A lexicographic approach to the study of copolysemy relations

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Universitй de Lorraine

A lexicographic approach to the study of copolysemy relations

Alain Polguиre

CNRS, ATILF

Abstract

The notion of lexical polysemy is considered under very different angles depending on the context in which it is called on, e.g. in theoretical lexicology, practical lexicography or so-called cognitive approaches to the lexicon. We adopt an approach where polysemy is defined as a property of vocables (roughly, entries in dictionary word lists): the property to regroup several word senses, monosemy being the opposite property. Polysemy is the consequence of a more basic fact: the relation that holds between lexical units grouped within the same vocable. This relation we term copolysemy. The notion of copolysemy is required to not only account for such a well-known phenomenon as regular polysemy, but also to model the polysemy structures of vocables and the incidence these structures may have on lexical dynamics, vocabulary acquisition, analogical reasoning based on lexical information, etc. As for many other aspects of lexicology, the study of copolysemy has to be anchored in a thorough analysis of lexical data. In this paper, we present the current results of an exploration of copolysemy in French, which allowed us to systematically retrieve patterns of copolysemy (on which we believe regular polysemy is built) and achieve formal description of the polysemy structure of several thousand French vocables. The descriptive work is embedded in a large-scale lexicographic project, namely the construction of the French Lexical Network (fr-LN). Though based on the study of the French lexicon, the approach to the modeling of polysemy presented here is expected to be applicable to natural languages in general.

Keywords: polysemy, copolysemy, lexical relation, Lexical System, French Lexical Network (fr-LN), Explanatory Combinatorial Lexicology and Lexicography

Лексикографический подход к изучению кополисемических отношений

Ален Польгер

Лотарингский университет, CNRS, ATILF, Нанси, Франция

Понятие лексической полисемии рассматривается c разных точек зрения в теоретической лексикологии, практической лексикографии и при так называемом когнитивном подходе к изучению лексики. В данной статье полисемия определяется как свойство вокабулы (заглавного слова словарной статьи) объединять несколько значений слова, в то время как моносемия рассматривается как противоположное этому свойство. В основе полисемии лежат отношения между лексическими единицами в рамках одной вокабулы. Такие отношения мы называем кополисемией. В статье обосновывается необходимость изучения данного явления, подчеркивается, что понятие кополисемии важно не только для объяснения хорошо известного понятия регулярной полисемии, но и для моделирования полисемической структуры вокабул, понимания того, как эта структура влияет на изменения в лексике, освоение новой лексики и т. д. Изучение кополисемии должно основываться на тщательном изучении лексических данных. В данной статье мы представляем последние результаты исследования кополисемии во французском языке, которое позволило нам системно выявить модели кополисемии (на которых, как нам кажется, основана регулярная полисемия) и формально описать полисемические структуры нескольких тысяч французских вокабул. Эта практическая работа является частью широкомасштабного лексикографического проекта по созданию Французской лексической Сети (йт-ТЫ). Несмотря на то, что данное исследование провидится на материале французской лексики, такой подход моделирования полисемии может быть применен к естественным языкам в целом.

Ключевые слова: полисемия, кополисемия, лексические отношения, лексическая система, Лексическая сеть французского языка фг^^, толково-комбинаторная лексикология и лексикография

1. On and around the notion of polysemy

1.1 Object of the Study

We present a theoretical and descriptive study of lexical polysemy in French that is based on the notion of copolysemy -- relation among various senses of a single word -- rather than directly on polysemy -- property of words to express more than one meaning. The descriptive work is embedded in a large-scale lexicographic project, namely the construction of the French Lexical Network or fr-LN. Though based on the study of the French lexicon, the approach to the modeling of polysemy presented here is expected to be applicable to natural languages in general.

Section 1 examines the very notion of polysemy, which has been extensively discussed in the literature -- e.g. Apresjan (1974), Bejoint (1990), Picoche (1993), Cruse (1995), Zalizniak (2007), Gries (2015), Courbon (2015), to name only a few references. Note that polysemy is often reinterpreted through the notion of ambiguity, especially in cognitive linguistic approaches: a word is said to be polysemous if its usage generates for the Addressee ambiguity in the Speaker's speechWe write Speaker, with a capital S, to refer to the producer of given linguistic utterances, as opposed to the speaker of a language (no capital). By analogy with Speaker, Addressee is also written with an initial capital.. Ambiguity, however, will not be taken into consideration by us, and this is the third and last time we shall use this term. For us, a word is polysemous if its signifier can be used by the Speaker to express several distinct but related meanings. We adopt the perspective of the Speaker encoding a message in a linguistic utterance rather than the perspective of the Addressee decoding the Speaker's utterance.

In studying polysemy, we proceed, for the most part, according to theoretical and descriptive principles of Explanatory Combinatorial Lexicology, the lexical component of the Meaning-Text linguistic theory (Mel'cuk et al. 1995, Mel'cuk 2006a). However, this being a paper in honor of, and greatly inspired by, Anna Wierzbicka's linguistics, it is normal that we position our work relative to the Natural Semantic Metalanguage approach (Wierzbicka 1985, Goddard and Wierzbicka 2002, 2014), whenever it appears to be relevant to do so.

