1. Introduction

1Latin texts have a wide diachronic and diatopic extension that corresponds to a similarly large diversity of the textual genres they represent. Besides literary ones, a huge amount of Latin texts of several different genres can be found spread all over Europe and beyond. An important textual genre is represented by scientific treaties, which in many cases are interesting not only for their contents, but also because of the technical terminology they feature.

2This is precisely the case for the Liber Abbaci ‘the book of the abacus’ by Leonardo of Pisa (also known as Fibonacci). Written in the very first years of the 1200s, it is a book on arithmetic promoting a style of calculation based on Arabic numerals without aid of an abacus. Fibonacci 1202-2021 is a project financed by the Tuscany Region and involving the University of Pisa and the Galilei Museum in Florence, following the publication of a critical edition of the Liber Abbaci by Enrico Giusti (Fibonacci 2020). The goal of the project is to produce an enhanced digital edition of this work by leveraging advanced publishing tools and investigating the use of computational linguistics techniques in order to uncover the wealth of linguistic, scientific and historical information contained in the book.

3Besides its scientific interest, the Liber Abbaci features a very peculiar lexicon, not often represented in the currently available (linguistically annotated) corpora for Latin. In order to fill this gap, in the context of the project Fibonacci 1202-2021 we have started performing the linguistic annotation of the Liber Abbaci, beginning from part-of-speech (PoS) tagging and lemmatization of a specific chapter of the book, chosen for its linguistic and historical interest. The dataset is freely available online1.

4This paper describes the process of annotation of the Liber Abbaci and two applications of its results, namely (a) the evaluation of a number of trained models for PoS tagging and lemmatization for Latin in out-of-domain fashion and (b) the interlinking of the annotated chapter with other linguistic resources for Latin through the Lila Knowledge Base (KB)2.

2. Related Work

5The research area dealing with the creation of linguistic resources and Natural Language Processing (nlp) tools for ancient languages has seen a remarkable growth during the last decade (Sprugnoli and Passarotti 2020). This has primarily concerned Latin and Ancient Greek as essential media to access and understand the so-called Classical heritage. In particular, several annotated corpora of Latin texts are currently available in digital format: they follow different guidelines and tagsets and feature different layers of linguistic annotation. This section wants to provide a (far from exhaustive) overview of such resources to show how the dataset presented in this paper stands with respect to the state of the art.

6The lasla corpus contains 2,500,000 semi-manually annotated tokens. It covers a large portion of the extant Classical Latin literature. It was started in 1961 by the lasla research center at the Université de Liège3 and is still being expanded4. The corpus is considered to be a gold standard, since the annotation of every token has been manually verified by a philologist. The linguistic information consists of lemmatization, morphological tagging, and an additional syntactic layer for verbs (Verkerk et al. 2020). Texts cover various literary genres (theater, poetry, prose) and have a chronological extension ranging from the comedies of Plautus to the texts of Suetonius and Pliny the Younger. Recent additions reach later stages of Latin literature,5 but include neither Medieval nor Neo-Latin works. Natural sciences and technical works are weakly represented in the corpus, the treatise De Agri Cultura ‘on agriculture’ by Cato and the recently added Naturales Quaestiones ‘investigations about nature’ by Seneca being the only examples.

7The corpus of Latin Lemmatized Texts released by Thibault Clérice (Clérice 2021b) is formed by 21,222,911 tokens (17,804,769 without punctuation marks) and includes a large set of Classical and Late Latin texts available in a a number of open access corpora6. Clérice’s corpus covers a very ample chronological span (up until the 9^th century) as well as different genres: from Classical literature (Horace, Ovid, etc.), to Christian religious texts and legal texts. The linguistic annotation consists of lemmatization and full morphological description of the tokens , produced automatically by applying the Pie Latin lasla+ model 0.0.6 (Manjavacas, Kádár, and Kestemont 2019), fine-tuned on ca. 1,500,000 tokens taken from the lasla corpus (Clérice 2021a), with very good results concerning lemmatization and PoS tagging7. However, results appear to be less good on unknown tokens8. This difference underlines the difficulty of using automatic annotation tools on texts with a very specialized language, surely not found in lasla, as is the case for Fibonacci’s Liber Abbaci.

