Linguistic modality

In standard formal approaches to linguistic modality, an utterance expressing modality is one that can always roughly be paraphrased to fit the following template:

The set of propositions which forms the basis of evaluation is called the modal base. The result of the evaluation is called the modal force. For example the utterance in (2) expresses that, according to what the speaker has observed, it is necessary to conclude that John has a rather high income:

The modal base here is the knowledge of the speaker, the modal force is necessity. By contrast, (3) could be paraphrased as ‘Given his abilities, the strength of his teeth, etc., it is possible for John to open a beer bottle with his teeth’. Here, the modal base is defined by a subset of John's abilities, the modal force is possibility.

A more elaborate account of formal semantic approaches to modality is given in section 1.

Cross-linguistically, modality can be expressed by a variety of means, such as auxiliary verbs as in the examples (2) and (3), verbal morphology (mood) or adverbs. An overview of the various modal expressions across languages is given below in section 2.

Typological approaches to modality usually favour a slightly wider definition of modality and also include meanings which do not fit the template in (1) exactly. Section 3 provides an overview over the range of meanings commonly associated with modality.

Semantic approaches dealing with modality are traditionally based on the principles of modal logic. Both work with the notion that propositions can be mapped to sets of possible worlds, that is, a proposition can be defined as the set of worlds in which that proposition is true. For example, the proposition ‘the earth is flat’ corresponds to the set of possible worlds in which the earth is in fact flat.

In this framework, modal expressions such as must and can are then analyzed as quantifiers over a set of possible worlds. This set of worlds is given by the modal base and is said to be the set of accessible worlds: For example, in sentence (2) above, the modal base is the knowledge the speaker has in the actual world. Therefore, the set of accessible worlds is defined by the information the speaker has about John. Assume for example that the speaker knows that John just bought a new luxury car and has rented a huge apartment. The speaker also knows that John is an honest person with a humble family background and doesn't play the lottery. The set of accessible worlds is then the set of worlds in which all these propositions which the speaker knows about John are true.

...
Wikipedia