1. Working with network models of natural language lexicons

This paper addresses the topic of regular polysemy from a lexicographic perspective, more precisely from the perspective of lexical network lexicography.1 The present section lays the ground for the discussion, with a general characterization of natural language lexical networks (Section 1.1), some considerations about lexical functions that are at the core of our methodology (Section 1.2) and the relational perspective on polysemy adopted here (Section 1.3). Later, we proceed with a detailed presentation of the Gener lexical function (Section 2) whose interest in the exploration and modeling of regular polysemy we intend to demonstrate (Section 3).

1.1. Shape and size of the lexicon in lexical network terms

We are using as theoretical and descriptive framework Explanatory Combinatorial Lexicology and Lexicography (Mel’čuk, 2013: ch. 11) augmented by the lexicography of Lexical Systems: an approach to the construction of lexical models where lexical networks rather than dictionaries or other “textual” representations of lexical knowledge are targeted (Polguère, 2014). Lexical Systems are network models of natural language lexicons whose graph structure belongs to the family of small-world networks (Watts & Strogatz, 1998). Such lexical models can be formally characterized in layperson terms as “social networks” of lexical units: huge graphs of dispersed nodes – lexical units – connected by arcs – lexical relations – whose number is small in comparison with the number of nodes. Expressed in mathematical terms, such graphs have a low density, i.e., a low average node degree – a node’s degree being the number of connecting arcs for this node. Within this globally dispersed structure, many clusters are formed of mutually interconnected nodes – “parties” of lexical units. Additionally, the existence of highly connected nodes – nodes with exceptionally high density corresponding to lexical units with many “friends” – ensures that within this widely dispersed structure, there is always a relatively short path (sequence of arcs) that connects any two nodes. Hence the “small world” metaphor. Let us now estimate the size of the lexical network of natural languages; the reasoning at this stage is based on the English language.

As for lexical nodes, standard general-public dictionaries (American Heritage, Oxford Learners’ dictionary, etc.) can help estimate the size of the basic English lexicon. To make things simple, let us consider that the wordlist of such dictionaries may contain around 60,000 entries; with a conservative average polysemy of three senses per entry, we obtain an estimated size of 180,000 lexical units that constitute a significant and representative part of the English lexicon. A minimal lexical graph of the English language should therefore contain at least 180,000 nodes – a node is a specific word sense, not a polysemous word. This is a rough number that gives us a minimal order of magnitude. Additionally, entries in most commercial dictionaries are lexemic (i.e., single word) entities and the description of idioms is embedded in lexemes’ articles. Idioms are nonetheless full-fledged lexical units and they number many thousands in all natural languages. Consequently, we should revise our largely underestimated calculation up to a still conservative 250,000 lexical units. Though this number may seem huge from the perspective of manual lexicographic modeling, it is relatively small in comparison to the node cardinality of graphs representing other types of natural entities: e.g., a graph of the world’s population or a graph of all celestial objects in the galaxy (this latter having literally and metaphorically astronomical proportions).

As for the number of lexical relations, doing an estimate is trickier than for lexical nodes, for two reasons. Firstly, lexical units can entertain very diverse relations: formal, semantic, combinatorial, etc. Secondly, in line with the characteristics of small-world networks (see first paragraph of the present section), some lexical units can entertain a large number of direct relations – e.g., the noun feeling and the verb do – while others do not occupy such strategic structural position of “crossroad” lexical units (see, Section 2.2). Let us then take a purely formal strategy to solve the problem of estimating the number of lexical relations in lexicons. If we take as axiom the fact that lexical networks are small-world networks, it is possible to use the mathematical properties of such graphs to approximate the number of relations in lexicons once we have an estimate for the total number of nodes: let us call this latter N. The average degree (number of connecting arcs) of a node in a small-world network is estimated (see e.g., Gaume et al., 1988, p. 88) to have a maximal value of ln( N ).2 We just made an estimate of the value of N by reasoning on the English language: 250,000 lexical nodes. We can now estimate the number of arcs with a simple formula: ln( 250,000 ) × 250,000. If we round up the returned value,3 we can conclude that the estimated size of a complete Lexical System model of English, or of any natural language, is thus: 250,000 nodes and 3,110,000 arcs. It is big, but not that big.

The conclusion one can draw from the above reasoning is that natural language lexical networks are vast and rich structures but their manual (lexicographic) construction remains a feasible task provided lexicographers develop special computational tools for weaving and processing them (Gader et al., 2012).

Basic terms and writing conventions. By lexical unit, we mean a unit of the lexicon and, consequently, a unit of lexicographic description associated with a well-specified meaning; formally, lexical units can be either lexemes or idioms. Names of lexical units are written in small capitals, eventually accompanied by a lexicographic number in case different senses of a polysemous vocable have to be distinguished – e.g., moon(N) I.1 ‘satellite of the earth’, moon(N) I.2 ‘satellite of a planet’, moon(N) II ‘what is seen of the moon(N) I.1 in the sky’, etc. are lexemes of the polysemous vocable moon(N). Names of idioms are written between ⌜...⌝ to highlight the fact that these lexical units are semantically non-compositional expressions that function as a whole – e.g., ⌜ask for the moon⌝ ‘have exaggerated expectations’. Names of lexical functions (see 1.2) are written in a monospaced font – e.g., Gener, Magn, etc. Finally, names of copolysemy relations (see, Section 1.3) are written in a bold monospaced font – e.g., Extension, Metonymy, Metaphor, etc.

1.2. Remarks on the universal system of simple standard lexical functions

The lexical function Gener is at the core of the present work. Before we deal specifically with it (Section 2), it is important to briefly recapitulate the purpose and characteristics of the system of simple standard lexical functions. We presuppose in what follows a minimal familiarity with lexical functions on the part of the reader, one that can be achieved by studying, for instance, Wikipedia’s “lexical function” entry4 or any succinct presentation such as Mel’čuk (2007). In other words, we do not offer a new “lexical function in a nutshell” presentation but we try to increase the reader’s familiarity with lexical functions by proposing an operational definition of the notion suited for the present paper.

