Hence, generally, a foundationalist might offer the following theory of justification:
A basic belief, on the other hand, does not require justification because it is a different kind of belief than a non-foundational one.
Historically, two varieties of foundationalist theories were rationalism and empiricism (or British Empiricism). Strictly speaking, neither empiricism nor rationalism is necessarily committed to foundationalism (it is possible to be an empiricist coherentist, for example, and that was a common epistemological position in 20th century philosophy).
Rationalism is the general name for epistemological theories that maintain that reason is the source and criterion of knowledge. Rationalists generally hold that so-called truths of reason are the (most important) epistemologically basic propositions. The historical, continental rationalism expounded by René Descartes is often regarded as antithetical to empiricism, while some contemporary rationalists assert that reason is strongest when it is supported by or consistent with empirical evidence and hence relies heavily on empirical science in analyzing justifications for belief. Descartes famously held that some of these truths are known innately and therefore constitute basic innate knowledge, a view not always held in contemporary rationalism.
Empiricism is the general name for epistemological theories that maintain that sensation reports are the source and criterion of knowledge. Classical empiricists generally held that such reports are indubitable and incorrigible and therefore worthy of serving as epistemologically basic propositions.
Alternatives to foundationalism, usually called Anti-foundationalism, include coherentism, foundherentism, reformed epistemology. Many forms of reliabilism are foundationalist, but reliabilist theories need not be foundationalist. Also see Pragmatism.