A great page from John Sofwa, a math PhD and founder of Vivomind Intelligence (who could really use a new website), gives a thorough explanation of many of the basic types of computer logic. What's so worthwhile about this page is that although the math starts to get complex in places, John's descriptions of each element or so clear and concise that someone who had never used a computer could still pick up and understand the system.

I especially liked John's take on propositional logic:

Symbolic logic has two main branches: propositional calculus and predicate calculus, which are also called propositional logic and predicate logic. Propositional logic deals with statements or propositions and the connections between them. The symbol p, for example, could represent the proposition Lillian is the mother of Leslie. Predicate logic, however, would represent that proposition by a predicate Mother applied to the names of the two individuals: Mother(Lillian,Leslie). Whereas propositional logic represents a complete statement by a single symbol, predicate logic analyzes the statement into finer components.

And the table he presents to help explain the different types of logic that can exist:

The following table, called a truth table, shows the outputs generated by the five truth functions , , ~, , and for all possible combinations of the two inputs p and q.

Inputs		Outputs
p	q	pq	pq	~p	pq	pq
T	T	T	T	F	T	T
T	F	F	T	F	F	F
F	T	F	T	T	T	F
F	F	F	F	T	T	T

While this probably isn't for everyone, it's always good to get to know the machines you spend 12+ hours a day sitting with.