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## Section: New Results

### Discourse dynamics

Participants : Philippe de Groote, Sylvain Pogodalla, Maxime Amblard, Jirka Maršík, Aleksandre Maskharashvili.

#### Effects and Handlers in Natural Language

In formal semantics, logical meanings are assigned to natural language utterances. This process is guided by the principle of compositionality: the meaning of an expression is a function of the meanings of its parts. These functions are often formalized using the λ-calculus. However, there are areas of language which challenge the notion of compositionality, e.g. anaphoric pronouns or presupposition triggers. These force one to either abandon compositionality or adjust the structure of meanings. In the first case, meanings are derived by processes that no longer correspond to pure mathematical functions but rather to context-sensitive procedures, much like the functions of a programming language that manipulate their context with side effects. In the second case, when the structure of meanings is adjusted, the new meanings tend to be instances of the same mathematical structure, the monad. Monads themselves being widely used in functional programming to encode side effects, the common theme that emerges in both approaches is the introduction of side effects. Furthermore, different problems in semantics lead to different theories which are challenging to unite. We claim that by looking at these theories as theories of side effects, we can reuse results from programming language research to combine them.

Our work extends the $\lambda$-calculus with a monad of computations. The monad implements effects and handlers, a recent technique in the study of programming language side effects. We have proven some of the fundamental properties of our extended calculus: subject reduction, confluence and termination. We have then demonstrated how to use our calculus to implement treatments of several linguistic phenomena: deixis, quantification, conventional implicature, anaphora and presupposition.

#### Discourse Modeling with Abstract Categorial Grammars

We have studied several TAG-based grammatical formalisms for discourse analysis (D-LTAG [38], G-TAG [34], and D-STAG [33]), and we have proposed an ACG encodings of them. G-TAG is a formalism introduced for generating natural language texts out of conceptual (semantic) representation inputs. D-STAG is a synchronous formalism for modeling the syntax-semantics interface for discourse. It was introduced for discourse analysis (parsing). The ACG encodings of G-TAG and D-STAG shed light on the problem of clause-medial connectives that TAG-based formalisms do not account for. To deal with a discourse that contains clause-medial connectives, D-LTAG, G-TAG, and D-STAG, all make use of an extra grammatical step. In contrast, the ACG encodings of G-TAG and D-STAG offer a purely grammatical approach to discourse connectives occupying clause-medial positions. The method we propose is a generic one and can serve as a solution for encoding clause-medial connectives with the formalisms based on TAGs. The ACG encodings of G-TAG and D-STAG that we propose are second-order. Importantly, the class of second-order ACGs consists of intrinsically reversible grammars. Grammars of this class use the same polynomial algorithm to build parse structures both for strings and for logical formulas. Thus, second-order ACGs can be used both for parsing and generation. Therefore, the problems of parsing and generation with the ACG encodings of G-TAG and D-STAG are of polynomial complexity.