Symbolic logic is the form of logic that is based on the process of taking sentences and symbolizing their component parts as letters.

In this way, the content of arguments can be abstracted away to a simple and more precise form that is not necessarily concerned with the specific referents of each symbol but the validity of the argument.

For example, if I were to say that "If a cat purrs, then the cat is happy" I could make "A cat purrs" equal to the letter "p" and "The cat is happy" equal to the letter "q". I could then say that "If p then q" as a way of saying "If a cat purrs, then the cat is happy".

This can be symbolized completely as "p q".

Symbolic logic typically uses the following symbols, though many more are possible:

		The symbol for necessity, read "it is necessary that". Used in the following form: p. Read "it is necessary that p".
		The symbol for possibility, read "it is possible that". Used in the following form: p. Read "it is possible that p".
		The symbol for the universal quantifier. Used in the following form: (x)Tx, read "for all x such that x is T", or "all x are T", or "Given any x, x is T". The addition of the upside down "A", or "" is new and the "x" was originally used, in isolation, to signify universal quantification. Thus, (x)Tx is the same as (x)Tx.
		The symbol for the existential quantifier. Used in the following form: (x)Tx, read "there exists at least one x such that x is T", or "there are some x that are T", or "there is one or more x that are T"
	&	The symbol for conjunction. Read "and". Used in the following form: p & q. Read "p and q"
	V	The symbol for disjunction. Read "or". Used in the following form: p V q. Read "p or q"
		The symbol for the conditional. Read "if, then" or "implies". Used in the following form: p q. Read "if p then q" or "p implies q". p q can be rewritten as ~(p & ~q) because if p is true then q is true and, p and ~q can not both be true.
		Another symbol for the conditional. Read "if, then" or "implies". Used in the following form: p q. Read "if p then q" or "p implies q". p q can be rewritten as ~(p & ~q) because if p is true then q is true and, p and ~q can not both be true.
		The symbol for the biconditional. Read "if, then" and its contraverse. Used in the following form: p q. Read "if p then q and if q then p". p q can be rewritten as ((p q) & (q p)).
	~	The symbol for negation. Used in the following form: ~p. Read "not p".
		The symbol for the conclusion. Read "therefore". Used in the following form: p. Read "Therefore p".