King says that there is something that binds together the constituents of propositions and imposes a structure on them.
King assumes that individuals, properties and relations are the constituents of propositions.
1. Names, demonstrative pronouns, and indexicals contribute the individuals they designate in contexts to the propositions expressed in those contexts by sentences in which they occur.
2. n-place predicates contribute n-place relations to propositions.
3. Truth functional sentential connectives contribute truth functions to propositions.
4. Determiners contribute to propositions two-place relations between properties.
There are two important constraints for how these constituents are bound together:
5. Any account of what holds together the constituents of propositions should leave no mystery about what propositions are and should give us confidence that propositions so construed really exist.
6. The account should shed light on the question of how it is that propositions are able to have truth conditions and so represent the world as being a certain way.
(5) is important because we have to show that these things really exist. (6) because that is what they are supposed to do.
King runs with the Tractatus notion of propositions as being facts. The proposition-fact has to map onto a world-fact to be true. So we can consider:
7. Rebecca swims.
The proposition expressed by (7) has Rebecca and the property of swimming as constituents. King claims that the proposition that Rebecca swims is a fact that has Rebecca and the property of swimming as components. But that proposition is not the fact consisting of Rebecca possessing the property of swimming.
So if Rebecca had failed to possess the property of swimming, that is, if there were no fact consisting of her possessing the property of swimming, the fact that is the proposition that Rebecca swims would still obtain, but sadly it would be false.
I think what King has in mind is that given the existence of certain things, like Rebecca and the property of swimming, there are possible worlds where Rebecca has the property of swimming; or there are regions of logical space where Rebecca and the property of swimming connect. (I guess it depends on how you like your metaphors.) So propositions are like 'possible states-of-affairs'. They encode possibilities. If those possibilities obtain, the propositions are true.
King holds that the best way to satisfy (5) and (6) while making use of his assumptions (1) - (5) is his way. Let us consider the sentence:
8. Rebecca loves Carl.
We can represent this sentence is tree form:
Rebecca loves Carl.
Now we only need to add the semantic values.
Rebecca* loves* Carl*
So then we have built the proposition (B) out of the relations the sentence has (A). Plus there is little room to doubt that these propositions really exist. So (5) is met. (B) is just our proposition!
It is also easy to see how (6) has been satisfied.
I'm sort of tired and lazy with other things to do, so I hope you don't mind me not elaborating...