We will continue to use the term ʻpropositionʼ in its usual sense to refer to a statement or question. But it will be useful to introduce a parallel term to refer to offers and commands. As it happens, these correspond more closely to the everyday sense of the word ʻpropositionʼ, as in 'I have got a proposition to put to you'; so we will refer to them by the related term PROPOSAL. The semantic function of a clause in the exchange of information is a proposition; the semantic function of a clause in the exchange of goods-&-services is a proposal.
- Halliday (1985), a pag.71

In a proposal, the meaning of the positive and negative poles is prescribing and proscribing: positive ʻdo itʼ, negative ʻdon’t do itʼ. Here also there are two kinds of intermediate possibility, in this case depending on the speech function, whether command or offer. (i) In a command, the intermediate points represent degrees of obligation: ʻallowed to / supposed to / required toʼ; (ii) in an offer, they represent degrees of inclination: ʻwilling to / anxious to / determined to /ʼ.
- Halliday (1985), a pag.86

Proposals which are clearly positive or negative, as we have seen, are goods-&-services exchanges between speaker and hearer, in which the speaker is either (i) offering to do something, e.g. 'shall I go home?', (ii) requesting the listener to do something, e.g. 'go home!', or (ii) suggesting that they both do something, e.g. 'let’s go home!' They rarely have third person Subjects, except as prayers or oaths.
- Halliday (1985), a pag.86-88