License: Attribution-CC-BYAuthor(s): P.D. Magnus
In formal logic, sentences and arguments in English are translated into mathematical languages with well-defined properties. If all goes well, properties that were hard to discern in English become clearer in the formal language. This book covers translation, formal semantics, and proof theory for both sentential logic and quantified logic. Each chapter contains practice exercises, and solutions to selected exercises appear in an appendix. The book is designed to provide a semester’s worth of material for an introductory college course.
forallX: an Introduction to Formal Logic
PDF 1MB
1 What is logic?
1.1 Arguments
1.2 Sentences
1.3 Two ways that arguments can go wrong
1.4 Deductive validity
1.5 Other logical notions
1.6 Formal languages
Practice Exercises
2 Sentential logic
2.1 Sentence letters
2.2 Connectives
2.3 Other symbolization
2.4 Sentences of SL
Practice Exercises
3 Truth tables
3.1 Truth-functional connectives
3.2 Complete truth tables
3.3 Using truth tables
3.4 Partial truth tables
Practice Exercises
4 Quanti ed logic
4.1 From sentences to predicates
4.2 Building blocks of QL
4.3 Quanti ers
4.4 Translating to QL
4.5 Sentences of QL
4.6 Identity
Practice Exercises
5 Formal semantics
5.1 Semantics for SL
5.2 Interpretations and models in QL
5.3 Semantics for identity
5.4 Working with models
5.5 Truth in QL
Practice Exercises
6 Proofs
6.1 Basic rules for SL
6.2 Derived rules
6.3 Rules of replacement
6.4 Rules for quanti ers
6.5 Rules for identity
6.6 Proof strategy
6.7 Proof-theoretic concepts
6.8 Proofs and models
6.9 Soundness and completeness
Practice Exercises
A Other symbolic notation
B Solutions to selected exercises
C Quick Reference