This “theoretical” section of the paper continues with a definition of the notion of polysemy (1.2), followed by the introduction of the indispensable, but largely ignored, notion of copolysemy (1.3) and finally by methodological considerations on what a lexicography-based approach to the study of (co-)polysemy should be (1.4). Section 2 explains how lexicographic modeling of copolysemy relations in French is performed in the context of the construction of the French Lexical Network. Finally, Section 3 presents our model of polysemy proper, with the detailed description of copolysemy relations that were identified so far.

The following writing conventions are systematically used throughout the paper:

¦ names of lexical units and vocables are written in small capitals -- e.g., the vocable leg which contains the lexical units (senses) leg I.1, leg I.2 ...;

¦ the relation of copolysemy between two lexical units L₁ and L₂ is noted L₁ ^ L₂;

¦ names of copolysemy relations are written in non-proportional font with an initial capital letter -- Conversion, Extension, Metaphor ...;

¦ names of Meaning-Text lexical functions are written in bold non-proportional font -- Syn, Anti, Magn, Operi ...;

¦ important notions are written in sans serif font when first introduced -- lexical unit, copolysemy ...

1.2 Polysemy as "Natural" Grouping of Lexical Units

By polysemy, we shall exclusively mean in what follows `lexical polysemy'. The polysemy of such linguistic entities as grammatical constructions (Apresjan 1974: 5--6, Goddard 2000: 140--144) will not be considered. We believe grammatical polysemy to be quite distinct from lexical polysemy both in its structural organization and in the methodology that ought to be applied in order to explore and model it. There surely are important connections to be established between the two phenomena, but we are in no position to propose any significant insight on this topic.

Let us start with the definition of lexical polysemy, as it is used in the present study. In order to formulate such definition, two preliminary notions have to be specified: lexical unit and vocable.

Definition 1. A lexical unit of a given language is a linguistic entity characterized by a specific meaning expressed in that language either by wordforms -- in which case the lexical unit is a lexeme, e.g. SOFA -- or by semantically non-compositional phrases -- in which case it is an idiom, e.g. LOVE seat.

A lexical unit can be considered as being an abstraction over a set of linguistic signs. A lexeme, in particular, is the set of all wordforms that are inflectional variants expressing the same lexical meaning: SOFA = {sofa, sofas}. It is essential to consider that, when dealing with lexical units, three elements have to be simultaneously taken into consideration: 1) the meaning of the lexical unit, 2) the form that expresses this meaning and 3) the individual combinatorial properties of the wholeThis tripartite perspective on lexical units is a direct consequence of the Meaning-Text conceptualization of linguistic signs as triplets consisted of a signified (meaning), a signifier (form) and a syntactics (combinatorial properties). For a detailed presentation, see Mel'cuk (2006b: Chapter 7)..

Two or more lexical units can entertain a remarkable semantic and formal relation that justifies their grouping within higher level lexical entities than lexical units, namely vocables.

Definition 2. A vocable is either (i) a multi-element set containing lexical units whose forms of expression are identical and whose meanings, while different, display a significant intersection, or (ii) a singleton comprised of only one lexical unit for which there exists no other lexical unit that could be grouped with it in such a way.

Let us take the vocable balcony as illustration. It groups together two lexical units: balcony 1 [on the faзade of a building] and balcony 2 [in a theater]. Both balcony 1 and balcony 2 are expressed by the same signifiers (balcony, balconies) and though their meanings are distinct, one clearly perceives a significant semantic connection between them. It is, of course, possible to argue for the existence of a unique, extremely vague lexical unit balcony carrying a generic lexical meaning `balcony', to which various contexts -- balcony overlooking the square vs. to sit at the front row of the (theater) balcony -- would “give” a potentially unlimited number of richer derived meanings. It is no place to debate such extreme contextualist approach to lexical semantics -- for a discussion, see Polguиre (2015). Our main reasons for postulating two separate units balcony 1 and balcony 2 are the following:

¦ both lexical units denote architectural elements of totally different wholes -- a faзade wall vs. a theater hall;

¦ each of them controls its own specific network of paradigmatic and syntagmat- ic lexical relations (called its lexical cluster in 3.1 below) -- balcony 1 ^ wall, faзade, balustrade, ~ overhangs sth., to sit on a ~ ... vs. balcony 2 ^ theater, parterre, stage, seat, to sit in the ~ ...;

¦ in the context of language teaching, it is not unreasonable to present balcony 2 as a metaphorical derivative of balcony 1 based on shape analogy.

