The six German modals duerfen, koennen, moegen, muessen, sollen and wollen, which are generally regarded as the core set of modal verbs in German, are known to be used in two different functions, illustrated by the following examples:

(1) Durch ihr mutiges Verhalten konnte eine 65 jaehrige Frau einen jugendlichen
    Raeuber in die Flucht schlagen. 
    `By her courageous conduct a woman aged 65 was able to make a teenage robber
     run away.'
(2) Ich kann mich getaeuscht haben. 
    `I may have been mistaken.'

The function in (1) is usually called deontic, non-epistemic, or agent-oriented. Here the modals are stative verbs that predicate a complex state on the subject of the sentence. The function in (2), usually called epistemic or inferential, is known to have developed from the former and to be highly grammaticalized, i. e. integrated into the grammatical system of markers of factuality judgements. In these sentences the modals do not contribute to the semantic content of the proposition, they are used as auxiliaries and form a grammatical paradigm with the verbal moods.

I shall propose a description of the semantic structure of the modals that concentrates on two important characteristics that have not received much attention before. The first point is that the modals in sentences like (2) are deictic signs: their semantic structure incorporates an element "pointing back" to the position of the speaker. It is this deictic function that is central to the grammatical system of factuality judgements. The second point concerns the non-deictic function of the modals as illustrated in (1). I want to highlight the fact that the prototypical meaning of the non-deictic use contains information on underlying directive speech acts and on their sequencing.

Both functions share an abstract semantic structure which is best described in relational terms as a combination of several vectors (pointed relations between source, path, and goal). The different ways of linking these basic pointed relations and the different semantic specifications of single relational positions account for the distinct lexical meanings of the six modals as well as for their respective deictic and non-deicitic functions.