Modal operator
A modal connective (or modal operator) is a logical connective for modal logic. It is an operator which forms propositions from propositions. In general, a modal operator has the "formal" property of being non-truth-functional, and is "intuitively" characterized by expressing a modal attitude (such as necessity, possibility, belief, or knowledge) about the proposition to which the operator is applied.
Modality interpreted
There are several ways to interpret modal operators in modal logic, including:
alethic, deontic, axiological, epistemic, and doxastic.
Alethic
Alethic modal operators (M-operators) determine the fundamental conditions of possible worlds, especially causality, time-space parameters, and the action capacity of persons. They indicate the possibility, impossibility and necessity of actions, states of affairs, events, people, and qualities in the possible worlds.
Deontic
Deontic modal operators (P-operators) influence the construction of possible worlds as proscriptive or prescriptive norms, i.e. they indicate what is prohibited, obligatory, or permitted.