• USC Logic Web is an open-access platform designed to introduce users to the study of propositional and quantificational logic. 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 combine a tutorial with a set of interactive problems that help reinforce the core skills covered.

    The first unit introduces the subject matter of logic and explains why a formal framework is helpful for the study of validity. The rest of the course falls into two main parts: one on propositional logic, the other on quantificational logic. Each block covers the syntax and semantics of the relevant formal language, explains how to translate from English into that framework, and introduces a system of natural deduction.

    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 an open-source R package used to create ebooks from R Markdown documents.

    The interactive problems are powered by a family of purpose-built web applications, each written in plain JavaScript and hosted on GitHub Pages:

    Users receive immediate feedback upon submission: each application will tell them whether the answer is correct, and if it is not, it will often indicate which step or which clause is at fault.

    These applications require no accounts, no installation, and no server. They load no external libraries and run entirely in the browser, which means that nothing a student types is transmitted anywhere, and a page will continue to work if it is saved and opened again offline. Each exercise is written once, in a YAML file kept alongside the text, and travels in the address of the application, which means that a single application can serve a variety of different exercises, and each exercise can be handed out as an ordinary hyperlink. A separate set of practice pages collects the exercises for each unit in one place.

    Earlier versions of this website used the Carnap platform, a free and open software framework designed and maintained by G. Leach-Krouse and J. Ehrlich, and the present applications owe a great deal to that example.

    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.

    Propositional Logic

    Propositional logic accounts for the validity of a wide family of natural language arguments in terms of the behavior of a specific set of sentential operators called propositional connectives.

    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.

            Quantificational Logic

            Quantificational logic accounts for the validity of an even wider family of natural language arguments in terms of predication and the behavior of quantificational expressions.

            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.

              Practice

              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.

                      Contact Details

                      USC School of Philosophy

                      Gabriel Uzquiano

                      USC Logic Web © 2024 by Gabriel Uzquiano is licensed under Creative Commons Attribution-NonCommercial 4.0 International