At the time of writing, Mel’čuk and Polguère (2021) is the latest detailed presentation of the full system of standard lexical functions.5 We base the content of the present section on the explanations and presentation strategies adopted in this text.

Let us consider an elementary situation of language production where a Speaker has lexicalized a meaning with a given lexical unit L and needs to express another meaning ‘σ’ in the sentence in combination with the meaning of L. Two main cases can be envisaged: (i) either ‘σ’ is a “normal” meaning and its lexicalization can be performed by the Speaker independently from L itself – e.g., horse + ‘beautiful’ → beautiful/gorgeous/magnificent/... horse; (ii) or ‘σ’ belongs to a small set of meanings that are flagged by natural languages as having to be lexicalized contingent upon a preexisting lexicalization it is to be combined with – e.g., horse +‘to make use [of]’ → to mount/to ride a horse.

The idea that there exists a small set of meanings that are universally (i.e., in all natural languages) expressed contingent upon preexisting lexicalizations is at the heart of the system of standard lexical functions as stated in the definition of the notion offered by Mel’čuk and Polguère (2021, p. 81):6

[...] any LF [= Lexical Function] f possesses a meaning of the second type – noted ‘σ^f’ – whose expression is contingent upon the preliminary choice of a lexical unit L. The LF f takes L as argument – which is noted f(L) – and returns as value the set of all expressions of ‘σ^f’ that are suitable relative to L.

Meanings of standard lexical functions – hence standard lexical functions themselves – have the three following properties.

Property 1. They are vague (i.e., poor) and therefore compatible with a very large, heterogeneous set of lexical units; e.g., the meaning of the Real₁ lexical function – ‘to make use [of L]/to realize [L]/...’ or, more generally, ‘to do what is expected to be done [relative to L]’ – is compatible with lexemes that have semantically nothing in common such as horse and desire_(N):

Real1( horse ) = to mount, to ride [ART ~] Real1( desire(N) ) = to fulfill, to satisfy [ART ~]

Property 2. They are expressed by a large set of distinct lexical values, though semantic classes of lexical units may be associated with “joker” values for specific lexical functions – e.g., the Real₁ to play for names of musical instruments in English (to play the guitar, the piano, ...).

Property 3 (semiotic consequence of Properties 1 and 2). Because they are basic items of linguistic expression, such meanings have a special semiotic status: (i) they are universally expressed in all natural languages; (ii) these latter tend to offer morphological means of expression for such meanings.

Although lexical functions were originally discovered while reflecting on the problem of translating collocations (see, Mel’čuk, 2015, p. 269), it soon became obvious that the notion applies not only to syntagmatic (i.e., combinatorial) lexical relations but equally to paradigmatic (i.e., semantic) relations. Synonymy (Syn), antonymy (Anti) or typical names for actants (S_1/2/...), to cite only a few examples, correspond to semantic derivations (Mel’čuk, 2007, Section 2) and can also be accounted for by lexical functions. In prototypical (or true) cases of L₁⇨L₂ semantic derivation, L₂ is a semantic derivative of L₁ if (i) it is defined in terms of L₁ and (ii) the semantic difference between L₂ and L₁ corresponds to a meaning that possesses all three above-mentioned properties of standard lexical function meanings.

The system of standard lexical functions can thus be divided into two subsets:

• paradigmatic lexical functions that correspond to semantic derivations;
• syntagmatic lexical functions that correspond to base-collocate relations.

For lack of space – and also because there already exists an extensive literature on this topic –, we will not go further into the discussion of the notion of lexical function. Our goal in this section was to provide the reader with essential information that is relevant for the rest of the discussion.

1.3. Relational model of polysemy

Now that we have dealt with the topic of lexical functions, let us examine the second notion that is at the heart of the present study: polysemy and its relational modeling in Lexical Systems. This is treated in detail in Polguère (2018) and we will simply recall here essential elements of our relational approach to polysemy.

To start with, it is worth mentioning that the traditional, most common view of polysemy is based on a decoding (rather than encoding) perspective,7 where the polysemy “of a word” is explained in terms of ambiguity of a lexical form; e.g., Gries (2015, p. 472):

The probably most widely accepted definition of polysemy is as the form of ambiguity where 2+ related senses are associated with the same word; consider the meanings of glass in I emptied the glass (‘container’) and I drank a glass (‘contents of the container’).

We shall neither accept nor adopt such definition because the fact for a given lexical signifier to be ambiguous is nothing but a practical consequence of a vocable’s polysemy; ambiguity is by no means a definitional notion as regards to polysemy.

First of all, let us establish the fundamental distinction between the polysemy of a vocable, that is the property of a vocable to be a set of more than one lexical unit – e.g., the polysemy of the moon_(N) vocable previously mentioned (final paragraph of Section 1.1) –, and polysemy as a relation between two word senses of a polysemous vocable such that one “is accounted for” (in the most general sense) relative to the other.

We call copolysemy the relation holding between two lexical units L1 and L2 of the same polysemous vocable, and we represent it with the following formula: L1 ↦ L2. Lexical units involved in such relation are mutual copolysemes.

This being stated, it becomes obvious that what really matters in polysemy, as an immanent lexical phenomenon, is the existence of copolysemy relations throughout the structure of natural language lexicons. Each polysemous vocable is in fact a polysemy structure made up of lexical units connected by copolysemy relations. Figure 1 visualizes the polysemy structure of the moon_(N) vocable.

All lexemes in Figure 1 are copolysemes: they are connected either directly or indirectly by copolysemy relations. The lexeme that is at the top of such hierarchical structure is called the basic lexical unit of the vocable. This figure shows that, in our approach to modeling polysemy structures, each copolysemy relation L₁ ↦ L₂ is systematically labeled in order to identity the type of copolysemy relation that connects L₂ to L₁.

