## Welcome

USC Logic Web is designed to support the study of propositional and predicate logic. After reading a tutorial, practice what you've learned by trying the Problem Set below it.

## Tutorials

**Unit 1. Arguments and Validity.** What is a valid argument? Validity, truth preservation, and logical form.

**Unit 2. Propositional Logic: Syntax.** The vocabulary of propositional logic. How to check whether a string of symbols is a well-formed formula of the language of propositional logic. How to provide a construction tree for a well-formed formula of the language of propositional logic.

**Unit 3. Propositional Logic: Semantics.** The interpretation of propositional connectives: negation, conjunction, disjunction, material conditional, and biconditional. Special difficulties raised by the material conditional. Truth tables.

**Unit 4. Translation into the Language of Propositional Logic.** How to translate simple English sentences into the language of propositional logic. A translation method for more complex formulas. Special difficulties raised by phrases like 'either ... or ...', 'only if', 'unless'. How to translate real life arguments in English into the language of propositional logic. How to check whether they are propositionally valid.

**Unit 5. Derivations in Propositional Logic. **What is a derivation? Two deductive systems for propositional logic. A natural deduction system for propositional logic. Natural deduction rules for conjunction and disjunction. Natural deduction rules for the conditional and negation. How to construct a natural deduction proof. A tableaux system for propositional logic. Tableaux rules for propositional connectives. How to use tableaux to check for validity.

**Unit 6. The Syntax of Predicate Logic. **The limitations of propositional logic. Monadic predicates and designators. Polyadic predicates. Quantification. The language of predicate logic. The vocabulary of predicate logic. The syntax of predicate logic. Atomic formulas of predicate logic. Formulas of predicate logic. Subformulas of a formula of predicate logic. Open v. closed formulas of predicate logic. Free vs. bound occurences of a variable. The scope of a quantifier. Open and closed formulas of predicate logic.

**Unit 7. Translation into the Language of Predicate Logic. **A general strategy for translation. Quantification. Quantification and monadic predicates. Quantification and polyadic predicates. Some difficulties with the translation of quantificational phrases. Complex translation. Ambiguity.

**Unit 8. Predicate Logic: Semantics. **Models for the Language of Predicate Logic. How to evaluate a closed formula in a model. How to evaluate an open formula in a model. How to evaluate a quantified formula in a model. From `truth relative to an assignment' to truth in a model. Logical Truth, Logical Equivalence, Consistency, and Validity. The Search-for-Counterexample Method.

**Unit 9. Derivations in Predicate Logic. **Tableaux. Tableau Rules for Quantification. Common Mistakes and Strategies.