He has a coarse- and fine-grained semantics for propositions (snigification). On the coarse-grained account, propositions are the sum of their supposita--something out in the world and not necessarily in the head. On the fine-grained account, propositions are mental acts. It is clear that neither account alone can account for truth, since on the coarse-grained view, a proposition and its negation, for example, have the same meaning. And on the fine-grained account, the mere existence (actuality) of a mental propositions does not suffice for its truth.
Given how coarse-grained coarse-grained propositions are, it is not clear what role they actually play in an account of truth. (We know what role they play in propositional nominalizations, taken personally.) If anything, it looks more like the coarse-grained account yields a theory of aboutness or subject matter of propositions, since presumably a sentence and its negation have the same subject matter, namly whatever it is for which its terms supposit. E.g. 'Man is an animal' and 'Man is not an animal' are about the same thing, namely, men and animals.
It was held that a proposition is true just in case its significatum is actual. In contemporary terms, the significatum of a proposition would thus be something like an actual (rather than merely possible) state of affairs. It is clear why Buridan had to renounce the traditional account: it did not fit with his nominalist ontology, since the significatum of a proposition in the traditional sense would not have been anything like the ordinary objects of a nominalist ontology, such as chairs and tables.
Taken materially, nominalizations stand for tokened propositions (utterances, inscriptions, etc.) of the same type. It is important to note, however, that the type of a proposition is not something that exists (since it would be abstract), or if it does, it is nothing above and beyond (a property of) the tokens (of the type) themselves.
Taken personally, nominalizations stand for what the terms of the corresponding proposition supposit. For example, in 'That Socrates loves God is good', 'That Socrates loves God' supposits for Socrates if he in fact loves God, being the subject of 'Socrates loves God', and otherwise it supposits for nothing, and so the corresponding proposition is false.
There is a complication especially concerning negation. Consider 'That Santa does not love God is true'. For what does 'That Santa does not love God' supposit? It cannot be Santa, since he doesn't exist. We could then say that the corresponding proposition is false, since the subject supposits for nothing. But what about 'That Santa does not exist is true'? It is affirmative and true, so the nominalization must supposit for something, but it cannot be Santa, since he doesn't exist. So Klima's discussion of what Buridan might say in certain cases like 'That Santa does not love God is bad' does not cover more problematic cases such as negative existentials.
If it makes sense to refer to things that do not exist, that is, to have a theory of objects according to which some of them don't exist, or to have a theory of supposition according to which some supposita don't exist, then Buridan is not ontologically committed to possibilia. It seems to me that given Buridan's nominalism and what he says about ampliation and supposition, is more appropriate to say he holds a Meinongian view of supposition rather than saying that he is committed to possibilia.
Normore claims argues for just this. One reason for thinking this is in giving a coherent interpretation of the Eucharist. The wine and bread are destroyed though their color, taste and other qualities remain and do not inhere in the body and blood of Christ. (Christ's blood and body does not taste like bread and wine, I suppose.)
Another reason for thinking that Buridan had such commitments comes from what he says about movement/motion, magnitude, inherence and change. For instance, Buridan discusses three ways in which a thing may change. First, it may undergo a change in its extrinsic properties by the thing in relation to which it stands changing. E.g. the table can change with respect to having a cup on it if the cup is taken away. Second, it its parts may undergo extrinsic change. E.g. a piece of clay can be made longer by stretching it, which results by rearranging its parts. Third, it may undergo intrinsic change. In this case, Buridan holds that there is a generation or corruption of something, i.e. a quality (e.g. whiteness). E.g. the table changes from black to white by the corruption of inherence-of-the-blackness-in-the table and a generation of inherence-of-the-whiteness-in-the table.