Semantics
Modality
The term modality refers to a semantic category which expresses the attitude of the speaker towards the state of affairs expressed in the sentence. In this wider sense, modality can be expressed through a variety of formal and lexical means, such as the morphological mood of the verb (indicative, subjunctive, indicative), sentence adverbials (e.g. maybe, perhaps, possibly, necessarily), modal auxiliaries (e.g. can, may, must, should), and syntactic means.
In terms of the logical aspects of modality, it expresses necessity and possibility. Thus, a modal proposition includes the information that the basic proposition it contains is necessarily or possibly true: A necessarily true proposition is one which is true in any circumstances whatsoever, and cannot be false. A possibly true proposition is one which may or may not be true in fact, but is not necessarily false. Three different types of modality are usually distinguished:
Logical modality concerns the total truth possibilities for a proposition, according to the requirements of logic. Thus, a sentence like The diameter of a circle passes through the centre of the circle is an example of logical necessity, while a sentence like Napoleon might have won at Waterloo illustrates logical possibility.
In contrast to logical modality, epistemic modality expresses the necessity or possibility of a proposition being true, given what is already known. In other words, it refers to the conclusions drawn from actual evidence about the range of possibilities for what is the case in reality. Therefore, the sentence The dinosaurs must have died out suddenly illustrates epistemic necessity, and the sentence There might be intelligent life in deep space is an example of epistemic possibility.
The third type of modality is called deontic modality, which is concerned with adherence to some code of behaviour or set of rules. Deontic necessity expresses what is required, or what someone is obliged to do (You must be home by midnight), while deontic possibility expresses what is allowed or permitted (Harry is allowed to drive the tractor).
The examples are taken from Kearns, D. (2000). Semantics. Basingstoke: Macmillan. Chap. 3

Exercises on modality
- There might be intelligent life in deep space.
- Source of the picture: welt.de