Two important remarks about the notion of vocable have to be made. Firstly, as the above definition shows, there are in fact two kinds of vocables: those that contain more than one lexical unit -- e.g. balcony and arm (of a person vs. an animal vs. an object vs. a company) --, qualified as being polysemous; 2) those that contain just one lexical unit -- e.g. rhinoceros and tetrahedron --, qualified as being mono- semous. The former type is considered by us to be the default one and the latter type a marked case (see 1.4.1 below). One may wonder why the notion of vocable should also encompass “isolated” lexical units. This is justified both for theoretical and practical reasons which will become clearer shortly. The second important remark about the notion of vocable concerns the criterion of “significant meaning intersection”. What makes a meaning intersection significant? For instance, seals in (1a) and seal in (1b) below will be considered as being two wordforms of lexemes which are not connected by a significant meaning intersection and therefore belong to two separate vocables, or homonymsTo ensure naturalness, our examples are not constructed by us. They are extracted from corpora or from the Internet; some are slightly doctored for readability purposes. This remark does not apply to Section 3 where very compact examples illustrating senses of vocables are needed for practical reasons..

(1) a. There used to be a large population of seals in the Dutch delta region.

b. Any document bearing the impression of the royal seal was as good as a direct command of the King.

However, these wordforms do possess a semantic intersection, if only the very general meaning `physical entity'. This meaning is probably much too vague to be considered as being significant, when compared to the rich semantic intersection that is found between balcony 1 and balcony 2 mentioned above. But more importantly, what makes the latter intersection significant is the fact that, as speakers of English, we do not wish to consider that the formal identity of balcony 1 and balcony 2 is unrelated to their semantic intersection. In other words, we do consider that the formal identity bears semiotic significance and this significance justifies the grouping within a single vocable. The notions of significant meaning intersection and semiotic significance are related to what Apresjan (1974: 14--16) calls non-trivial common part (of lexical meanings and, therefore, of lexicographic definitions).

The formal similarity and meaning intersection that connect two lexical units L₁ and L₂ can be envisaged according to two perspectives, either separately or simultaneously: synchronic vs. diachronic perspectives.

Synchronic perspective: One may consider that, in the current state of the language, it is part of our lexical competence to acknowledge the semantic relation between L₁ and L₂ as being significant and non-coincidental, and that this acknowledgment allows us to better grasp the way both L₁ and L₂ should be used -- for instance, the fact that they share non-trivial combinatorial properties, such as the two senses of bombardment in (2a--b) below which control the same collocative intensifier heavy while having totally different meanings.

(2) a. Rebel-held areas of the city came under heavy bombardment.

b. The minister stormed out of the interview after a heavy bombardment of questions.

Diachronic perspective: One may believe/know that L₂ is an offspring of L₁ in the history of the language. In this case, what matters most is the (right or wrong) belief that the existence of L₂ in the language lexicon is the result of a process of lexical creation by which the signifier of L₁ has been “recycled” to express a new (= not associated to this signifier before) meaning because it is closely related to the meaning of L₁ in one way or another.

Both perspectives interact in the mind of speakers of the language, but it is healthy for lexicologists and lexicographers to clearly identify which one they adopt. Eventually, they may precisely want to focus on the interaction between synchronic and diachronic facts, but they have to state it explicitly. Nothing new here and it is a methodological principle that has been made clear at least since F. de Saussure. The present study is conducted from a strict synchronic perspective. This means that we do not presuppose any actual knowledge of the history of the language when deciding whether or not to group two lexical units within the same vocable. What matters is the semiotic significance or the “naturalness” of the grouping of lexemes for a hypothetical Speaker, totally unaware of diachronic facts when lexicalizing her/his thoughts. Clearly, such Speaker is a theoretical construct, but one that is useful and, even necessary, for conducting lexicographic work. We are, of course, fully aware that this way of proceeding is insufficient if one wants to account for what takes place in the mind of individuals when they use natural languages. It is, however, a necessary first step, the only one that allows for the actual construction of lexical models, as imperfect and incomplete as they may be.

Based on the above discussion of the two basic notions of lexical unit and vocable, we can propose a rather simple and straightforward definition of the notion of polysemy as it is used in this paperTerminological remark: this notion of polysemy does not belong to the standard notional system of Explanatory Combinatorial Lexicology, our theoretical framework of reference. For I. Mel'cuk, polysemy is not a property and the term polysemy is to be equated with polysemy relation. It is therefore more or less equivalent to our own term copolysemy, introduced below (Subsection 1.3)..

Definition 3. Polysemy is the property of a vocable to contain more than one lexical unit.

There is a striking difference between the above definition of polysemy and definitions usually found in the literature: our definition is absolutely minimal as it is entirely derived from the notion of vocable which, in our opinion, is primary. Therefore, vocables come first, as natural groupings of lexical units, and polysemy comes next, as property of a given vocable of not being a singleton. Apresjan (1974)'s definition of polysemy“The word A is called polysemantic if for any two of its meanings a_i and aj there exist meanings a₁, a^ ..., a_k, a such that a, is similar to a₁, a₁ to a^ etc., a_k to a and al to aj” (Apresjan 1974: 14)., for instance, is constructed around the undefined notion of word, which obviously cannot correspond to our notion of lexical unit but rather to that of vocable. To put it differently, definitions such as Apresjan's define polysemy by trying at the same time to partly explain what is meant by word.

