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)