• USC Logic Web is an open-access platform designed to introduce users to the study of propositional and quantificational logic with identity. The project began with a donation by the Linda L. Peterson Fund for the Study and Practical Application of Logic. The material is divided into ten units, which consist of a tutorial and a set of interactive problems designed to help consolidate comprehension and mastery of core skills introduced by the tutorial. Solutions to these problems are provided in a separate link.

The first unit introduces the subject matter of logic and motivates the use of a formal framework for the study of validity. The remainder of the course is structured into two main blocks, one on propositional logic and another on quantificational logic. Each part presents the syntax and semantics of the relevant formal language and explains how to translate from English into that framework. A system of natural deduction is introduced for each framework.

USC Logic Web is used as an online companion to PHIL 220g. Introduction to Logic at USC.

• The main text has been written with the help of the bookdown package created by Yihui Xie. Bookdown is open-source R package used to create ebooks from R Markdown documents.

The interactive problems are written in markdown and powered by the Carnap platform. This is a free and open software framework designed and maintained by G. Leach-Krouse and J. Ehrlich. The documentation explains how the problems are written and uploaded to the platform. Users receive immediate feedback upon submission, e.g., Carnap will tell them whether the answer is correct and if not, it will in some cases offer some hints.

The visual design of the main text and the interactive problems emulates the style of Edward Tufte, which has implementations in LaTeX and HTML/CSS.

• Please feel free to use this anonymous form to submit feedback on the platform, e.g., typos, comments, or suggestions for improvement.

## Unit 1

### Reason and Argument

What is an argument? How should we draw the distinction between valid and invalid arguments? Validity and form. Formal languages and logic.

### Practice

How to identify the conclusion of an argument. What makes an argument valid. How to tell whether an argument form is valid. What makes an argument sound.

## Unit 2

### Syntax of Propositional Logic

Syntax of the formal language of propositional logic. What is a well-formed formula of the formal language? How to provide a construction tree for well-formed formulas of the language. Some notational conventions.

### Practice

How to draw a construction tree for a well-formed formula of propositional logic. The implementation of notational conventions.

## Unit 3

### Semantics for Propositional Logic

How to populate a truth table. The use of truth tables to determine whether a formula is a tautology or a contradiction or neither. Truth tables and validity.

### Practice

How to interpret the language of propositional logic. Truth-functional connectives and their interpretation. The use of truth tables and validity.

## Unit 4

### Translation into Propositional Logic

How to translate from English into the language of propositional logic. Problems with translation. The formalization of real life arguments in English. How to use truth tables to determine whether they are propositionally valid.

### Practice

Translation into the language of propositional logic. Problems with translation. Formalization of complex arguments in English.

## Unit 5

### Natural Deduction for Propositional Logic

A system of natural deduction for propositional logic. Natural deduction rules for conjunction and the conditional. Rules for disjunction and negation. How to construct a natural deduction proof. Common mistakes and strategies.

### Practice

Natural deduction rules for conjunction, conditional, disjunction, and negation. Strategies for complex proofs.

## Unit 6

### Syntax of Quantificational Logic

Vocabulary and syntax of quantificational logic. How to provide a construction tree for well-formed formulas of the language. Some notational conventions. The distinction between free and bound variables. The distinction between open and closed formulas.

## Unit 7

### Semantics for Quantificational Logic

Models for quantificational logic. The evaluation of closed formulas in a model. What is for a closed formula to be true in a model. How to use models to test for equivalence and validity.

### Practice

How to model a set of formulas.  The use of models to test for consistency, equivalence, and validity.

## Unit 8

### Translation into Quantificational Logic

How to translate from English into the language of quantificational logic. Quantification. Issues with translation. Structural ambiguity.

### Practice

Translation into the language of quantificational logic. Issues with translation. Formalization of complex arguments in English.

## Unit 9

### Natural Deduction for Quantificational Logic

Natural deduction rules for the universal and existential quantifiers. How to construct a natural deduction proof in quantificational logic. Common mistakes and strategies.

### Practice

Natural deduction rules for the universal and existential quantifiers. Strategies for complex proofs.

## Unit 10

### Quantificational Logic with Identity

How to supplement quantificational logic with identity. Quantification and Number. Definite Descriptions.

### Practice

Quantification and Number. Definite Descriptions.