Adapting the P ortuguese B raille System to Formal Semantics (2021)

Abstract: Since the seminal work of Richard Montague in the 1970s, mathematical and logic tools have successfully been used to model several aspects of the meaning of natural language. However, visually impaired people continue to face serious difficulties in getting full access to this important instrument. Our paper aims to present a work in progress whose main goal is to provide blind students and researchers with an adequate method to deal with the different resources that are used in formal semantics. In particular, we intend to adapt the Portuguese Braille system in order to accommodate the most common symbols and formulas used in this kind of approach and to develop pedagogical procedures to facilitate its learnability. By making this formalization compatible with the Braille coding (either traditional and electronic), we hope to help blind people to learn and use this notation, essential to acquire a better understanding of a great number of semantic properties displayed by natural language.

## introduction in their attempt to describe and understand the multiple aspects that underlie the construction of sentential meaning in natural languages, philosophers and semanticists explored different conceptions and methodologies, which gave rise to a large number of theoretical approaches. a fruitful and promising way to tackle some of the most complex semantic problems, based on a formal notation, was initiated by richard montague in the decade of 1970 (see e.g., @xcite . formal approaches to semantics use logical and mathematical tools to account for various aspects of meaning in natural language. although the initial task of formal semantics was to describe and resolve ambiguities regarding quantification in the nominal domain, it was rapidly expanded to cover other areas of interest to semanticists, from tense and aspect relations (e.g., @xcite @xcite to complex modal descriptions involving the interaction of time, situations, and possible worlds (cf. @xcite and the papers collected in @xcite , for example). the adoption of formal outlines in the context of the semantic descriptions for natural languages has the advantage of giving rise to unambiguous representations for the meaning of sentences, which facilitate the confirmation or rejection of the suggested hypotheses and postulates. to illustrate this point, let us consider a simple example, classically discussed in the literature. a sentence like "every student read a book" is clearly ambiguous between two interpretations: it may mean that every student read a (non-specific) book, whatever it is; or it may mean that there is a (specific) book that every student read. the formal representations in (1) and (2) unambiguously spell out these two readings: in other words, in the representation in (1), the universal quantifier has wide scope over the existential one, which leads to the multiple book reading. conversely, in (2), it is the existential quantifier that has wide scope over the universal one, giving rise to the unique book reading. on the other hand, formal representations have been able to transcend the domain of simple sentences. in fact, @xcite discourse representation theory (drt) extends the semantic formalisation to more complex discourses @xcite segmented discourse representation theory (sdrt) even deals with pragmaticbased notions such as those underlying rhetorical relations. today, formal semantics supports a significant number of theories that describe meaning in natural language. in fact, formal approaches cover almost all areas that traditionally are ascribed to semantic studies, from simple word relations to the intricacies behind discourse structures. irrespective of the particularities that characterise the diverse frameworks departing from formal approaches to meaning, there are, nonetheless, some important principles that bring them together. in all cases, predicates are related to their argument(s), i.e., entities that fulfil the predicative relation. different kinds of operators are introduced in order to model the interactions that arise between the participants in a sentence or even between independent sentences in a discourse. the variables that may be introduced in a formula correspond to entities of distinct kinds: they can be individuals, intervals of time, situations or (possible) worlds. besides the predicative relations, entities may interact with a range of operators that include quantifiers, relations between elements and sets of elements or between two sets of elements, or even precedence or overlapping relations in the temporal domain. despite its undeniable relevance regarding the semantic studies on recent years, no attempt has been done, at least to our knowledge, to provide visually impaired people with adequate tools that enable them to learn and manage this kind of formalisation. the main goal of our project is, thus, to explore some ways that could make it possible to blind students and researchers to interact with the most common and widespread representations in formal semantics. to do so, we will make use of the immense potential that is offered to us by the braille system. 2 the braille system: some preliminary remarks braille is the most widespread and efficient means for blind people to read and write texts. it was created in france by louis braille in 1824 in order to provide a tactile representation for the french alphabet (cf. @xcite . based on the night writing encoding system developed by charles barbier, the braille system consists of rectangular cells placed sequentially. each cell corresponds to one character and it is traditionally constituted by two columns each of which presents three "slots" . the different combinations of salient or raised dots in each cell gives rise to the several braille characters. the six dots that form a cell are numbered, so that each character can be identified by the raised dots that represent it. for instance, the character "b" , in braille, is identified by dots 1 and 2, the character "t" by dots 2, 3, 4 and 5, and so on. there are 64 possible combinations, including no dots at all for spaces between words. as we have pointed out, the original purpose of the development of the braille system was to provide a tactile transcription of the printed alphabet, enabling blind people to read and write texts. since the languages of the world differ considerably from each other, either concerning the alphabets that are employed, or regarding the number and type of graphic accents and punctuation marks they use, braille encoding is language-specific, i.e., it varies according to the chosen language. braille has proven to be an immensely powerful and flexible system in various ways. first, it was fruitfully adapted to include a large number of languages and alphabets around the world. moreover, it was extended to cover other notations. music, mathematics, physics, chemistry, phonetics, or informatics are some of the multiple areas in which braille has been successfully employed to make knowledge more accessible to visually impaired people (cf. @xcite @xcite . second, braille has adapted easily to the emergence of new technologies, following its continuous development. the ancient slate and stylus -a handwriting device -has been substituted by braille writers, and, more recently, by refreshable braille displays, notetakers and tablets (cf. @xcite . in order to cover a greater range of symbols, as well as to be used with braille displays and notetakers, the six-dot braille has been enhanced with two additional dots at the bottom of the cell, giving rise to the so-called 8-dot braille system or 8-dot braille code. nowadays, braille is used with computers, tablets, and smartphones, making information and knowledge easily accessible: it allows blind persons to access technology and to write and read emails, books, newspapers, and scientific articles on practically equal terms with respect to sighted people. although its use is declining in some parts of the world, due mainly to the growing influence of audio media, such as speech synthesizers, braille remains essential for the learning process and for the general literacy of visually impaired people, facilitating their inclusion in the labour market and in other important social activities, especially when it is used in combination with new technologies (see, e.g., wiazowski 2014). of course, it was not our intention here to provide an in-depth approach to the internal structure and functioning of the braille system, having limited ourselves only to leave a few brief remarks on the aspects that seem most relevant and more useful to our purposes. for more details and information, see, among many others, @xcite , croisdale, @xcite , @xcite , and, for specific aspects of the portuguese braille system, @xcite , @xcite , @xcite or @xcite . ## the project given that our project is still at an exceedingly early stage, it will not be possible to offer here any relevant results and conclusions. nevertheless, i will expose our main goals and the methodology that was chosen to achieve them. ## conclusion our project aims to turn formal semantics more accessible to blind students and researchers who want to learn and investigate different aspects of this important area of linguistic knowledge. with this work, we want to contribute in some extent to a better inclusion of this part of the population into graduate and post-graduate programs, facilitating their participation in university advanced studies. we believe that accessibility for all is the better way to spread knowledge and information, to improve social inclusion and to favour the empowerment of impaired people, contributing to a more equitable society. our work hopes to constitute a small step to create better conditions of access and to open new horizons to blind people. for future research, it would be interesting to provide optical character recognition (ocr) software with the capacity of recognizing the symbols used in formal semantics; this would constitute an important step to turn printed texts fully accessible to screen readers. however, the complexities that this task involves are completely beyond the scope of our present work.