# Compositional Distributional Semantics with Syntactic Dependencies and Sectional Preferences
## 1 Introduction  
A key element in the process of language comprehension is the ability of humans to combine units of meaning into larger units by means of principles and mechanisms that are not yet well understood. In studies on formal semantics one of the main objectives is to account for the meaning of phrases and compound units from the meaning of their constituent lexical units. In these studies, the Principle of Compositionality, which takes into account the syntactic structure, has been defined to help formalize this semantic process. The Principle of Compositionality defines the meaning of a composite unit as \"a function of the meanings of the constituent words and of the way they are syntactically combined\" [1]. In the last decade, there have been some works within the distributional semantics approach that have attempted to build distributional semantic models taking into account syntactic structure and applying some version of the Principle of Compositionality to construct the meaning of compound units [2, 3, 4]. In these approaches, static word embeddings representing the constituent words of a complex expression or sentence are combined by operations associated with their syntactic categories and syntactic functions within the sentence, so as to elaborate a new embedding that would represent the compositional meaning of the sentence. In some of these syntax-based approaches, the meaning of the sentence is not a single vectorized representation, but the contextualized vectors of each constituent word [3, 5]. One of the main challenges is to provide the high-dimensional vector space with composition operations that have clear analogues with operations in formal semantics [6]. More recently, other approaches to contextual distributional semantics, mostly based on Transformers models, have emerged focusing on the same objective: the construction of dynamic and contextual word embeddings. Transformers using pre-training, like BERT [7], have shown impressive results in many natural language tasks, suggesting that these models represent compositional meanings in a very accurate way. However,because of their black box structure, it is unclear how and to what extent BERT-like Transformers combine word meanings into phrase and sentence meanings to capture high-level compositional information [8]. They do not use any explicit syntactic structure and therefore do not follow the compositional mechanism derived from the Principle of Compositionality. There are some Transformers that incorporate syntactic information in their models, but some doubts arise about the viability of these models in basic Natural Language Processing applications and Information Extraction tasks [9]. The increasing development and use of Transformers and other contextual word models has marginalized compositional distributional semantic models based on syntactic dependencies and compositional operations to meaning construction. One of the main reasons for the lack of interest in these models is their heavy reliance on datasets with simple and controlled syntactic constructions, e.g., noun-verb, noun-verb-noun, adjective-noun, etc. Purely compositional models, due to their linguistic complexity, are so far only successfully applied to datasets with syntactically controlled expressions. In contrast, contextual models derived from Transformers are fully adapted to expressions with open syntax. Therefore, most of the semantic datasets that are made available to the developer community and used in shared tasks contain open text without syntactic restrictions [10; 11]. Another important limitation for the development of compositional models is the lack of controlled datasets in different languages. This means that there is no work on multilingual compositional distributional semantics, contrary to what happens in the research focused on Transformers. In this article, our objective is to design a compositional model for several languages based on syntactic dependencies and to evaluate it on a syntactically controlled and multilingual dataset.