We will use tableaus as our primary proof procedure, but axiom systems are important in modal logic, and you should know something about them. Modal axiom systems build on classical ones, and modal completeness proofs use ideas from the classical one. So, here are notes developing a classical propositional axiom system, along with a completeness proof for it. Indeed, the completeness proof motivates the choice of axioms. Please understand, the notes cover much more than you will be responsible for, but you should know the broad outlines, at least. It is available by clicking below. If you use this in your computer, references to theorems and definitions are clickable. If you print the notes out this will not be the case, unless you print on very smart paper.

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