These notes cover in some more detail what the textbook discusses in Chapter 5. Some details of my presentation will be different in irrelevant ways from the details in the book. I will be somewhat terse in terms of examples. Let me know if you feel that they are sorely needed, and I’ll amend the notes accordingly.
Predicate logic extends propositional logic in that we now allow the presence of quantifiers, and therefore we also allow the presence of statements that depend on variables. This complicates the definition of semantics, and also introduces additional complications at the syntactic level. On the other hand, this new flexibility allows us to code in straightforward ways many theories actually used in practice. Set theory is but on example of a theory that can be formalized in this context, and we will see others.