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Logical Reasoning with Diagrams and Sentences

Table of Contents


Errata

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Table of contents

    • About Hyperproofx
      • How to use this bookx
      • Acknowedgelementsxi
      • Acknowledgements (2nd Edition)xii
      • What's new in this edition?xiii
      • Instructions about the exercisesxiii
  • IBasic Concepts1
    • 1Comparing Tarski's World and Hyperproof3
      • 1.1Worlds and Situations3
      • 1.2A new property and relation6
      • 1.3Language differences9
      • 1.4Kleene evaluation10
      • 1.5Proofs13
    • 2Proofs of Conseqeuence and Nonconsequence17
      • 2.1Observe17
      • 2.2Assumptions and Subproofs19
      • 2.3Check Truth of the Assumptions (CTA)23
      • 2.4Sentence Goals25
    • 3Sentential Consequence Rules33
      • 3.1Tautological Consequence33
      • 3.2First-Order Consequence39
      • 3.3Analytical Consequence44
    • 4Proofs of Consistency and Inconsistency48
      • 4.1Syntactic Close49
      • 4.2Semantic Close50
      • 4.3Consistency goals52
  • IIDiagrammatic Reasoning57
    • 5The Apply Rule59
      • 5.1Apply59
      • 5.2Some situation goals63
    • 6Reasoning by Cases68
      • 6.1Cases Exhaustive68
      • 6.2Merge and Inspect74
      • 6.3Recursive Close81
      • 6.4Name83
      • 6.5Review Exercises86
    • 7Independence Proofs88
      • 7.1Consequence, nonconsequence and independence88
      • 7.2More independence goals90
      • 7.3Constrained independence and consequence]94
      • 7.4Some final situation goals96
      • 7.5Review Exercises100
  • IIISentential Reasoning103
    • 8Sentential Connective Rules105
      • 8.1Reiteration106
      • 8.2Conjunction rules106
      • 8.3Disjunction rules108
      • 8.4Negation rules113
      • 8.5Conditional Rules123
      • 8.6Biconditional rules126
      • 8.7Matters of style129
    • 9Quantifier and Identity Rules132
      • 9.1Identity rules132
      • 9.2Existential quantifier rules134
      • 9.3Universal quantifier rules139
      • 9.4Multiple Quantifiers146
      • 9.5Numerical quantifier rules147
      • 9.6Review exercises150
    • 10Axioms and Analytical Consequence153
      • 10.1The axiomatic method153
      • 10.2Axiomatizing shape155
      • 10.3Axiomatizing size160
      • 10.4Location axioms163
    • 11Logic and Observation168
    • ASummary of Goals173
    • BUsing Hyperproof178
      • B.1Launching the program178
      • B.2Editing the situation180
      • B.3The body of the proof182
      • B.4Goals189
      • B.5Copying and pasting190
      • B.6Printing proofs192
      • B.7Setting up problems192
      • B.8Projecting Hyperproof in class193
    • CUsing Submit195
      • C.1Getting started195
      • C.2Choosing files to submit196
      • C.3How you know your files were received197
      • C.4Preferences and User Data198
    • Index of You Try It Files201
    • Exercise Index203
    • General Index204