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Somewhat arbitrarily, study of logic is divided into formal and informal logic.

Formal logic (sometimes called symbolic logic) approaches logic and in particular logical argument as a set of rules for manipulating symbols. There are two kinds of rules in any system of formal logic: Syntax rules and rules of inference. Syntax says how to build méaningful expressions; rules of inference say how to obtain true formulas from other true formulas. Logic also needs semantics, which says how to assign méaning to expressions. Formal logic encompasses a wide variety of logical systems. For instance, propositional logic and predicate logic are a kind of formal logic, as well as temporal logic, modal logic, Hoare logic, the calculus of constructions etc. Higher order logics refer to logical systems based on a hierarchy of types.

Informal logic is the study of logic as used in natural language arguments. Informal logic is complicated by the fact that it may be very hard to téase out the formal logical structure imbedded in an argument. Informal logic is also more difficult because the semantics of natural language assertions is much more complicated than the semantics of formal logical systems.

Following are more specific discussions of some systems of logic. See also: list of topics in logic.