Formally, the structure given in Figure 1 is a (tiny) subnetwork of the Lexical System of English, where coposlysemy relations cohabit with lexical function relations, among others. They play an important role in the topology of each Lexical System as they participate in its small-world structure by connecting areas of the graph that are otherwise topologically rather distant; for instance, in the polysemy of moon_(N), the areas corresponding to the semantic fields of celestial bodies (to which moon_(N) I.1 belongs) vs. time periods (moon_(N) III). This is even more so when copolysemes are connected by the relation of Metaphor – e.g., lotus I ‘flower’ ↦ lotus II ‘yoga position’.

Copolysemy graphs such as Figure 1 make clear why we refer to our approach to polysemy as being relational. Though it may seem obvious that polysemy is based on relations, it is worth noting that the standard approach to its modeling is enumerative and not relational: dictionaries – including Explanatory Combinatorial Dictionaries such as Mel’čuk et al. (1984, 1988, 1992, 1999) – and other types of lexical resources simply list senses under entries for polysemous vocables without explicitly accounting for their relational structure. Two types of indications are used to vaguely guide dictionary users toward polysemy structures that remain largely implicit:

• a more or less elaborate system of sense identification signs – Roman/Arabic numbers and/or various symbols (•, ◊, etc.) – that weakly reflects an implicit hierarchical organization of the vocable without systematically identifying copolysemy relations;
• the use of indications such as by metaph., by meton., by ext., etc., that are often ambiguous as regards to the exact source of the copolysemy relation and are used very sporadically throughout the dictionary.

In spite of the recourse to such techniques, the standard lexicographic approach to modeling polysemy remains largely enumerative and non-relational.

Note that we adhere to a strictly synchronic approach. We do not rely on the historical development of vocables to identify copolysemy relations between their senses. For each identified L₁ ↦ L₂ relation, the diagnosis is based on a synchronic analysis of the meanings of both L₁ and L₂, by drafting their respective lexicographic definition, and on a measurement of their semantic relation – for an extensive exploitation of lexicographic definitions in the study of (regular) polysemy, see Barque (2008). Of course, if no such relation between definitions is found, we are faced with a case of homonymy rather than copolysemy.8

The model of copolysemy relations presented in Polguère (2018) was built inductively based on the French lexicon through the lexicographic construction of a Lexical System for that language: the French Lexical Network, hereafter fr-LN. At the time of writing, twelve types of copolysemy relations have been identified, with additional subtypes. The fr-LN contains 29,463 lexical nodes grouped into 18,720 vocables and 9,569 copolysemy links have been woven.9 We can safely say that we already have at our disposal enough linguistic data on copolysemy relations to undertake large-scale studies on polysemy, and regular polysemy in particular.

At this point in our exposé, we have achieved the presentation of the core notions of network lexicography that underlie our proposal for exploring regular polysemy. We can now proceed with the examination of the Gener lexical function (Section 2) and its potential for studying and modeling regular polysemy (Section 3).

2. The Gener lexical function

The Gener lexical function belongs to the family of paradigmatic lexical functions. A lexical unit that is a Gener( L ) is a generic term for L. As stated in Mel’čuk and Polguère (in preparation), “it stands for the name of one of the semantic classes to which L’s denotation belongs”; for instance:

Gener( daffodil ) = flower(N) Gener( crawl(V) ) = move(V) Gener( visual ) = perceivable

Just like Syn (synonym), Gener applies to lexical units of all parts of speech (Verbs, Nouns, Adjectives, Adverbs and Clausatives) and returns values of the same part of speech, though it is mostly relevant to nouns because large clusters of lexical units forming denotational classes develop mainly among nouns. Unlike Syn, the mother of all paradigmatic lexical functions, Gener possesses a borderline status for at least two reasons that we shall detail using properties of lexical functions introduced in Section 1.2. Firstly, a prototypical Gener( L ) is a hyperonym of L10 and is therefore included in the meaning of L : ‘tulip’ = ‘flower_{Gener( tulip )} [...]’, ‘to crawl’ = ‘to move_{Gener( to crawl )} [...]’, etc. It is therefore clearly not a semantic derivative of L. Secondly, Gener, unlike other standard lexical functions, is not associated to a given semantic content ‘σ^f’ (see Section 1.2 above). Whatever content is associated to Gener in Gener( L ) depends entirely on the meaning of L.

Clearly, Gener occupies a special place in the system of standard lexical functions within which it appears isolated.11 The aim of this section is to characterize the “true nature” of the Gener lexical relation (Section 2.1) and to explain its structuring role in Lexical Systems (Section 2.2).

2.1. Linguistic rather than “conceptual” foundation

Lexical units that function as values for Gener are lexical classifiers. They are directly related to “concepts” that Wierzbicka (1985, ch. 3) identifies as categories of categories: a significant number of lexical units denote specific instances of these concepts. As Wierzbicka (1985, p. 189) puts it:

We can safely assume that tree is conceptualized in English as a category of categories because there are many other words in English which clearly designate ‘a kind of tree’, for example oak, maple or fir. Similarly, we can safely assume that bird is conceptualized in English as a ‘category of categories’ because there are many words in English which clearly designate ‘a kind of bird’, for example swallow, magpie or parrot. The same holds for the concept fish (see cod, trout or herring), animal (see dog, cat or squirrel) and flower (see rose, tulip or carnation).