Though the notion of polysemy is built on that of vocable, one should note that if polysemy did not exist in natural languages -- i.e. if all vocables were monosemous -- there would be no need for the notion of vocable in lexicology. This fact explains why researchers who are either not particularly interested in polysemy or are negating its relevance outright do not feel the need for a distinct notion of vocable; the terms dictionary entry or word suffice to satisfy their metalinguistic needsWe found in the literature an interesting substitute for the term vocable, namely: [a] polysemy. See Traugott and Dasher (2001: 11) when they talk about sense creation through polysemy: “Our theory of meaning embraces the hypothesis that families of related meanings, or polysemies, can, and indeed must be identified.” This terminological practice is preaching by the example as it makes the vocable POLYSEMY be polysemous..

1.3 From the Property of Polysemy to the Relation of Copolysemy

1.3.1 Definition of Copolysemy

Contrary to homonymy, that is conceived of by linguists as well as laypeople as a relation between two words (formally identical but with unrelated meanings), polysemy is commonly envisaged as a property of wordsWe allow ourselves to use word -- which is not part of our terminology -- when it is appropriate to remain vague; for instance, when adopting a layperson's perspective on language.. There is therefore no possible direct connection between polysemy (a property) and homonymy (a relation); these notions are indirectly connected. To illustrate this conceptualization of polysemy as property, let us briefly examine how two renown general language dictionaries, the Longman Dictionary of Contemporary English and the American Heritage Dictionary of the English Language⁹, describe the term polysemy. First of all, they have no entry for it! They have an entry for the adjectivepolysemous, defined approximately by the formula: “[a word] that has more than one meaning”. The adjectival entry mentions a corresponding noun polysemy, without any definition, as if this noun were a semantic derivative of the adjective polysemous. From this, we can infer an implicit definition of the noun polysemy, something like: “property of a word such that it is polysemous”. This illustrates clearly to what extent polysemy is conceptualized as a property of something, and not as a relation between two things. And this is perfectly in accordance with the definition we proposed for this notion in Subsection 1.2https://www.ldoceonline.com. http://www.ahdictionary.com. Note that Apresjan (1974)'s definition -- quoted in Subsection 1.2, Footnote 5 -- is also using polysemous as starting point (more precisely, polysemantic) rather than the noun polysemy itself. M. Brйal being a philologist, he is primarily concerned by the dynamic phenomenon of word creation through polysemy (diachronic perspective). For this reason, his term polysйmie denotes a specific process of “sense multiplication” rather than a property of a vocable: “Nous appellerons ce phйnomиne de multiplication la polysйmie” (Brйal 1897: 154--155)..

Now, while polysemy is a property of a vocable, it is indeed based on a relational fact, i.e. the existence of one or more lexical relations within the lexicon. If vocable V is polysemous, it is because there exist at least two lexical units in the language that are linked by a complex formal and semantic relation ^ (characterized in Subsection 1.2 and still unnamed for now) and whose grouping constitutes V. In other words:

Interestingly, there is to our knowledge no established term that denotes the ^ relation holding between two lexical units of the same vocable. There exist terms to denote specific types of ^ -- lexical metonymy, lexical metaphor, etc. --, but nobody seems to have cared to name the generic relation itself since the original coinage of the term polysйmie by the French philologist Michel Brйal (Brйal 1897: Chapters IX and X)¹¹. When the recourse to the underlying ^ relation is needed, the term polysemy is used as if it were denoting a relational fact, for instance by mentioning a relation of polysemy or the polysemy relationship -- see, for instance, Sigman and Cecchi (2002) or current practice in Explanatory Combinatorial Lexicology described earlier in Footnote 4.

To fill this terminological gap, we propose two essential notions: copolysemy and copolyseme (Polguиre 2016a: Chapter 7).

Definition 4. Copolysemy between two lexical units L₁ and L₂ -- symbolized as L₁ ^ L₂ -- is the formal and semantic relation linking L₂ to L₁ which conditions their grouping within the same polysemous vocable.

The above definition implies that, by default, the relation of copolysemy is oriented, from L₁ to L₂; this is the reason why we chose the arrow-like symbol “^” to represent it. More precisely, L₁ ^ L₂ implies that, in the couple of formally identical lexical units

Lj and L₂, it is the meaning of L₂ that is perceived as existing relative to the meaning of L₁. We use the vague formulation relative to in order to avoid the more specific derived from. Section 3 will provide reasons for this choice of terms, which relates to the fact that the directionality of an L₁ ^ L₂ relation does not imply that the meaning of L₂ is constructed from the semantic material found in the meaning of L₁.

In relation to this, note that symmetric configurations of copolysemy relations L₁ !^i L₂, where copolysemy holds both from L₁ to L₂ and from L₂ to L₁, are a theoretical possibility -- though we have no concrete example to offer. It goes without saying that symmetric configurations of copolysemy relations can only be envisaged within a purely synchronic approach. In the context of diachronic studies, it would be contradictory to consider that a lexical unit L₂ can simultaneously originate from another lexical unit L₁ and be the origin of L₁.

To complement our notional toolkit and conclude on the presentation of copolysemy, we need a relational term denoting lexical units involved in a copolysemy relation (L₁ and L₂ involved in L₁ ^ L₂).

