An Introduction to Formal Logic

Jul 15, 2026

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Textbook introduction to formal logic, covering key notions such as arguments, entailment, satisfiability, and ambiguity. Develops truth-functional logic with symbolization, connectives, truth tables, and natural deduction, then extends to first-order logic including quantifiers, identity, definite descriptions, and interpretations. Includes natural deduction for first-order logic and modal logic, concluding with metatheory topics such as normal forms, completeness, equivalences, and soundness.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages428

Reading Time17 h 59 min

CALGARY An Introduction to Formal Logic P. D. Magnus Tim Button with additions by J. Robert Loftis Robert Trueman remixed and revised by Aaron Thomas-Bolduc Richard Zach Fall 2021+ forall x: Calgary An Introduction to Formal Logic By P. D. Magnus Tim Button with additions by J. Robert Loftis Robert Trueman remixed and revised by Aaron Thomas-Bolduc Richard Zach Fall 2021+ This book is based on forallx: Cambridge, by Tim Button (University College London), used under a CC BY 4.0 license, which is based in turn on forallx, by P.D. Magnus (University at Albany, State University of New York), used under a CC BY 4.0 license, and was remixed, revised, & expanded by Aaron Thomas-Bolduc & Richard Zach (University of Calgary) . It includes additional material from forallx by P. D. Magnus and Metatheory by Tim Button, used under a CC BY 4.0 license, from forallx: Lorain County Remix, by Cathal Woods and J. Robert Loftis, and from A Modal Logic Primer by Robert Trueman, used with permission. This work is licensed under a Creative Commons Attribution 4.0 license. You are free to copy and redistribute the material in any medium or format, and remix, transform, and build upon the material for any purpose, even commercially, under the following terms: ⊲ You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. ⊲ You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits. The LATEX source for this book is available on GitHub and PDFsat [forallx.openlogicproject.org. This](forallx.openlogicproject.org. This) version is revision e1996fc (2022-11-19) . The preparation of this textbook was made possible by a grant from the Taylor Institute for Teaching and Learning. Cover design by Mark Lyall. Contents Preface vi I Key notions of logic 1 1 Arguments 2 2 The scope of logic 7 3 Other logical notions 18 II Truth-functional logic 26 4 First steps to symbolization 27 5 Connectives 32 6 Sentences of TFL 49 7 Ambiguity 56 8 Use and mention 62 III Truth tables 68 9 Characteristic truth tables 69 10 Truth-functional connectives 72 11 Complete truth tables 77 12 Semantic concepts 85 CONTENTS iv 13 Truth table shortcuts 96 14 Partial truth tables 101 IV Natural deduction for TFL 108 15 The very idea of natural deduction 109 16 Basic rules for TFL 112 17 Constructing proofs 141 18 Additional rules for TFL 161 19 Proof-theoretic concepts 169 20 Derived rules 173 21 Soundness and completeness 181 V First-order logic 190 22 Building blocks of FOL 191 23 Sentences with one quantifier 200 24 Multiple generality 214 25 Identity 229 26 Sentences of FOL 236 27 Definite descriptions 244 28 Ambiguity 254 VI Interpretations 258 29 Extensionality 259 30

Jul 15, 2026

Upload by Aurelia