Modal operator

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A modal operator is a logical connective, in the language of a modal logic, which forms propositions from propositions. In general, a modal operator is formally characterised by being non-truth-functional, and intuitively characterised by expressing a modal attitude (such as necessity, possibility, belief, or knowledge) towards the proposition which it is applied to.

[edit] Examples

• In the alethic modal logic of C.I. Lewis, the modal operator expresses necessity: if the proposition A is read as "it is true that A holds", the proposition A is read as "it is necessarily true that A holds".
• In the tense logic (more commonly now called temporal logic) of A.N. Prior, the proposition A is read as "A is true at the present time"; F A, as "A will be true at some time in the future"; and G A, as "A is true now and will always be true".
• The previous two examples are of unary or monadic modal operators. As an example of a dyadic modal operator -- which produces a new proposition from two old propositions -- is the operator P in the dyadic deontic logic of G.H. von Wright. P(A,B) expresses that "A is obligatory under the circumstances B".