Modal operator

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.

In literary and fiction theory, the concept of modal operators has been explored by Lubomir Dolezel in Heterocosmica (1998), a book that articulates a complete theory of literary fiction based on the idea of possible worlds. Dolezel works with the concept of modalities that play the crucial role in formative operation, i.e. in shaping narrative worlds into orders that have the potential to produce stories. Based on the theories of modal logic, Dolezel introduces a set of modal systems that are appropriated for fictional semantics, expanding on the table used by Georg Henrik von Wright (1968). There are four kinds of modal operators that function in the modal systems: alethic, deontic, axiological and epistemic.

Alethic modal operators (M-operators) determine the fundamental conditions of fictional 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, qualities in the fictional worlds. Alethic modal operators play an important role in distinguishing a natural fictional world from the supernatural and intermediate ones. “The natural world generates stories of human condition” and such stories tend to be tragic from the very beginning, for example J.W. Goethe’s The Sufferings of the Young Werther. The structure of the supernatural worlds is usually revealed by the alethic modal operators (a) when they show the presence of physically impossible beings in the fictional world (gods, spirits, monsters); (b) when selected natural-world persons are granted properties and action capacities that are not available to ordinary persons of that world: becoming invisible, flying on a carpet, etc.; (c) when inanimate objects are anthropomorphized (for example the legend of Don Juan in Alexander Pushkin’s The Stone Guest.) The intermediate worlds are usually represented in dreams within a fictional world.

Examples

• In the alethic modal logic of C.I. Lewis, the modal operator ${\displaystyle \Box }$  expresses necessity: if the proposition A is read as "it is true that A holds", the proposition ${\displaystyle \Box }$ 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".