Claim: Algebraic logic has five Logical system and Lindenbaum–Tarski algebra which includes Physics algebra and Nodal algebra (provide models of propositional modal logics).
Evidence: In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. In mathematical logic, the Lindenbaum–Tarski algebra (or Lindenbaum algebra) of a logical theory T consists of the equivalence classes of sentences of the theory (i.e., the quotient, under the equivalence relation ~ defined such that p ~ q exactly when p and q are provably equivalent in T). The Lindenbaum–Tarski algebra is considered the origin of the modern algebraic logic. The Lindenbaum–Tarski algebra is thus the quotient algebra obtained by factoring the algebra of formulas by this congruence relation. Boolean algebra Heyting algebra MV-algebra Modal algebra Interior algebra Monadic Boolean algebra Complete Boolean algebra, polyadic algebra, predicate functor logic Cylindric algebra Combinatory logic, relation algebra 
Classical sentential logic Intuitionistic propositional logic Łukasiewicz logic Modal logic K Lewis's S4 Lewis's S5, monadic predicate logic First-order logic First-order logic with equality Set theory