8As for syntactically annotated corpora, five treebanks are currently available for Latin. They are the Index Thomisticus Treebank (it-tb) (Passarotti, 2019), the proiel treebank (Haug and Jøhndal 2008; Eckhoff et al. 2018), the Latin Dependency Treebank by the Perseus Digital Library (part of the Ancient Greek and Latin Treebank) (Bamman and Crane 2007), the Late Latin Charter Treebank (llct) (Flavio Massimiliano Cecchini, Korkiakangas, and Passarotti 2020) and the UDante treebank (Flavio M. Cecchini et al. 2020). The treebanks include texts of different genres (literary, historical, philosophical and documentary) and periods (from Classical to Medieval), but technical works are not represented.

3. Dataset Creation and Analysis

9The Liber Abbaci is made up of more than 270,000 tokens and is divided into 15 chapters of varying length. The choice of starting our manual annotation from chapter viii de reperiendis pretiis mercium per maiorem guisam ‘on finding out the price of goods through the “greater means”’ is due to the peculiarity of its content. Here, Fibonacci treats many simple business negotiations using proportions and referring to many examples taken from the entire Mediterranean world. The examples concern weight and monetary systems as well as the main products bought and sold in the 13^th century. This means that the text is rich of terminology specific of the mathematical domain but also of trade and commerce. Chapter viii is made up of 29,858 tokens (including punctuation marks), thus covering about 10% of the total length of the Liber Abbaci.

3.1 Data Annotation

10The manual annotation of chapter viii is carried out by a master’s degree student in Classical languages, with excellent knowledge of Latin but without any previous expertise in either linguistic annotation or computational linguistics. The overall effort of the work amounts to a total of 227 hours, including: training sessions, study of the guidelines and of terminology related to measures, coins and trade in the Middle Ages (Marcinkowski 2003; Martinori 1915), the actual annotation, the reconciliation after evaluation of inter-annotator agreement (iaa, see Section 3.2), periodic checks with supervisors, the linking of the annotated text to the LiLa KB (see Section 5). We make use of a large number of dictionaries as references: the Oxford Latin Dictionary (old) (Souter 1968), the Lexicon Totius Latinitatis (Forcellini 1965), the Dictionnaire illustré latin-français (herafter: Gaffiot) (Gaffiot 2016) and the Thesaurus Linguae Latinae9 for Classical Latin, but also the Dictionary of Medieval Latin from British Sources (Latham and Howlett 1975) and the Glossarium mediae et infimae latinitatis (Cange et al., n.d.) for Medieval Latin. Tokenization and sentence splitting are performed manually on a text editor, then lemmatization and PoS tagging are carried out on a shared spreadsheet following the Universal Dependencies (ud) formalism (Marneffe et al. 2021), in particular both the universal and the language-specific guidelines relative to the latest release of the ud treebanks (v 2.9)10.

11The implementation of the ud guidelines to the linguistic peculiarities of the text does not always happen straightforwardly. Chapter viii of the Liber Abbaci, as well as the work in its entirety, presents several typical features of Medieval Latin, both graphically (e. g. the monophthongization ae\rightarrow e and the spelling nichil instead of the Classical nihil ‘nothing’), morphologically (e. g the presence of analytical verb forms such as the “perfect”, i. e. present perfective, subjunctive habeat …honeratum, instead of the Classical onerauerit, from onero ‘to load’) and syntactically (e. g. the nearly exclusive use of quod ‘that’ to introduce declarative clauses, instead of accusative and infinitive11). It is also worth noting the very limited use of enclitic particles (in the whole chapter viii, Fibonacci uses the enclitic conjunction que ‘and’ only 3 times, appended to the auxiliary verb form erunt ‘they will be’) and the presence of syntactic calques of vernacular constructions (e. g. secundum quod uadis multiplicando ‘according to what you are multiplying’, where uado is preferred to the more Classical eo ‘to go’ and further assumes an auxiliary function, and the use of the gerundive form multiplicando is an innovation).

12But the main peculiarities of the text concern the lexicon. Chapter viii presents indeed a rich set of toponyms, units of measurement, names of coins and Arabisms often not even reported by Medieval Latin dictionaries. This is the case, for example, of some names of places, such as Bugea, today’s Biğāya/Bgayet in Algeria (a city where Fibonacci spent a period of his childhood, learning the art of calculation), and Septis, today’s Ceuta/Sabta on the Strait of Gibraltar; or, among the numismatic terms, of bolsonalia, a word designating a certain amount of broken silver or mixture coins which were sold to goldsmiths because they were adulterated or out of date.

