Logic sytem conforming with the principle of bivalence.

In this system possibilities are given a variable, or atomic formula. A well formed formula is defined thus:

	wff ::= wff connective wff
		| not(wff)
		| wff
		| atomic formula

	connective ::= and | or | implies | two-way implication

Implies is often written →
two-way implication is often written ↔
And is written ^
Or is written as an upside-down ^.

For example, the statement "If I am in a house, I am inside and off the streets" could be expressed as a well formed formula of propositional logic thusly: H -> (I ^ O)

Propositional logic is, duh, made up of propositions, which are statements. Propositional logic can make statements about specific entities, but it doesn't really have the machinery to deal with generalizations. See predicate logic for that. Break down regular sentences into this language, remember to use a consistent naming system, apply the Rules of Inference, and you're off, doing something almost semi-useful.

Propositions consist of names, which are generally capital letters, and logical relations between them, represented by symbols. What symbols are used depends. Some people use a · for and, some use a ^, or even a *. I use a &. Unlike mathematics, logic has a lot more variation in its notation, but rest assured, the particular symbols may vary but the meaning behind them does not:

~ NOT (negation)
& AND (conjunction)
v OR (disjunction)
→ IF....THEN (implication)
↔ IF AND ONLY IF (equivalence) (by the by, you can write "if and only if" as "iff" in logic circles.)

You can then separate components of a sentence with parentheses.

EXAMPLES OF PROPOSITIONS

A → B
If A, then B.

~A &harr B
Not A if and only if B. Another way to notate this relation is (A → B) & (B → A).

((A v B) v C & D) & ~((A v B) & C & D))
Either A or B, or C and D, but not both.