Definition 5. Copolysemes are lexical units that belong to the same vocable -- they are connected either directly or indirectly by a copolysemy relation within this vocable.

It is necessary to take into consideration both direct and indirect copolysemy relations between copolysemes because in cases like L₁ ^ L₂ ^ L₃, for instance, we want to consider L₁ and L₃ to be copolysemes within their vocable. The relation of copolysemy is therefore transitive.

1.3.2 Regular Polysemy and Lexical Dynamics

Polysemy would not be that interesting a phenomenon if there were no regular polysemy: patterns of copolysemy relations that are recurrently instantiated in natural language lexicons. Regular polysemy is believed to be an essential vector of word creation. In his seminal publication on regular polysemy, Yuri Apresjan highlights the direct connection between polysemy and lexical productivity (Apresjan 1974: 18): there obviously is an intimate connection between the two phenomena. Consequently, within a synchronic approach to polysemy, it would be a mistake to lose sight of the fact that “underlying the state of affairs [of polysemy] is a process” (Hanks 2013: 357). In the synchronic study of polysemy, lexical dynamics (Traugott and Dasher 2001, Vanhove 2008, Hanks 2013, Ludlow 2014) will always play the role of the uninvited guest.

However, caution is required when establishing the connection between polysemy (or copolysemy) and lexical dynamics, more specifically sense creation. The copolysemy relation (^i) is not necessarily the result of a diachronic change (>). Two lexical units with identical signifiers and with significant meaning intersection, with a perceived copolysemy linkage, may very well possess their own parallel history, the resulting formal and semantic relatedness being perfectly coincidental -- for a discussion and illustrations, see Traugott and Dasher (2001: 13--14). Conversely, some synchronic homonymy can be the result of the historical degeneration of a copolysemy relation, where semantic proximity is no longer perceived. A classical illustration is found in French with the two homonyms voler¹ `to fly' and voler<sup>2</sup> `to steal' which are probably related in diachrony through a now extinct use of voler¹ in falconry (Ullman 1959: 326).

At this point, we are equipped with essential notions that will allow us to conduct a rigorous lexicographic study of polysemy (Sections 2 and 3). Before we proceed, let us comment on some basic facts about the methodology that guides such study.

1.4 Methodological Considerations

1.4.1 Anticipating Polysemy

This paper's approach to polysemy is different from that of Natural Semantic Metalanguage mainly in the way it considers polysemy in the lexicographic process. As stated by Goddard (2000: 132): “The NSM [= Natural Semantic Metalanguage] school follows the traditional `definitional' approach (Geeraerts 1994) to lexical polysemy. one assumes to begin with that there is but a single meaning, and attempts to state it in a clear and predictive fashion, in the form of a translatable reductive paraphrase. Only if persistent efforts to do this fail is polysemy posited”. Contrary to Natural Semantic Metalanguage, we postulate, when dealing with a given vocable, that it contains more than one single sense -- i.e. that it is polysemous --, and only if no evidence can be found of the presence of separate senses is monosemy accepted.

There are two reasons for proceeding this way. Firstly, it is the recognition of the fact that polysemous creation is one of the main vectors of lexical dynamics (Subsection 1.3.2 above). Word creation is, of course, performed by creating morphologically derived or totally new signifiers for new lexical signifieds; but it is also very commonly performed by associating new lexical signifieds to existing lexical signifiers with which they entertain a meaning relation (extension, metonymy, metaphor, etc. -- Section 3 below). Even within a conservative lexicographic approach to polysemy, where proliferation of senses is not welcome in lexicographic descriptions, it is somehow rare to be faced with monosemous vocables, especially if specialized vocabulary, such as names of chemical molecules, botanical species, etc., is left aside. The second reason why polysemy is postulated by default is that our focus is not lexical meanings and their lexicographic definition per se, but lexical units as wholes: which includes their meaning, of course, but also their combinatorial properties and, more generally, all differentiating lexicographic information (Mel'cuk 2013: Chapter 11, 3.2.2) that may demonstrate its singularity. It is often the case that meanings that can be blended together when considered from a strictly conceptual perspective (e.g. I, as an individual describing language, decide that house balconies and theatre balconies are the same kinds of entities) are better considered as related to two separate meanings when taking into consideration how the corresponding word behaves in actual speech.

An important methodological consequence in lexicographic analysis of what has just been stated is that the very first operation performed when conducting the description of a vocable should be to make an initial hypothesis about its polysemy structureThe notion of polysemy structure, as understood here, is presented in Subsection 2.2 below..

Lexicographers should first try to identify -- through introspection and the study of occurrences in oral and written texts -- the various senses that can be expressed by a given word. True, the distinction may sometimes be hard to establish at first, without digging deeper into the word behavior, such as for legs and leg in (3a-b).

3 a. He put on his jacket hood, crossed his legs, folded his arms and let his head fall.

leg of a human being]

b. Up on a plank, high above her in the sky, was a black cat who was making slurping noises as he licked his leg.

[^ leg of an animal]

More often than not, however, one can safely hypothesize the presence of polysemy, for instance, when contrasting (3a-b) above with (4).

