1. HowcanwereasoninFOL? . . . . . . . . . . . . . . . . . 153 5.3. SemantictableauxinFOL. . . . . . . . . . . . . . . . . . . . . . . . . 154 5.4. Unificationinthemethodofsemantictableaux . . . . . . . . . . . . . 166 5.5. Towardasemi-decisionprocedureforFOL . . . . . . . . . . . . . . . 169 5.5.1. Prenexnormalform . . . . . . . . . . . . . . . . . . . . . . . . . 169 5.5.1.1. Skolemization . . . . . . . . . . . . . . . . . . . . . . . . . 174 5.5.2. Skolemnormalform . . . . . . . . . . . . . . . . . . . . . . . . 176 5.6. SemantictreesinFOL . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 5.6.1. Skolemizationandclausalform . . . . . . . . . . . . . . . . . . 188 5.7. TheresolutionmethodinFOL . . . . . . . . . . . . . . . . . . . . . . 190 5.7.1. Variablesmustberenamed . . . . . . . . . . . . . . . . . . . . . 201 TableofContents vii 5.8. Adecidableclass: themonadicclass . . . . . . . . . . . . . . . . . . 202 5.8.1. Somedecidableclasses . . . . . . . . . . . . . . . . . . . . . . . 205 5.9. Limits: Gödel’s(first)incompletenesstheorem. . . . . . . . . . . . . 206 Chapter6.FoundationsofLogicProgramming . . . . . . . . . . . . . . . 213 6.1. Specificationsandprogramming . . . . . . . . . . . . . . . . . . . . . 213 6.2. Towardalogicprogramminglanguage . . . . . . . . . . . . . . . . . 219 6.3. Logicprogramming: examples . . . . . . . . . . . . . . . . . . . . . . 222 6.3.1. Actingontheexecutioncontrol: cut“/” . . . . . . . . . . . . . 229 6.3.1.1. Translationofimperativestructures . . . . . . . . . . . . . 231 6.3.2. Negationasfailure(NAF) . . . . . . . . . . . . . . . . . . . . . 232 6.3.2.1. SomeremarksaboutthestrategyusedbyLPand negationasfailure . . . . . . . . . . . . . . . . . . . . . . . 238 6.3.2.2. CanwesimplydeduceinsteadofusingNAF? . . . . . . . 239 6.4. ComputabilityandHornclauses . . . . . . . . . . . . . . . . . . . . . 241 Chapter7.ArtificialIntelligence . . . . . . . . . . . . . . . . . . . . . . . . 245 7.1. Intelligentsystems: AI . . . . . . . . . . . . . . . . . . . . . . . . . . 245 7.2. WhatapproachestostudyAI? . . . . . . . . . . . . . . . . . . . . . . 249 7.3. Towardanoperationaldefinitionofintelligence . . . . . . . . . . . . 249 7.3.1. TheimitationgameproposedbyTuring . . . . . . . . . . . . . 250 7.4. Canweidentifyhumanintelligencewithmechanical intelligence? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 7.4.1. Chineseroomargument. . . . . . . . . . . . . . . . . . . . . . . 252 7.5. Somehistory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 7.5.1. Prehistory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 7.5.2. History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 7.6. SomeundisputedthemesinAI . . . . . . . . . . . . . . . . . . . . . . 256 Chapter8.Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 8.1. Deductiveinference . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 8.2. Animportantconcept: clausesubsumption . . . . . . . . . . . . . . . 266 8.2.1. Animportantproblem. . . . . . . . . . . . . . . . . . . . . . . . 268 8.3. Abduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 8.3.1. Discoveryofexplanatorytheories . . . . . . . . . . . . . . . . . 274 8.3.1.1. Requiredconditions . . . . . . . . . . . . . . . . . . . . . . 275 8.4. Inductiveinference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 8.4.1. Deductiveinference . . . . . . . . . . . . . . . . . . . . . . . . . 279 8.4.2. Inductiveinference . . . . . . . . . . . . . . . . . . . . . . . . . 280 8.4.3. Hempel’sparadox(1945) . . . . . . . . . . . . . . . . . . . . . . 280 8.5. Generalization: thegenerationofinductivehypotheses . . . . . . . . 284 8.5.1. Generalizationfromexamplesandcounterexamples . . . . . . 288 viii LogicforComputerScienceandArtificialIntelligence Chapter9.ProblemSpecificationinLogicalLanguages . . . . . . . . . . 291 9.1. Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 9.1.1. Whenisitused? . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 9.1.2. Somequestionsaboutequality . . . . . . . . . . . . . . . . . . . 292 9.1.3. Whyisequalityneeded? . . . . . . . . . . . . . . . . . . . . . . 293 9.1.4. Whatisequality? . . . . . . . . . . . . . . . . . . . . . . . . . . 293 9.1.5. Howtoreasonwithequality?. . . . . . . . . . . . . . . . . . . . 295 9.1.6. Specificationwithoutequality . . . . . . . . . . . . . . . . . . . 296 9.1.7. Axiomatizationofequality . . . . . . . . . . . . . . . . . . . . . 297 9.1.8. Addingthedefinitionof=andusingtheresolution method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 9.1.9. Byaddingspecializedrulestothemethodofsemantic tableaux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 9.1.10. Byaddingspecializedrulestoresolution . . . . . . . . . . . . 300 9.1.10.1.Paramodulationanddemodulation . . . . . . . . . . . . . 300 9.2. Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 9.3. SecondOrderLogic(SOL):afewnotions. . . . . . . . . . . . . . . . 319 9.3.1. Syntaxandsemantics . . . . . . . . . . . . . . . . . . . . . . . . 324 9.3.1.1. Vocabulary . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 9.3.1.2. Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 9.3.1.3. Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Chapter10.Non-classicalLogics . . . . . . . . . . . . . . . . . . . . . . . . 327 10.1.Many-valuedlogics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 10.1.1. Howtoreasonwithp-valuedlogics? . . . . . . . . . . . . . . . 334 10.1.1.1.Semantictableauxforp-valuedlogics . . . . . . . . . . . 334 10.2.Inaccurateconcepts: fuzzylogic . . . . . . . . . . . . . . . . . . . . 337 10.2.1. InferenceinFL . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 10.2.1.1.Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 10.2.1.2.Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 10.2.2. Herbrand’smethodinFL . . . . . . . . . . . . . . . . . . . . . 350 10.2.2.1.ResolutionandFL . . . . . . . . . . . . . . . . . . . . . . 351 10.3.Modallogics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 10.3.1. Towardasemantics. . . . . . . . . . . . . . . . . . . . . . . . . 355 10.3.1.1.Syntax(languageofmodallogic). . . . . . . . . . . . . . 357 10.3.1.2.Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 10.3.2. Howtoreasonwithmodallogics? . . . . . . . . . . . . . . . . 360 10.3.2.1.Formalsystemsapproach . . . . . . . . . . . . . . . . . . 360 10.3.2.2.Translationapproach . . . . . . . . . . . . . . . . . . . . . 361 10.4.Someelementsoftemporallogic . . . . . . . . . . . . . . . . . . . . 371 10.4.1. Temporaloperatorsandsemantics . . . . . . . . . . . . . . . . 374 10.4.1.1.Afamousargument . . . . . . . . . . . . . . . . . . . . . 375

