A crash course in arrow logic
Yde Venema · 1994
Modal Logic ' & $ % b T T T T TT c a It has manifestations for a manifold of logical formalisms; for instance, in the case of classical propositional logic (which we may see as a degenerate kind of modal logic) the relational frames are just unstructured sets, and the algebras are boolean algebras without extra operators. Let us now mention some key words to explain the connections in the picture. The relation (a) between abstract modal logic and boolean algebras with operators 5 (BAOs) is very tight; for instance, BAOs appear as the Lindenbaum-Tarski algebras of extended modal logics. As we saw in the introductory section, (b) relational frames are the central structures in the semantics of modal logic, and this is so since the work of Kripke. Note however that, years before the terminology of `possible worlds' connected by `accessibility relations' was introduced, J'onsson and Tarski (cf. [32]) had already investigated the relation (c) between BAOs and relational frames -...