Algebraic logic

Summary

Algebraic logic studies logical systems by means of algebraic structures. Formulas are identified when they are provably equivalent, and the logical connectives become operations on the resulting classes, as in the Lindenbaum–Tarski algebra. Classical propositional logic corresponds to Boolean algebras, intuitionistic logic to Heyting algebras, and Łukasiewicz infinite-valued logic to MV-algebras. For predicate logic there are cylindric algebras and polyadic algebras, and relation algebras treat the calculus of binary relations.