Assume a sentence which is specified for its information structure. Its meaning is represented as a set of propositions. This set breaks down into two subsets:

• The presuppositions of a sentence are those propositions comprised by its meaning which are implied to be established in at least one of the referential spaces of the speech situation.
• The assertion¹ of a sentence is that proposition comprised by its meaning which is at stake. i.e. not assumed to be already established.

An informal representation of the meaning of in terms of presuppositions and assertion is as follows:

• Presuppositions: There is a specific x which is a room. There is a point in time t which coincides with the time of the utterance. x was warm at some time < t.
• Assertion: x is not warm at t.

The analysis of the meaning of a sentence in these terms applies a set of criteria which may be subsumed under the notion of ‘constancy under propositional operations’: If a propositional operation like negation or conversion of sentence type is applied to the sentence, it only changes the assertion, while the presuppositions remain constant. Thus, all of the transformations in and applied to share the above set of presuppositions, but lack the above assertion. (In the particular case of persistence of time spans, switch of polarity is a bit irregular in that a is normally said as #b; but this does not affect the argument.)

Establishment of a referent or a proposition in one of the reference spaces is to be understood as follows:

• It may mean ‘existence in the physical world’ (one of the reference spaces). Such a proposition is then regarded as a fact. However, it may also mean ‘existence in one of the other spaces’, e.g. the universe of discourse. Then it may not be a fact.
• If the speaker of a sentence takes a piece of its meaning to be established, he engages the hearer in this presupposition; i.e. he regards that piece of meaning as uncontroversial. In conformity with the effect of the negation test just presented, for the hearer to deny the speaker's sentence generally amounts to denying its assertion while accepting its presuppositions.

The latter effect of a presupposition may be illustrated by (the celebrated example) :

A polar interrogative expects one of the answers ‘yes’ or ‘no’. But this denies the hearer a chance to reject its presuppositions. If he wants to do so, he avoids the expected answers and insteads replies something like ‘But I never did beat her!’.

¹ Assertion here does not mean ‘contention’ or ‘claim’. Sentences of all sentence types, not only declarative sentences, have an assertion.