4 These grand piano leg dollies are manufactured in the United States.

[^ leg of an object]

Note that, if it is doubtful that we are with (3a-b) and (4) in the presence of one single meaning, some may argue that (4) involves a totally unrelated lexical unit, which would boil down to rejecting the very notion of polysemy and replace it with wall-to-wall homonymy. We believe such approach to be counterproductive if one wants the lexicographic description to be compatible with perceived semantic connections -- semantic bridges -- by the Speaker and with resulting usage in speech: wordplay, teaching and acquisition by metaphor, etc. Sentence (5), for instance, makes sense only if we understand that the Speaker presupposes a link of metaphor between two senses of leg -- cf. the term analogy.

5 Bunuel had already played with the piano leg/woman's leg analogy in his earlier film Tristana.

1.4.2 "Back to Definitions" (Wierzbicka 1992)

A common credo the present study shares with Natural Semantic Metalanguage, and with Apresjan (1974)'s approach as well, is that the key to polysemy is to be found in lexicographic definitions. There is no polysemy without copolysemy relations between senses, and there is no copolysemy relation -- in the most standard cases -- without corresponding semantic bridges or other, more indirect, form of connection between the respective definitions of copolysemes. Consequently, copolysemy will be solely postulated based on actual or hypothesized lexicographic definitions. By hypothesized lexicographic definition, we mean that one does not need to formulate in writing a complete lexicographic definition (though, it is always preferable to do so) in order to gather enough semantic information about a given lexical unit. A teacher in class, for instance, should be able to mentally “draft” almost instantly a definition of a lexical unit in order to address a student's question or propose an exercise. In the same vein, a trained lexicographer should be able to mentally draft definitions -- for instance for leg(s) in (3 a) vs. (3b) vs. (4) -- that are rich and precise enough to establish preliminary diagnostics. Again, such semantic approximations, without their materialization in the form of bona fide definitions, is in no way satisfactory and can only be used as an intermediary stage in lexicography. However, definition drafting can be done, the technique can be learned, and it does have useful applications if lexicographic abilities are not only applicable in the context of the theoretical lexicography, where one can be satisfied with spending weeks on perfecting the definition of a single lexical unit.

Additionally, it is possible to question the fact that the proper definition of a derived copolyseme, such as leg in (4) above, can be achieved without a preliminary hypothesis on the kind of relation it entertains with its lexical source, legs in (3 a). It is not because we finalize complete and exact definitions of legs [of a person] in (3a) and leg [of an object] in (4) that we “discover” a metaphorical relation between the two. It is right the opposite: we postulate and want to account for a perceived metaphorical link, and this leads us to propose lexicographic definitions that do the job. After all, in the case of metaphor, as well as with many other copolysemy relations, encoding the semantic bridge is seldom a necessity if the goal is only to account for the type of referents the lexical unit we define may have in speech. We do it because we believe it has something to do with how the lexicon is structured. For instance, both leg(s) in (3 a) and (4) share the collocate strong to mean `that has the ability to function as it should' and we feel that this is not a mere coincidence, but somehow the consequence of a metaphorical transfer of combinatorial properties.

6 a. Strong legs are important in all aspects of cheerleading, from stunts to gymnastics. b. The heavy marble must be supported by strong legs, so the legs of this table are made of forged iron.

To conclude, the approach to polysemy presented here can be characterized as follows:

¦ it is postulated that polysemy of vocables, not monosemy, is the norm;

¦ polysemy should be modeled based on the description of copolysemy relations between senses that make up the corresponding vocable's polysemy structure (Section 2 below);

¦ the study of copolysemy relations is conducted inductively through lexicographic analysis;

¦ a postulated copolysemy relation between two lexical units is, in most standard cases, based on a postulated semantic bridge or other more indirect connectionThe Coderivation copolysemy relation introduced in Subsection 3.4.3 below is a case of indirect connection between copolysemes. between the lexicographic definitions of these lexical units;

¦ it can be sufficient as a first step, for a trained lexicographer, to (mentally) draft such lexicographic definitions in order to postulate a semantic relation.

As mentioned earlier, using lexicographic definitions as basic modeling tools for polysemy is in accordance with the methodology of Natural Semantic Metalanguage: “In a system of semantic analysis based on a finite set of indefinables and on the principle of reductive paraphrase, meanings re-emerge as discrete, determinate entities, and the “riddle of polysemy” ceases to seem insoluble” (Wierzbicka 1996: 244). Two major methodological differences between what is proposed here and Natural Semantic Metalanguage should, however, be stressed: (i) it is doubtful that Natural Semantic Metalanguage practitioners would agree with the systematic recourse to drafted definitions; (ii) their lexicographic definitions are not designed to explicitly explain copolysemy relations and there is no “cross-fertilization” of copolysemes' definitions (Wierzbicka 1996: 269--270). On this latter point, we believe cross-fertilization can be a necessity, at least in such cases as metonymies and metaphors, for instance. Wierzbicka (1996)'s requirement that each definition should “stand alone” holds in the context of Natural Semantic Metalanguage, where the leading principle in defining is maximal decomposition of meanings based on the use of semantic primitivesAs has been rightfully pointed out to us by one of the anonymous reviewers of this paper, this statement is no longer entirely true since semantic molecules have been introduced in Natural Semantic Metalanguage. They are indeed convenient tools in the approach for implementing definition crossfertilization. See, for instance, Goddard (2011: 377--378)'s definition of `head 2' [of an animal] in terms of `head 1 [of a person]', which has the status of semantic molecule in the definitional metalanguage.. Within Explanatory Combinatorial Lexicology, where minimal instead of maximal decomposition is postulated (Mel'cuk 1989), cross-fertilization is inevitable and is, even, a necessity: for instance, neck [of a shirt, dress ...] will necessarily be defined in terms of neck [of a person].

