The purpose of this article is to give a survey of some results I have found in investigations concerning logical modalities. The results refer: (1) to semantical systems, i.e., symbolic language systems for which semantical rules of interpretation are laid down; (2) to corresponding calculi, i.e., syntactical systems with primitive sentences and a rule of inference; (3) to relations between a semantical system and the corresponding calculus.

The semantical systems to be dealt with are the following: pro positional logic (PL), functional logic (FL), and the corresponding modal systems, viz. modal propositional logic (MPL) and modal functional logic (MFL).