Clearly, one would not expect a lexeme such as napkin to be a value for Gener as this would require the English language to possess multiple names for kinds of napkins. But Gener is strictly a lexical function; it operates independently of anthropological perspectives on natural languages. Consequently, there is nothing that theoretically forbids a lexeme such as napkin to be a Gener. It could be if we consider the terminology of the industry of napkin making, provided that such industrial sector exists and that many terms have been coined by “napkin makers” to denote kinds of napkins. The reason that makes a lexical unit of a given language be a Gener is not to be found in the extralinguistic realm of concepts but in the structure of the lexicon of that language itself. Of course, it goes without saying that general ontological classes must exist and that the existence of Gener relations in lexicons is not fully autonomous from human ontologization of the World. It is nonetheless essential to make it clear that Gener is only remotely connected to ontological and/or taxonomic approaches to the structure of natural language lexicons. Psycholinguistics, in particular, has a soft spot for classificatory approaches to the lexicon and the identification of taxa as structuring principle for modeling lexicons. The classificatory anthropological notion of “unique beginner” (Berlin et al., 1975), for instance, played an essential part in the initial organization of the English nominal vocabulary in WordNet (Miller et al., 1990).12 Within WordNet’s taxonomy of nouns, Miller (1990, p. 251) defines a unique beginner as being “[...] a primitive semantic component of all words in its hierarchically structured semantic field” and postulates 25 such unique beginners expressed as synsets = sets of (quasi-)synonyms (see Miller, 1990, Table 1, p. 252): {act, action, activity}, {animal, fauna}, {artifact}, {attribute, property}, {body, corpus}, {cognition, knowledge}, {communication}, {event, happening}, {feeling, emotion}, {food}, etc. This establishes the roadmap for organizing English nouns in WordNet.

Taxon, unique beginner, generic term are mainstream notions in current approaches to the formal structuring of lexical models. But this goes against the non-taxonomic Lexical System approach (see, Section 1.1) or, even, against traditional, dictionary-based Explanatory Combinatorial Lexicology. For this reason and because of its atypical properties as lexical function, Gener is a black sheep that has to be kept at arm’s length for fear of letting the taxonomic perspective sneak into our lexical models through the back door. On the other hand, generic groupings allow for the modeling of regularities in lexical networks, as will soon be demonstrated, and the extensive weaving of Gener relations in Lexical Systems has proven to be an important task that has unfortunately been overlooked in our methodology until recently.

In order to have a true lexicographic approach to the weaving of Gener relations, we should distance ourselves from psychological or anthropological prejudices about the taxonomic structure of natural language lexicons and characterize this lexical function in “purely” linguistic terms. For this, we need to find within natural languages themselves criteria for the identification of Gener relations. Following Mel’čuk and Polguère (2021, Section 2.1, pp. 101-102), we propose below a two-fold characterization of Gener based on (i) general semantic properties and (ii) a combinatorial criterion for identifying a given Gener( L₁ ) = L₂ relation.

General semantic properties. Gener( L ) is a lexical unit that denotes a class of “things” all possible referents of L belong to and, therefore, that can be used as a generic term for L.13 By extension, Gener( L ) designates a semantic lexical class L belongs to. For a set of lexical units to qualify as a class, it has to possess a minimal cardinality: two elements is insufficient, fifty is largely enough. The proposed definition needs to be paired with combinatorial criteria that can be used to test if, indeed, a candidate generic term qualifies as true Gener – i.e., is considered by the language itself as being classifying.

Combinatorial criterion. There exist specific constructions that function as some sort of linguistic reactants allowing for the identification of a Gener relation. The compatibility of the candidate generic term for L with these constructions has to be tested in order to validate its Gener( L ) status. The most significant construction is (in its version for the English language):14

• for nouns, “L, L’, L’’, ... and other Gener( L )” – e.g., daffodils, roses, hyacinths and other flowers ⇒ flower_(N) is a Gener of daffodil.
• for verbs, adjectives and adverbs, “L, L’, L’’, ... and Gener( L ) in other ways” – e.g., to crawl, to walk, to run and to move in other ways ⇒ move_(V) is a Gener of crawl_(V).

No extralinguistic consideration comes into play here. We simply follow what the English language tells us: the above combinatorial property of a Gener( L ) demonstrates its ability to function as some sort of “semantic pronoun” for L, as illustrated below.

(1)	a.	Daffodils are dangerous if eaten: they can poison badly.
	b.	Daffodils are dangerous if eaten: these flowers can poison badly.

Let us conclude with an important remark about Gener and lexicographic definitions in preparation for the discussion in Section 3. We consider here analytical definitions only – see, for instance, Mel’čuk and Polguère (2018). An analytical definition for a lexical unit L is an equivalence between two elements:

1. the definiendum (= what is defined) that is a linguistic expression featuring L together with the actant slots it controls – e.g., X steals Y from Z, admiration of X for Y, finger of X, etc.;
2. the definiens (= what is defining), or definition proper, that is a structured paraphrase of the definiendum made up of meanings that are simpler than (≡ included in) the meaning of L.

It is essential to stipulate that the definiens is structured: it has to abide by some logical principles that organize its content. In particular, at the highest level of organization, it is structured into:

• a central component (sometimes called generic component or closest kind) that corresponds to the core of L’s meaning;
• a series of peripheral components that present specific semantic content in L’s meaning as regards to (i) the central component and/or (ii) the meaning of other lexical units whose definitions possess the same or a similar central component as L’s definition.

Clearly, Gener( L ) is a good candidate as central component of L’s definition, but this is by no means systematic, for at least two reasons. Firstly, L may not possess any Gener. For instance, there is no Gener( sky_(N) ) and the central component of the definition of sky_(N) needs to be formulated as a nominal phrase expressing a configuration of semantemes and not by a single lexicalized meaning. Secondly, L can very well possess more than one Gener( L ) that are not even quasi-synonyms; for instance:15

Gener( flute(N)3 ) = glass(N)2a; tableware

The semicolon in bold that separates glass_(N)2a and tableware in the above formula indicates a significant semantic distance between these two lexemes.16 Their validity as Gener( flute_(N)3 ) is illustrated below:

(2)	a.	flutes, coupes, highballs and other glasses
	b.	flutes, carafes, plates and other tableware

However, only the lexeme glass_(N)2a qualifies as central component of the definition of flute_(N)3 – of which it is a hyperonym, by the way – because only glass_(N)2a denotes a class of actual objets: to use Wierzbicka (1984)’s formulation, a flute is a kind of glass. The lexeme tableware, on the other hand, denotes a very heterogenous class of objects that are brought together with respect to shared characteristics of function/usage; it would be extremely odd to say that a flute is a kind of tableware – for this reason, this second Gener( flute_(N)3 ) cannot be at the same time a hyperonym. There are other cases where lexical units can have multiple Gener (e.g., in cases of semantic ambivalence analyzed in Milićević & Polguère, 2010) but exploring further this question would lead us astray while our reader is probably getting more and more impatient to hear about regular polysemy. We are almost there.

