If two propositions p and q are immediately adjacent in a discourse, they are not necessarily directly related to each other. For instance, if p ends a paragraph and q starts a new paragraph, the only textual relation existing between them may derive from the overarching plot of the entire discourse. In the following, we are dealing with sequences of p and q in a discourse, and typically in one utterance, such that p and q bear a semantic relation to each other. Such a relation is an interpropositional relation.
The entities related by an interpropositional relation are of any of the propositional layers. That is, they may be a bare proposition – a thought or a state of affairs –, a typed proposition or an utterance.
The subdivision of this section largely follows a hierarchical classification of interpropositional relations which is shown in a separate diagram. At the highest level, the relations between the two propositions involved in junction are classified by the criterion of whether they are inherent in one of the two propositions or are something outside both of them. In the former case, one proposition is typically an argument of the predicate of the other proposition, while in the latter case, they are typically connected by an additional interpropositional relator. This yields the following subdivision of this section:
The problem of whether an intrinsic relation should be considered an interpropositional relation is treated in the respective subsection.
Apart from this, a proposition may be used to enrich a concept, which in turn may be used to pin down a referent. The proposition then works as a kind of modifier of that concept. This operation therefore belongs into the functional domain of concept anchoring. It is dealt with suo loco.
1 In Halliday 1994, ch. 7, a secondary clause bearing an extrinsic relation to a primary clause results from expansion, while a secondary clause bearing an intrinsic relation to a primary clause results from projection.
Reference
Halliday, Michael A.K. 1994, An introduction to functional grammar. London: Edward Arnold.