3.2 Inter-Annotator Agreement

13The iaa is calculated on 30 sentences (1,010 tokens), with the participation of a second scholar with a background in Classical languages. We register an almost perfect agreement with a Cohen’s κ (Artstein and Poesio 2008) of 0.97 for lemmatization and 0.94 for PoS tagging.

14The comparison between the two annotations highlights two main issues. The first concerns the choice of the upos (Universal Part Of Speech) tag (Marneffe et al. 2021, sec. 2.2.2) for terms such as nam ‘certainly’ and enim ‘namely’, because different corpora and dictionaries adopt different conventions: e. g. nam is labeled as adverb in the Lila KB and Df in the Latin proiel treebank, both possibly equivalent to upos ADV12; as S13, standing for conjonction de coordination (upos: CCONJ) in the lasla corpus, and more generically conjonction (servant à confirmer/causale) (upos either CCONJ or SCONJ) in the Gaffiot; finally particle (not necessarily corresponding to upos PART) in the old, and similarly particule in one sense in the Gaffiot. The treatment of the etymologically related and functionally similar enim is mostly identical for all sources, only with the Gaffiot reporting a sense as adverbe instead of particule, followed by the lasla corpus in using both labels S and M (generic for adverbe), the latter though very marginally. These terms have been discussed and finally assigned the upos PART, used in the latest Latin ud treebanks to label discoursive particles like these. Such difficulties derive on one hand from the “volatile” and diachronically variable nature of similar elements, but on the other hand, and relatedly, to traditional grammars overlooking them and more generally skipping over pragmatic phenomena, in favour of “more Classical” parts of speech (hence the frequent inclusion of nam, enim, etc. in the catchall category of “adverbs”).

15The second issue is the upos to be used for unus ‘one’. Fibonacci often uses unus to indicate a generic entity, as is clearly visible when paralleled by alter ‘other’. In this case, unus is tagged as DET (determiner), like alter14. In a number of other contexts, however, unus specifies the quantity of a certain object. In such cases it is considered a NUM (numeral)15. The difficulty here originates from a well known and complex linguistic change that will eventually produce a clear indefinite article from the numeral in Romance languages, but for which, being so gradual, we cannot pinpoint an exact historical moment; cf. (Ledgeway 2012, vol. 1, sec. 4.2.1).

4. Comparing nlp Models

16Table 1 reports accuracy scores computed on our gold standard processed with UDPipe using the ud v2.6 models for Latin (Straka and Straková 2017). The scores clearly show that current models are not good enough to process the Latin of Fibonacci. The best accuracy for lemmatization is achieved by the model trained on the llct treebank, which contains a set of Early Medieval charters written in Tuscany. However, this scores are lower than state-of-the-art ones: the best participating system at the EvaLatin 2020 evaluation campaign achieves an accuracy of 96,19% for lemmatization and 96,74% for PoS tagging on the corresponding test set (Sprugnoli et al. 2020), i. e. about 33 and 15 points more than the results obtained on Fibonacci.

17Taking into consideration lemmatization, the percentage of out-of-vocabulary lemmas, that is, lemmas present in the text by Fibonacci but not in the training texts of the models, is very high (>50% of lemma types). The majority of errors are registered for numbers and common nouns. The first problem is due to the fact that some models do not recognize Arabic numbers, because they have not seen them in their training data, while others lemmatize them with a special “metalemma” of the kind of num. arab., eschewing lexical forms. As for common nouns, most errors related to lemmatization concern the lexical classes discussed in Section 3. For example, the tokens libris and libre are often lemmatized as liber ‘free’ (ADJ) instead of libra ‘pound’ (NOUN).

