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There are several frameworks that have been built by both linguists and computer scientists to deal with the problem of semantic representation of sentences, most notably Abstract Meaning Representation (https://amr.isi.edu/), Framenet(https://framenet.icsi.berkeley.edu/), PropBank. However, AMR explicitly only provides representations of sentences, and PropBank deals with the sort of predicate-argument structures which effectively are bound within a sentence.

There has also been research in NLP in determining basic relationship categories between sentences - whether one entails, paraphrases, or contradicts another one. However, most paragraphs contain sentences with much richer relationships.

Has anyone come up with a way of reasoning about the semantics of a paragraph, as opposed to a sentence, that lends itself to developing annotation tools and datasets? For instance, let's say I perform AMR parsing and then have a list of graphs, each of which represents a sentence - is there any other data structure I could transform this into which would be more useful than just a list of graphs which I know are somehow related?

I guess a more theoretical question would be - are paragraphs semantically just the union of all the propositions in each sentence, or is there more internal structure?

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    The theoretical question is one that's been argued for decades, but under slightly different terms: Is discourse structure even part of semantics, or part of pragmatics? And, assuming the latter, does pragmatics have some input into semantics during comprehension, or is it a one-way street, where semantics just generates propositions with variables in them, and then some non-linguistic part of the brain connects them up pragmatically? – abarnert Jan 14 '19 at 22:07
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    But as I understand things, most people working on theories of pragmatics just ignore those questions from theoretical semantics, and most people working on practical NLP mostly ignored all theory that came after early-1970s formal semantics until the fields somewhat recently started talking again, so I'm not sure the historical debate on the theoretical question is all that useful to you. – abarnert Jan 14 '19 at 22:12
  • This is one reason why theoretical semantics and pragmatics are not as useful as they could be. It's worthwhile reading what McCawley said about them, and about research in general. In particular, "it's impossible to talk in any detail about any of these three fields without getting into the other two, so I don't even try to keep them separate". – jlawler Jan 15 '19 at 2:54
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I'm surprised you don't mention DRT (Discourse Representation Theory). DRT is a semantic framework that developed, amongst others, from the need to account for anaphoric references (pronouns) across sentence boundaries. As you already suspect, a discourse (roughly what you mean by "paragraph") is seen as a conjunction of individual propositions.
DRT is not so much concerned with relations between sentences such as entailment, but mostly with the treatment of variables and their interpretation in context as discourse referents (= the individuals that are being referred to in the propositions), e.g., the question which entity introduced by a previous sentence a pronoun like he can refer to, and which links are not possible. A very typical question that DRT would attempt to answer is

In the sequence of sentences Peter walks in the park. He whistles., how can we formally account for the fact that by he in the second sentence we mean the same individual as by Peter in the first sentence - and what is semantically wrong with the syntactically similar looking sequence of sentences Peter doesn't have a wife. * She knits.?

Not sure if that's something you'd be interested in.
A very accessible introudction to DRT (which, however, presuposses knowledge of first-order logic - available in the first volume) can be found in the first chapter of P. Blackburn & J. Bos: Representation and Inference for Natural Language, Vol. 2, or here.
However, I am not sure if at all or to what extent this theory is used in modern NLP. It has mostly been of theoretical interest and can be neatly implemented in Prolog (as introduced in the remaining chapters of Blackburn & Bos Vol. 2).

Related to DRT is Dynamic Predicate Logic (DPL), also sketeched in the introductory chapter of Blackburn & Bos Vol 2 and discussed in more detail e.g. here. (And just to give credit to the beautiful title of the work, I should also mention Paul Dekker's dissertation captioned Transsentential Meditations). This provides a yet more formal account of discourse semantics, although I can hardly imagine it has actual applications in nowadays NLP, and is probably not as intuitive to get into as the boxes employed in DRT.

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  • How useful that is this in contrast to simply removing punctuation, which, as far as I know, is frequently done in NLP. If you drop the fullstop or replace it with and, the two sentences work as one, so where's the difference to sentence parsing? I get that other examples might not work out so easily, but looking at e.g. one of your sentences we might have "something you'd be interested in" and "you'd be interested in A very accessible introudction to DRT", a construction that must have some relevance on account of how it's been used in advertisement recently using similar word plays. – vectory Jan 14 '19 at 14:21
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    @vectory The problem is that in classical semantic analysis, the basic unit of analysis is a proposition, so whether you decide put a fullstop in between or an and (or a comma or whatever), the expression Peter walks in the park and whistles is technically still two sentences/propositions, just conjoined together to one larger sentence. The problems arising between mine and your examples would be exactly the same, whether two sentences they are orthographically separated by a fullstop or a comma. As I said, I don't know much about how these problems are dealt with in modern NLP. – lemontree Jan 14 '19 at 15:54
  • The second part of I don't understand. What does my example sentence have to do with advertisement or word play? – lemontree Jan 14 '19 at 15:54
  • Yeah, I'm realizing that my problem is less with the sentence-paragraph boundary, and more with the "union of propositions without internal structure" formalist approach. AMR represents a more practical slant, if not alternative, to turning "Sally walked the dog on Sunday" into person(p) /\ name(p, Sally) /\ event(p1) /\ walked(e1, p, d) /\ dog(d), because it uses graph theory to represent the internal structure - but only over the course of a sentence – lightning Jan 14 '19 at 20:42
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    @lightning That last question is interesting. And it's even plausible that the difference is different in reading vs. listening. And it seems like a relatively easy thing to do basic psycholinguistic tests on (without needing any kind of theory of discourse, or even a very detailed theory of sentential semantics), so there's a good chance someone has done some research that you could search for. – abarnert Jan 14 '19 at 22:19
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When we implemented our software for 'paragraph analysis' it ended up looking like a 'union of propositions' with two minor changes. 1. paragraphs were often preceded by headings which we used to set the context of the paragraph (like a topic model/domain) 2. We used a modification of this simple framework: http://depts.washington.edu/pswrite/Handouts/Paragraphs.pdf to tag 'paragraph intents'.

We found very little information on the paragraph as the unit of analysis in the literature. Frameworks like AMR, DRT, Framenet were better at describing the sentence elements and discourse connectives. It's really odd that there isn't more written on the subject.

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