We now proceed, in Section 2, with the presentation of our methodology for studying polysemy in the context of the lexicographic construction of the French Lexical Network.

2. Lexicographic modeling of polysemy structures

We introduce our lexicographic approach to polysemy modeling in two steps. Firstly (2.1), we briefly summarize the theoretical and methodological principles on which the lexicographic project of the French Lexical Network is based, highlighting its main characteristics which distinguish it from more traditional products of Explanatory Combinatorial Lexicography: namely, Explanatory Combinatorial Dictionaries (Mel'cuk and Zholkovsky 1984, Mel'cuk et al. 1984--1999). Secondly (2.2), we focus on the notion of polysemy structure of vocables and on its encoding in the French Lexical Network.

2.1 The French Lexical Network (fr-LN) Project

The present study targets a deepening of the notion of polysemy through descriptive practice. As mentioned at the very beginning of the paper, this research is anchored in Explanatory Combinatorial Lexicology (Mel'cuk et al. 1995), from which it borrows most of it theoretical notions and descriptive principles. The most significant difference in the study presented here and “classical” Explanatory Combinatorial Lexicology is that it is based on a new form of lexicography, namely the lexicography of Lexical Systems, presented in Polguere (2014). We cannot explain in detail the characteristics of this lexicographic practice, and we concentrate on a brief presentation of the lexicographic models it produces: Lexical Systems.

Lexical Systems are network models of natural languages lexicons -- i.e. unlike dictionaries, they are non-linear and non-textual. They were first presented in Polguere (2009), based on an experiment in automatically compiling a dictionary-like Explanatory Combinatorial lexical database for French into a network structure closer to what we expect is a plausible representation of the organization of the logical mental lexicon (Polguere 2016b)Polguere (2016b) establishes a distinction between two notions of mental lexicon: the physiological mental lexicon -- the lexicon as information stored in the brain of individual speakers -- vs. the logical mental lexicon -- the lexicon as main structural component of langue in the Saussurian sense. The physiological mental lexicon is the object of study in such disciplines as neurolinguistics and its structuring is in great part constrained by human physiology. The logical mental lexicon is the true object of study in lexicology. Its organization follows mathematical and logical principles while being structurally compatible with (though radically distinct from) the physiological mental lexicon. For a discussion of a cognitive-based approach to the modeling of polysemy, see Zalizniak (2007).. Since then, the notion of Lexical System has been refined through large-scale lexicographic work centered mainly around the construction of the first handmade Lexical System: the French Lexical Network, hereafter fr-LN (Lux-Pogodalla and Polguere 2011).

A Lexical System of a given language, such as the fr-LN, is formally a huge graph whose nodes are in most cases lexical units of the language (lexemes and idioms) and whose arcs are in most cases paradigmatic and syntagmatic relations that connect these lexical units. The bulk of the graph structuring of Lexical Systems, in terms of lexical node connections, relies on the system of Meaning-Text standard lexical functions (Mel'cuk 1996, 2007): paradigmatic lexical functions corresponding to semantic derivatives of lexical units -- Syn, Anti, Convij, Si ... -- and syntagmatic lexical functions corresponding to collocations controlled by lexical units -- Magn, Ver, Bon, Oper! ...A brief but informative introduction to lexical functions -- with a list of simple standard lexical functions -- can be found in the English Wikipedia entry for the notion: https://en.wikipedia.org/ wiki/Lexical_function [consulted on July 31, 2018].

The graph that makes up a Lexical System is a non-taxonomic structure, unlike the graph of well-known lexical networks such as WordNet (Fellbaum 1998) and BabelNet (Navigli and Ponzetto 2012). A Lexical System graph closely resembles, in terms of global structuring, common social networks -- e.g. the graph of “friend” connections in Facebook. This type of information structure is called small-world network (Watts and Strogatz 1998) and it possesses specific topological characteristics which make it particularly suitable for such operations as automatic node clustering and analogical reasoning.

At present, lexicographic work focuses on Lexical Systems for three languages: French -- the fr-LN, on which the present study is based --, Russian (Krylosova 2017) and English (Gader et al. 2014). Small samples have also been constructed for Arabic, Italian, Korean and Spanish.