18Table 2 shows the f1 score per upos tag. We observe that an f1 above 70% is achieved by any model only on 5 tags: ADP, NOUN, NUM, SCONJ and VERB. No model recognizes the SYM tag (used for mathematical operators such as parentheses), because it is not present in their respective training data. The same is true for the tag PART in it-tb (up until ud v2.8)16, Perseus and proiel, and for the tag DET in Perseus. In old versions of the it-tb, DET is limited to the proto-article ly (8 occurrences), while in Perseus the tag PROPN appears only for the lemma Aefulanus (1 occurrence). The it-tb-based model, too, registers a near-zero f1 score for PROPN: in the corresponding training data, this tag is used for a restricted (116 types of lemmas) set of terms mostly specific to the domains of philosophy and religion (e. g. Aristoteles, Maria), not present in our dataset. Low performances are registered also for the AUX tag, the annotation of which is not consistent in training data: in Perseus, this tag is not used at all, while in EvaLatin 2020 it marks only the auxiliaries in periphrastic passive (including deponent) constructions, while in the other treebanks it is applied also to verbal copulas, as per ud guidelines. Further, the Liber Abbaci sees the rise (1 occurrence) of habeo ‘to have’ as a possible auxiliary (cf. Section 3.1), unheard of in Classical Latin and only attested (albeit marginally) in llct.

5. Linking and Querying in LiLa

19The LiLa KB makes linguistic resources for Latin interoperable by linking tokens in corpora and entries in dictionaries/lexica to a collection of canonical forms for Latin called Lemma Bank (Passarotti et al. 2020). In order to connect the lemmas of chapter viii to LiLa’s KB, a string match is first performed between the lemmas in the texts and those in the KB, also taking into account their parts of speech. Using this strategy, 88.8% of the lemmas are directly connected to a single entry in the KB. The remaining unconnected lemmas fall into two possible categories: ambiguous lemmas, that is, with possible connection to more than one entry in the KB; and lemmas absent from the KB. More specifically, we find 44 ambiguous lemmas (corresponding to 631 tokens): for example, colligo can be connected to two entries: either a first-conjugation verb colligare17 ‘to bind’, or a third-conjugation verb colligĕre18 ‘to gather’. These cases are manually disambiguated, checking each context of use. The remaining, not directly connected lemmas are not present in the KB and need to be manually added: these are mainly words denoting weight and monetary units (e. g. karatus ‘carat’), or different written representations of lemmas already in LiLa (e. g. torscellus is a graphic variant of torcellus19, a unit of length). Thanks to the linking, each lemma of our dataset becomes part of an interoperable ecosystem made of resources of different kinds. We can thus query different interlinked resources using sparql and the LiLa endpoints20. For example, we can find the lemmas appearing only in chapter viii21 and not in the other texts that are currently linked to the KB: the Summa Contra Gentiles by Thomas Aquinas (from the Index Thomisticus), those found in UDante (a corpus of 5 works mostly by Dante Alighieri, or attributed to him, manually annotated following the ud formalism), and the Querolus siue Aulularia (an anonymous comedy dating back to the 5^th c. ad).

20Table 3 shows the 5 most frequent distinctive, i. e. exclusively found in the Liber Abbaci, lemmas retrieved using a sparql query22. They are all related to mathematics, coins and units of measurement, confirming the specificity of the domain of our dataset. In particular, rotulus and cantāre are two units of weight, both deriving from Arabic, respectively from raṭl (in turn, a metathetical adaptation of Greek λίτρα litra ‘pound’) and qinṭār, which designates a weight of 100 rotuli23. The term soldus, instead, indicates a unit of measurement used for monetary quantities. Among the many currencies mentioned in chapter viii, Fibonacci often cites the byzantius, a golden coin minted in Constantinople24. Finally, virgula (diminutive of virga, properly a ‘rod’, used by Fibonacci in the same sense of virgula) primarily denotes the bar between the numerator and denominator of a fraction, but it can also designate the fraction itself (Bocchi 2004).

6. Conclusions and Future Work

21This paper describes the annotation of one chapter of the Liber Abbaci by Fibonacci, and reports on the linguistic peculiarities of this text and the ensuing challenges.

22The results of existing UDPipe models in lemmatization and tagging show low accuracy and f1 scores when compared to the state of the art for these tasks in the recent EvaLatin 2020 evaluation campaign. This, on the one hand, can be attributed to the characteristics of the genre of Fibonacci’s texts, which are representative of scientific Medieval Latin texts, and on the other hand can be explained with the different choices in annotation style of Latin treebanks released under the ud project. Substantial improvements can be expected with models trained on new releases of Latin treebanks which have already undertaken the effort of resolving annotation discrepancies and of making the annotation style across treebanks more homogeneous. Further improvements will however require new annotated chapters and experiments in domain adaptation, which are scheduled as future work.