Editing Lindenbaum–Tarski algebra (section)

== Related algebras ==

[[Heyting algebra]]s and [[interior algebra]]s are the Lindenbaum–Tarski algebras for [[intuitionistic logic]] and the [[modal logic]] '''S4''', respectively.

A logic for which Tarski's method is applicable, is called ''algebraizable''. There are however a number of logics where this is not the case, for instance the modal logics '''S1''', '''S2''', or '''S3''', which lack the [[rule of necessitation]] (⊢φ implying ⊢□φ), so  ~ (defined above) is not a congruence (because ⊢φ→ψ does not imply ⊢□φ→□ψ). Another type of logic where Tarski's method is inapplicable is [[relevance logic]]s, because given two theorems an implication from one to the other may not itself be a theorem in a relevance logic.<ref name=BP/> The study of the algebraization process (and notion) as topic of interest by itself, not necessarily by Tarski's method, has led to the development of [[abstract algebraic logic]].