2.2. Role of Gener in the topology of the lexicon as lexical network

Lexical units whose corresponding node in a Lexical System is the target of Gener relations belong to the topological category of crossroad lexical units (Polguère, 2014, p. 18): they are significant meeting points in the lexical network that can be loci for the identification of lexical regularities. From a graph-theory perspective, the existence of such nodes is predicted by the small-world nature of Lexical Systems (see, Section 1.1): while the average degree (i.e., number of connecting arcs) of nodes in small-world networks is low, a minority of nodes set themselves apart by their (very) high degree. Returning to the social network metaphors, they are the nodes of “famous” lexical units, those with many “friends” in the lexicon. Gener lexical units participate actively in the small-world structure of natural languages lexicons (at least, as we model them) because, through their semantic content, they establish classes of lexical units.

We shall call Gener clusters in Lexical Systems those groupings of lexical units that are united by one (or more) identical Gener. The display of these Lexical System clusters with the Spiderlex graphical browser,17 at least for prolific generic terms, results in characteristic “dandelion” structures, as illustrated in Figure 2 with the generic French noun fleur 1.2 ‘flower’ of the French Lexical Network (fr-LN).

The polysemy of the French vocable fleur and the numbering of its senses are discussed in Section 3.1 below. Note that Figure 2 shows more than just the Gener cluster controlled by fleur 1.2: other lexical units than flower names appear – e.g., plante¹ ‘plant_(N)’, jardin ‘garden_(N)’, bosquet ‘copse’, etc. This is due to the design of the underlying algorithm used by Spiderlex to conduct the topological exploration of the lexical graph – see, B. Gaume’s principle of proxemy (Gaume, 2004; Gaume et al., 2008) – and to the actual content of the fr-LN at the time the figure was generated.18

Crossroad lexical units, as mentioned earlier in the present section, are access points to lexical regularities and can be used to identify general lexical regularities that structure each natural language lexicon. Another family of crossroad lexical units can help illustrate this point: “joker” collocates for given semantic classes, such as Fr. éprouver ‘feel_(V)’ as support verb of the Oper₁ type for nouns of feelings – éprouver de l’amour, du désir, de l’antipathie ... ‘to feel love, desire, antipathy ...’. A lexeme such as éprouver is the target of a large number of Oper₁ lexical function links in the French lexicon and as such it can be used to:

• classify lexical units and establish correlations between various lexical function connections – e.g., there is a logical correlation in French between the class of lexical units L for which Oper₁( L ) = éprouver [ART ~] and those for which Gener( L ) = sentiment ‘feeling’;
• systematically explore the lexical and grammatical combinatorics of collocational lexical units, dealing with collocations the other way round, from the lexicographic description of the collocate to that of the base.

To our knowledge, Mel’čuk and Wanner (1994) is the first exploration of regularities among collocations performed within Explanatory Combinatorial Lexicology: its target was German names of feelings. This work later inspired lexicological and lexicographic research on Spanish (Barrios Rodríguez, 2008, 2009; Barrios Rodríguez & Boguslavsky, 2019). For Lexical Systems, punctual studies have been conducted on French (Delaite, 2012) and Russian (Mikhel, 2018).

This shows the important role crossroad lexical units can play in the structure of natural language and in lexicography as well. We can now proceed with an account of an experiment we conducted on the use of Gener relations for the exploration of regular polysemy.

3. Using Gener clusters to study and model regular polysemy

In order to experiment with the extraction of Gener-induced lexical generalizations, we applied the technique of upstream weaving of Gener relations – from a given generic term to lexical units it is a Gener of – using the French generic term fleur ‘flower’. There were two reasons for doing so. Firstly, we wanted to go off the beaten tracks and work on other semantic domains than, for instance, the overused feelings/emotions. Secondly, we knew that, with flower names, we were dealing with (i) a sizable Gener cluster, (ii) in a field where regular polysemy was definitely present and (iii) that was barely developed in the fr-LN at the time the experiment started.

This section is organized as follows: first, we give essential information on the actual generic term we worked on that is a specific sense of the French vocable fleur (Section 3.1); second, we propose a definition template for French nouns that are names of flowers and we detail the method we followed to weave the Gener cluster and build the definition template (Section 3.2); finally, we present the patterns of regular polysemy we extracted (Section 3.3).

3.1. Picking the right fleur ‘flower’

Any lexicographic work performed on a “word” must first consider a vocable and its potential polysemy, that is, its different senses. In line with this cardinal principle, our initial task is to clearly identify the generic term we are working on and, for this, identify the polysemy of the vocable it belongs to.

In the version of the fr-LN we used, three lexemes (i.e., word senses) make up the vocable fleur. They are listed below with approximate lexicographic definitions expressed in English: the definienda – see, Section 2.1, above – are highlighted in gray and bold parentheses indicate weak/optional components. Each definition is accompanied by illustrative examples; copolysemy relations are also indicated between square brackets.