Description:
Logic and its components (propositional, first-order, non-classical) play a key role in Computer Science and Artificial Intelligence. While a large amount of information exists scattered throughout various media (books, journal articles, webpages, etc.), the diffuse nature of these sources is proble
ebook img

Logic for Computer Science and Artificial Intelligence PDF

537 Pages·2011·5.32 MB·English
by  Ricardo Caferra
Save to my drive
Quick download
Download

Download Logic for Computer Science and Artificial Intelligence PDF Free - Full Version

by Ricardo Caferra| 2011| 537 pages| 5.32| English

Download Logic for Computer Science and Artificial Intelligence by Ricardo Caferra in PDF format completely FREE. No registration required, no payment needed. Get instant access to this valuable resource on PDFdrive.to!

Free Download PDF

About Logic for Computer Science and Artificial Intelligence

Logic and its components (propositional, first-order, non-classical) play a key role in Computer Science and Artificial Intelligence. While a large amount of information exists scattered throughout various media (books, journal articles, webpages, etc.), the diffuse nature of these sources is proble

Detailed Information

Author:Ricardo Caferra
Publication Year:2011
Pages:537
Language:English
File Size:5.32
Format:PDF
Price:FREE
Download Free PDF

Safe & Secure Download - No registration required

Why Choose PDFdrive for Your Free Logic for Computer Science and Artificial Intelligence Download?

  • 100% Free: No hidden fees or subscriptions required for one book every day.
  • No Registration: Immediate access is available without creating accounts for one book every day.
  • Safe and Secure: Clean downloads without malware or viruses
  • Multiple Formats: PDF, MOBI, Mpub,... optimized for all devices
  • Educational Resource: Supporting knowledge sharing and learning

Free Books Similar to Logic for Computer Science and Artificial Intelligence

Frequently Asked Questions

Is it really free to download Logic for Computer Science and Artificial Intelligence PDF?

Yes, on https://PDFdrive.to you can download Logic for Computer Science and Artificial Intelligence by Ricardo Caferra completely free. We don't require any payment, subscription, or registration to access this PDF file. For 3 books every day.

How can I read Logic for Computer Science and Artificial Intelligence on my mobile device?

After downloading Logic for Computer Science and Artificial Intelligence PDF, you can open it with any PDF reader app on your phone or tablet. We recommend using Adobe Acrobat Reader, Apple Books, or Google Play Books for the best reading experience.

Is this the full version of Logic for Computer Science and Artificial Intelligence?

Yes, this is the complete PDF version of Logic for Computer Science and Artificial Intelligence by Ricardo Caferra. You will be able to read the entire content as in the printed version without missing any pages.

Is it legal to download Logic for Computer Science and Artificial Intelligence PDF for free?

https://PDFdrive.to provides links to free educational resources available online. We do not store any files on our servers. Please be aware of copyright laws in your country before downloading.

The materials shared are intended for research, educational, and personal use in accordance with fair use principles.

We use cookies

We use cookies to ensure you get the best browsing experience on our website. By clicking "Accept Cookies", you agree that we can store cookies on your device in accordance with our Terms and Privacy.