A type-theoretical reduction of morphological, syntactic and semantic compositionality to a single level of description

Proceedings of Recent Advances in Natural Language Processing, pages 664–673, Varna, Bulgaria, Sep 2–4, 2019. https://doi.org/10.26615/978-954-452-056-4_078 664 A Type-Theoretical Reduction of Morphological, Syntactic and Semantic Compositionality to a Single Level of Description Erkki Luuk Institute of Computer Science, University of Tartu, J. Liivi 2, Tartu 50409, Estonia erkkil@gmail.com Abstract The paper presents NLC, a new formal- ism for modeling natural language (NL) compositionality. NLC is a functional type system (i.e. one based on mathematical functions and their types). Its main fea- tures include a close correspondence with NL and an integrated modeling of mor- phological, syntactic and semantic compo- sitionality. The paper also presents an im- plementation of NLC in Coq. The imple- mentation formalizes a diverse fragment of NL, with NLC expressions type check- ing and failing to type check in exactly the same ways that NL expressions pass and fail their acceptability tests. Among other things, this demonstrates the possi- bility of reducing morphological, syntac- tic and semantic compositionality to a sin- gle level of description. The level is ten- tatively identified with semantic compo- sitionality — an interpretation which, be- sides being supported by results from lan- guage processing, has interesting implica- tions on NL structure and modeling. 1 Introduction As shown by Asher (2014), Luo (2010, 2014) and Ranta (1994), in a logical approach (i.e. in one with simpler alternatives such as zeroth, first, sec- ond and higher order logic), complex type theo- ries outshine simpler ones in accounting for nat- ural language (NL) phenomena like anaphora, se- lectional restrictions, etc. The basic judgement in type theory, a : A, is read “term a has type A”, where (i) type := a category of semantic value. Since the notion of type is inherently semantic, it is by definition suited for analyzing universal phe- nomena in NL, as NL semantics is largely univer- sal (as witnessed by the possibility of translation from any human language to another). 2 Interpreting Natural Language NL functions and function applications have a dis- tinctive form. Specifically, any morphosyntac- tically admissible concatenation c(a, e1, ..., em), which is parsed as a(e1, ..., em), is a function or function application term (FFAT) in NL (e1, ..., em may be null). For example, red, red book, livre rouge, etc., are FFATs in idiosyncratic notations (viz. English, French, etc.). As linguistic expres- sions are FFATs, they are naturally parsed as func- tions or function applications. How to decide whether a particular application a(e1, ..., em) holds? Usually, one has a basic intu- ition about what modifies what (modification is a subcase of function). The main sources for the in- tuition are morpheme or word classes and seman- tic contribution tests. For example, -s modifies (i.e. is a relation over) work in works rather than vice versa, as (1) affixes modify stems not vice versa, (2) person/tense and plural markers modify flexibles1 rather than vice versa, and (3) -s con- tributes to the meaning of work in works rather than vice versa. By a similar argument, …

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