I.1	fleur I.1 of X ‘part of a plant X, (that is colorful,) that participates in its reproduction process’ – Ex.: On admire les magnifiques fleurs blanches des géraniums. ‘We admire the beautiful white flowers of the geraniums’
I.2	[Metonymy of I.1] fleur I.2 in X (used by Y) ‘(part of a) plant growing in X that comprises its flower(s) I.1 (used by Y for decorative or similar purposes)’ – Ex.: Il a disposé les fleurs dans un vase. ‘He arranged the flowers in a vase’
II	[Metaphor of I.1] fleur II of X ‘part of X that is at the very surface of it, like flowers I.1 at the extremity of a plant’ – Ex.: J’admirais sa délicate fleur de peau. ‘I was admiring the delicate surface of her/his skin’

The last lexeme, fleur II, does not have a corresponding sense in the English vocable flower_(N) and does not translate easily; very surface is only an approximate translation. The presence of this sense in the structure of the vocable may seem odd even to native speakers of French as it is mainly used not to express its individual meaning but as lexical component of some idioms, such as in ⌜fleur de sel⌝ ‘high-grade sea salt’, ⌜fine fleur [de N]⌝ ‘elite [of a group of people N]’, etc. The only relevance of fleur II to the present discussion is that it highlights the presence of a semantic component in the meaning of fleur I.1 that has to do with the position of flowers, on branches or stems. When writing a complete definition for fleur I.1, the lexicographer shall include a specific ‘position’ component to which the metaphorical sense can be hooked. Otherwise, the last sense does not concern us here and we have to concentrate on the first two. Among them, only the second, fleur I.2, is the Gener we are going to exploit. Botanical terminology may include a class of terms for specific kinds of fleur I.1, but it is surely not what we talk about when we say in non-specialized language:

(3)	des roses, des tulipes, des œillets et autres fleurs ‘roses, tulips, carnations and other flowers’

Clearly, the generic term used in (3) is fleur I.2; it is the node in the fr-LN that will be at the center of the Gener cluster we target (visualized earlier in Figure 2, Section 2.2).

Now that we have zeroed in on the precise sense of the vocable fleur around which the Gener cluster will be built, we need to deal with another issue: the additional availability of plante¹ ‘plant’19 as Gener for names of flowers. Some names of flowers in French (and in English) are lexicalized as names of plants as well. For instance, in French, tulipe ‘tulip’ can rightfully be used to designate both a flower I.2 and a plant; rose, on the other hand, designates only a flower I.2, and a part of something bigger: a plant called rosier ‘rose tree’. This means that for each flower name we process while weaving the Gener cluster of fleur I.2, we need to examine if one or more values of Gener have to be woven.20

3.2. Definition template for flower names

Any regular polysemy is hooked to the definition of the basic lexical unit of vocables it applies to. For instance, the well-known regular metaphorical copolysemy relation L₁ ‘animal’ ↦ L₂ ‘person having a characteristic analogous to a characteristic of L₁’ (see snail I ↦ snail II ‘slow person’) is by essence connected to/triggered by a component of L₁’s definition. The identification of regular polysemy in the paradigm of flower names is therefore interwound with that of building a template for the definition of flower names. Types of regular polysemy we identify among flower names have to be connected to “regular” components found in the corresponding definition template. Though we start, in the present section, with the presentation of the definition template for flower names, the two tasks of building it and identifying types of regular polysemy (see Section 3.3 below) are interdependent.

The definition template is presented here in three steps: (i) definiendum, (ii) central component of the definiens and (iii) peripheral components.

Definiendum. It is not unfounded to base the definiendum of the definition of flower names on that for the generic term flower I.2, whose drafted definition was given in Section 3.1. The definiendum of this definition is phrased as follows: fleur I.2 in X (used by Y). It features a first actant slot X corresponding to the place where flowers grow. There are many indications in French of the existence of this actant slot; for instance, the following adjectival lexicalizations of X (we use fr-LN’s lexicographic numbers):

(4)	A1 ( fleur I.2 ) = fleuri I.b, en(Prép) III.1 [~ (s)]; couvert(Adj) I.1 [de ~ s], recouvert 2 [de ~ s] 21

The second actant slot Y, for the “user” of the flower, is indicated as optional because a vegetal can very well be designated as being une fleur even if it is not associated with any typical utilization. On the other hand, there is a proliferation of linguistic evidence pointing to the fact that fleur I.2 is conceptualized as denoting something that can be used (to decorate, to serve as a gift, etc.). Note that the fact that fleur I.2 controls two actant slots does not imply that lexical units for flower names all control the same actantial structure, but it is an indication that they have this potential.

Central component of the definiens. The central component of the definiens for flower names is of course ‘fleur I.2’. This means that, recursively, the central component of the definiens for fleur I.2 given above (Section 3.1) – ‘(part of a) plant’ – is by default inherited by definitions of flower names. It indicates that what is called fleur I.2 in French is a plant: either a rooted stem with flower(s) I.1 (e.g., tulipe ‘tulip’) or a more complex vegetal structure (e.g., géranium ‘geranium’).22 Additionally, the weak component ‘part of’ indicates that so-called ⌜cut flowers⌝ (Fr. ⌜fleurs coupées⌝) can be designated by flower names as well (tulips in a garden vs. tulips in a vase).

Peripheral components of the definiens. We have been able to identify, through the lexicographic process summarized at the end of the present section, 8 recurrent peripheral components listed below. They are the basis for the establishment of regular polysemy patterns among French flower names presented in Section 3.3.23

A) Color of the flower(s) I.1 (obligatory?). This is the first component in our list that provides a characterization of the flower(s) I.1 part of the flower I.2. It is an important component (see, Section 3.3) that may have to be flagged as obligatory. Even for types of flowers I.2 that can have flowers I.1 of many different colors, this information about diversity should be included in the corresponding lexicographic definitions: for instance, with a component ‘of various colors’.

B) Scent of the flower(s) I.1. This is the second most important component concerning the specification of the flower(s) I.1 part of the flower I.2. We do not think it should be obligatory, though: in the absence of (a specific) scent, we propose to simply omit Component B.

Remark on polarity in Components A and B. Speaking in the “language of lexical functions” (see 1.2 above), color and scent definiens components for flower names are by default oriented towards Bon ‘good’ rather than AntiBon ‘bad’. A flower name with a lexicographic definition containing AntiBon of color or scent24 (we did not encounter any) would definitely qualify as denoting an AntiVer flower I.2: a flower I.2 that is not as it is expected to be.