The main change introduced in Explanatory Combinatorial Lexicology by the use of Lexical Systems as structural models of lexicons -- as opposed to “textual” dictionaries -- is that each lexical unit in this approach is first and foremost characterized by its lexical cluster (see 3.1 below): the micro-system of paradigmatic and syntagmatic relations the lexical unit is at the center of. Within the framework of Lexical System lexicography, the lexical cluster of each lexical unit is systematically taken into consideration while interpreting linguistic data and making decision on how to model them. This methodological aspect of the work will very clearly manifest itself in the remainder of the paper.

We cannot delve further into the topic of Lexical Systems and their lexicographic construction for lack of space. In next subsection, we concentrate on how polysemy structures of vocables are modeled in Lexical Systems and, in particular, in the fr-LN.

2.2 Polysemy Structure of Vocables in the fr-LN

Standard dictionaries describe vocables' polysemy following what has been termed the enumerative approach (Falkum and Vicente 2015: 3--5): one by which all senses of a given vocable are listed in its dictionary entry with minimal information (if any) to reflect its actual polysemic organization. Structural information on polysemy takes mainly the form of lexicographic numbering, symbols (bullets, punctuation signs ...) and sense labels such as Figur(ative), By extension, etc., which are supposed to reflect some form of internal hierarchical organization of the vocableFigurative means that sense L₂ in the vocable's entry is figurative relative to sense L₁; By extension means that L₂ is a semantic extension of L₁; etc..

Sense enumeration is the lexicographic dead horse that everybody seems to love to flog, especially when it comes to justify a refusal to undertake the painstaking and endless endeavor of describing lexical polysemy. We believe in a more constructive attitude. The approach adopted in describing French polysemy in the fr-LN is non-enu- merative as senses are not simply listed, or collected, in the lexical network: they are explicitly connected by a set of clearly identified L₁ ^ L₂ copolysemy relations (Subsection 1.3.1 above). The result is a tree-like hierarchical structure, such as the one given in Figure 1 below for the French vocable jambeAll polysemy relations appearing in Figures 1 and 2 are explained in detail in Section 3 below..

Figure 1. Polysemy structure of the French vocable jambe in the fr-LN

Though polysemy structures of vocables are by default acyclic graphs (i.e. trees), such as in Figure 1 above, they may exceptionally contain cycles, where one sense appears as direct copolyseme of more than just one other sense. This is a consequence of the fact that, from a strict theoretical viewpoint, nothing forbids a sense to be synchronically derived from several other senses. For instance, a sense can be simultaneously a form-based metaphor copolyseme and a function-based metaphor of another copolyseme, though this kind of configuration can be expected to be very rare. An example can be found in the fr-LN with the vocable taille², whose polysemy structure is visualized in Figure 2The superscript number in the name of the vocable TAILLE² is an indication of the fact that there is a TAILLE¹ homonym in the fr-LN..

Figure 2. Polysemy structure of the French vocable taille² in the fr-LN

The collection of all copolysemy relations weaved in the fr-LN makes an important contribution to the overall relational structuring of this Lexical System, together with lexical function relations. At the moment of writing, the fr-LN contains 8,890 copolysemy relations against 59,336 paradigmatic and syntagmatic lexical function relations; all these relations connect 28,353 lexical nodes, grouped into 18,196 vocablesThe fr-LN is freely distributed through the ORTOLANG platform (https://www.ortolang.fr). Contact should be made directly with us for up-to-date versions of the database.. The system of copolysemy relations identified in the fr-LN corresponds to only part of the polysemy of the French language; it is, however, significant enough to be considered as being far beyond the stage of sampling. To our knowledge, the fr-LN is the only network-like model of a natural language lexicon that embeds such an extensive and explicit description of copolysemy relations. vocable polysemy lexical french

Now that the general lexicographic principles underlying our approach to polysemy modeling have been introduced, we can proceed with the description of copolysemy relations identified through lexicographic construction of the fr-LN.

3. Copolysemy relations identified in the fr-LN

3.1 General Picture

We explained in some detail earlier (Subsection 1.4.2) that the key to the identification and characterization of copolysemy relations L₁ ^ L₂ is the comparison of (drafted or hypothesized) lexicographic definitions for both L₁ and L₂. In that sense, the name of each given copolysemy relation we have identified is, first of all, a representation of the ratio between the meaning `L<sub>1</sub>' and the meaning `L₂'. However, it has also been noted in Subsection 2.1 that, beside L₁ and L₂'s lexicographic definitions, another fundamental parameter is taken into consideration in the context of the lexicography of Lexical Systems: L₁ and L₂'s lexical clusters.

Definition 6. The lexical cluster of a lexical unit is the system of paradigmatic and syntagmatic relations it controls and that positions this lexical unit within the topology of the lexical graph of the language.

The lexical cluster of a given lexical unit acts as its fingerprint within the Lexical System of the language and represents a significant proportion of the differentiating lexicographic information (cf. 1.4.1 above) to be examined when comparing two copolysemes. Each lexical unit can be considered from the viewpoint of either its semantic lexical cluster or semantic space (Polguere 2014: 11--12) -- the system of semantically relevant relations that connects it to other lexical units -- or its full lexical cluster -- the system of all relations, including semantically empty ones (e.g. purely formal ones), that connects it to other lexical units.