In the Spring of 2009, I began writing Symbolic Logic: Syntax, Semantics, and Proof. The first edition took the form of lecture notes and handouts that I distributed in the summer of 2009, a course packet in the fall of 2009, and finally I used it as a textbook in the Summer 2010, Fall 2010, and Spring 2011 semesters.

The development of the textbook benefited greatly from the feedback I received from instructors and students at Penn State: Deniz Durmus (Spring 2011); Mark Fisher (Spring 2011); Cameron O'Mara (Summer 2011); Ryan Pollock (Fall 2011), Christopher Allaman, Ashley Brooks, Aurora Cooper, Maureen Dunn, Elliannies Duran, Ariel Endresen, Nayib Felix, Joy Garcia, Alex Kirk, Edward Lackner, Brooke Santkiewicz, Ariel Valdez, Isaac Bishop, Kristin Nuss, Karintha Parker, Sarah Mack, Amanda Wise, Meghan Barnett, Alexander McCormack, and Kevin Bogle.

The textbook is in its 2nd printing. The erratum (list of corrections from the first printing) can be found here: Errata for Symbolic Logic: Syntax, Semantics, and Proof.

I warmly welcome any constructive feedback you may have about the book. I'm always looking for new ways to make logic easier to learn!


PL - Symbols, Syntax, Semantics, Translation

PL: Symbols
PL: Syntax, Part 1 (well-formed formulas)
PL: Syntax, Part 2 (subformulas and scope)
PL: Syntax, Part 3 (five wffs, literal negation, conventions)
PL: Semantics, Part 1 (Interpretations and valuations)
PL: Semantics, Part 2 (valuations rules)
PL: Translation, Part 1 (atomic and negated wffs)
PL: Translation, Part 2 (conjunctions)
PL: Translation, Part 3 (disjunctions)
PL: Translation, Part 4 (conditionals)
PL: Translation, Part 5 (biconditionals)
PL: Translation, Part 6 (complex translations)

PL - Truth Trees

PL: Truth Trees, Part 1 (Introduction and Setup)
PL: Truth Trees, Part 2 (Decomposition Rules)
PL: Truth Trees, Part 3 (Tree Terminology)
PL: Truth Trees, Part 4 (Recovering an Interpretation)
PL: Truth Trees, Part 6 (Contradiction, Tautology, Contingency)
PL: Truth Trees, Part 7 (Equivalence)
PL: Truth Trees, Part 8 (Validity)
PL: Tips for Trees

PL - Derivations / Proofs

PL, Derivations: Syntactic entailment and proof
PL, Derivations: How to set up a proof
PL, Derivations: Conjunction introduction
PL, Derivations: Conjunction elimination
PL, Derivations: Conditional elimination
PL, Derivations: Conditional introduction
PL, Derivations: Disjunction introduction
PL, Derivations: Negation introduction and negation elimination
PL, Derivations: Disjunctive Syllogism
PL, 5 Tips for Proofs

Predicate Logic (RL) - Symbols, Syntax, Semantics, Translation

RL: Symbols
RL: Basic Syntax
RL: Semantics (Models)
RL: Valuation of Unquantified Formulas
RL: Valuations, Part 2 (Quantified Wffs)
RL: Basic Translation
RL: Semantics with Variable Assignments (Part 1)
RL: Semantics with Variable Assignments (Part 2)

RL - Truth Trees

RL Trees: Introduction
RL Trees: Negated decomposition
RL Trees: Completed open branch
RL Trees: Recovering a model from a completed open branch

RL - Proofs

RL, Proofs: Introduction
RL, Proofs: Universlal Elimination
RL, Proofs: Existential Introduction
RL, Proofs: Universal Introduction
RL, Proofs: Existential Elimination
RL, Proofs (Practice), Part 1
RL, Proofs (Practice), Part 2