C) Size of the flower(s) I.1. The lexicographic definition of the lexeme fleur I.1 has to specify that it denotes small entities (relative to the size of the human body) that are part of a plant. However, specific types of flowers I.2 are often characterized by the fact that their flower(s) I.1 are relatively small or, on the contrary, relatively big.

D) Form of the flower(s) I.1. See the presentation of polysemy Pattern 4 in Section 3.3 below.

E) Disposition of the flower(s) I.1. We did not find any evidence of the relevance of this component in the polysemy of the vocables we examined. It is obvious, however, that many types of flowers I.2 are characterized by the disposition of their flower(s) I.1 on their stem. We include in this component the (approximate) indication of the number of flower(s) I.1 for each flower I.2: a single one, several, clusters, etc.

F) Environment in which the flower I.2 grows. It can be the immediate physical environment – for instance, it is essential to mention in the definition of nénuphar ‘water lily’ that it denotes a flower I.2 found on waterbodies – and/or it can be a geographical area – for instance, édelweiss ‘edelweiss’ that denotes a mountain flower I.2.

G) Seasonality of the flower I.2. This is important, for example, for flowers I.2 that are associated with springtime and whose corresponding lexical unit can carry associated connotations – see le temps du muguet ‘the time of lilies of the valley’ as a metaphor for springtime in a famous French song.25

H) Utilization of the flower I.2. See the presentation of polysemy Pattern 3 in Section 3.3 below.

For lack of space, we cannot go deeper into the topic of patterns of lexicographic definitions for flower names and, more generally, lexical units sharing identical generic terms. The reader interested in a Natural Semantic Metalanguage perspective on this question should consult Wierzbicka (1985, ch. 4 & 5), in particular the notion of “mental questionnaire” proposed by the author (Section 5.3, pp. 332-336). For “practical” (i.e., non-theoretical) lexicography, one should examine the definition component of template entries presented in Atkins and Rundell (2008, Section 4.5).26

At this stage, we can summarize the three-step method we applied in order to build the targeted Gener cluster, displayed earlier in Figure 2 (Section 2.2).

1. Gathering of an extensive (though not exhaustive) list of close to 150 flower names – we started from the list of hyponyms of fleur in the dictionary of synonyms embedded in the Antidote linguistic software (Druide, 2021).
2. For each element of this list, creation of the corresponding vocable, with its polysemy, if it is not already present in the fr-LN – often, when the vocable preexisted in the fr-LN’s wordlist, its polysemy had to be completed.
3. For each lexicographic article of a lexical unit that is created or updated, introduction of minimal lexicographic information: grammatical characteristics (part of speech, gender ...), inflections (singular and plural forms), semantic label, propositional form (actant structure), Gener and other essential lexical function relations, lexicographic examples.

Note that, following our relational approach to polysemy (see Section 1.3 above), each copolysemy relation that participates in the structure of the vocables we worked on is explicitly encoded as a typed copolysemy link in the lexical graph.

In the process of executing the above tasks, we extracted interesting lexical generalizations by the sheer fact of being confronted to a mass of linguistic data forming the lexical galaxy of fleur I.2. Generalizations concerning lexicographic definitions have just been discussed; we are now examining patterns of regular polysemy.

3.3. Extraction of patterns of regular polysemy

Le parfum lourd des sauges rouges
Les dahlias fauves dans l’allée
Le puits, tout, j’ai tout retrouvé
Hélas
Barbara, Mon enfance27

We postulate the existence of a pattern of regular polysemy among flower names if at least two distinct copolysemy relations of the same type are present in the lexical network. Based on this minimalist interpretation of the notion of “pattern,” we identified four polysemy patterns that are explicated below. Each pattern description starts with an illustration, followed by comments. Remember that lexical units whose Gener is fleur I.2 frequently possess plante¹ ‘plant’ as Gener as well; their derived copolyseme can therefore be anchored in either of their semantic facets. We decided to order the patterns according to their degree of relevance to the Gener cluster of fleur I.2, not plante¹. Based on copolysemy relations we found and on common qualifiers attached to names of flowers in texts, it seems clear that flower names (at least, in French) are about first color, then odor, etc. Our polysemy patterns are ordered accordingly.

Pattern 1. Metonymy-based metaphor: ‘L’ ↦ ‘of a certain color as if it were the color of L’

(5)	cyclamen(N) I ‘cyclamen’ ↦ cyclamen(Adj) II ‘that is mauve, similarly to the color o C. I’

The high productivity of this pattern highlights the fact that the ‘color’ peripheral component in the definition of flower names – see Component A (Section 3.2 above) – is probably the most significant one. Some comments are needed in order to explain (i) the name/conceptualization of Pattern 1 and (ii) the peculiar inter part of speech copolysemy relation it implements (N↦Adj).

The notion of metonymy-based metaphor and its role in the modeling of copolysemy relations are discussed in Polguère (2018, Section 3.4.1). There are two flavors in copolysemy relations such as the one illustrated in (5) above. They contain some form of metonymy because a color is named after the name of a flower prototypically associated with this color: this mauve is one of the prototypical colors of cyclamens. However, the metonymy is approximate and has to be formulated as an analogy – ‘of a certain color as if it were the color of cyclamens’ – because, firstly, cyclamens can be of other colors (white, etc.) and, secondly, it is not necessarily the case that the mauve the Speaker is referring to is precisely the mauve of cyclamens. This is why Pattern 1 is a case of metonymy-based metaphor and not a “pure” metonymy, or metaphor.28

