Metamathematics of modal logic

The techniques employed in the semantic analysis of propositional languages fall roughly into two kinds. The algebraic method treats formulae as polynomial symbols by interpreting logical connectives as operators on certain kinds of lattices. In the set-theoretic approach the models, or frames, carry structural features other than finitary operations, such as neighbourhood systems and finitary relations. Formulae are interpreted as subsets of the frame in a manner constrained by its particular structure.