There are grammatical issues with Pattern 1. The actual lexical creation process in French, in such cases, is first the derivation of a nominal expression denoting a color with the name of the flower (or fruit, etc.) as appositive noun: la couleur cyclamen ‘the cyclamen color’. It is from this structure that an adjective is produced: un rideau cyclamen ‘a cyclamen curtain’. The appositive nominal nature of the derivational source manifests itself through remarkable grammatical characteristics of the derived adjective: it is invariable in all its inflections (see the unchanged feminine plural form in des robes cyclamen ‘cyclamen dresses’) and it is mainly postposited (which is the position for appositive nouns). In spite of this particular behavior, the derived copolyseme is indeed an adjective; for instance, it can be modified by an adverb: une robe intensément cyclamen ‘an intensely cyclamen dress’.29 Of course, as for all adjectives, it is also possible to derive on-the-fly a corresponding noun – e.g., J’aime le cyclamen_[couleur] ‘I like the cyclamen_[color]’ – but this is perceived as a lexical creation on the part of the Speaker. To make the situation even more complex, such nominal derivatives produced by ricochet from the metonymy-based pattern can end up being lexicalized, probably because the type of color they denote is very popular (for clothing, etc.). Such is the case of the color noun amarante_(N) II.b ‘purple red color’:

(6)	Alice et Bob vont maintenant choisir chacun une autre couleur secrète. Après maintes hésitations, Alice s’arrête sur de l’amarante. ‘Alice and Bod are now going to choose each of them a secret color. After much hesitation, Alice decides on the amaranth color’.30

This color name is undoubtedly a lexicalized noun in French: an S0 derivative (in terms of lexical function) of amarante_(Adj) II.a; this latter is itself created from the flower name amarante_(N) I, following Pattern 1.31 Finally, a last grammatical goody: color nouns in French are always masculine while flower nouns can be either masculine or feminine. In the sequence of copolysemy relations found in the vocable amarante, the flower noun numbered I (basic lexical unit of the vocable) is feminine, and the resulting color noun, numbered II.b, is masculine. This can get some dictionaries quite confused as they are more reluctant than us to put under the same vocable entry feminine and masculine nouns, and an adjective as well. Such is the case of the French dictionary of Antidote (Druide, 2021) that contains three separate vocable entries: for the feminine flower noun, the color adjective and the masculine color noun. The online Petit Robert (https://dictionnaire.lerobert.com) puts the flower noun and the adjective under the same entry and ignores the lexicalization of the color noun. Just like Antidote, the online Larousse (https://www.larousse.fr/dictionnaires/francais-monolingue) has three separate vocables (no sense numbering) and offers a grammatical warning under a DIFFICULTÉS ‘difficulties’ section translated below:

"The noun amarante is feminine when it designates the plant with purple flowers and masculine when it designates the color: une amarante en pot ‘a[fem.] pot amaranth’; un amarante profond ‘a[masc.] deep[masc.] amaranth’. The adjective is invariable: des draperies amarante ‘amaranth[inv. fem. pl.] draperies’."

We gave a rather detailed account of Pattern 1 because it has a strategic importance in the Gener cluster of fleur I.2 and it possesses interesting characteristics. Due to lack of space, we shall be much more concise with the three remaining patterns.

Pattern 2. Metonymy: ‘L’ ↦ ‘fragrance product that has the scent of L’

(7)	lavande(N) I ‘lavender’ ↦ lavande(N) II ‘lavender fragrance that has the scent of L. I’

This pattern connects to what is, in our opinion, the second most significant peripheral component in the lexical definition of French flower names: the scent of the flower – see Component B (Section 3.2 above). Of course, not all flowers are characterized by their scent in the French language and, among those that are, only a limited number has triggered Pattern 2.

Note that Pattern 1 has also been triggered in the case of lavande_(N) I, used in illustration (7): the French lexicon contains the metonymy-based metaphor lavande_(N) I ↦ lavande_(Adj) III ‘of a color similar to that of L._(N) I’. Our lexicographic numbering favors in this case Pattern 2 copolysemy relation over Pattern 1. This reflects the fact that the use of lavande as a scent name is very widespread, unlike its use as a color adjective; this latter can even be unknown to native speakers of French. (There is a similar situation with English lavender.)

Pattern 3. Metonymy: ‘L’ ↦ ‘food/drink made with L’

(8)	gentiane I ‘gentian’ ↦ gentiane II ‘alcoholic drink made with the root of G. I’
(9)	a.	camomille I ‘chamomile’ ↦ camomille II.a ‘food substance made of C I used for hot drinks’
	b.	camomille II.a ↦ camomille II.b ‘hot drink prepared with C. II.a’

This metonymic pattern is well known and productive with names of plants in general. It is related to the ‘utilization’ component in the definition of flower names – see Component H (Section 3.2 above). The productivity of Pattern 3 is motivated firstly by extra-linguistic reasons: many plants are used to derive products for human consumption as food, medicine or both. However, we find this pattern to be not as relevant as the first two as regards to the Gener cluster of fleur I.2. Pattern 3 addresses in most cases the ‘plant’ semantic facet of the noun. In the same vein, we decided to exclude altogether from our list a similar pattern where names of materials are derived; for instance bruyère I ‘heather’ ↦ bruyère II ‘wood material from B. I root’.

The second illustration above, (9a–b), shows that Pattern 3 can generate a double-shot copolysemic lexical creation. Because this dual creation is quite productive – e.g., chicorée I ‘chicory’ ↦ chicorée II.a ‘food substance made with roasted root of C. I for hot drink’ ↦ chicorée II.b ‘hot drink prepared with C. II.a’ –, it should be modeled as such instead of being accounted for as the combination of two totally separate patterns (though those exist autonomously as well).

Pattern 4. Form metaphor: ‘L’ ↦ ‘something whose form evokes the form of L’

(10)	lotus I ‘lotus flower’ ↦ lotus II ‘yoga position that evokes the form of a L. I’

This pattern is marginally activated in the French lexicon, at least in the set of vocables we analyzed. This came as a surprise because it is clear that the ‘form’ peripheral component – see Component D (3.2) – is relevant in the lexical definition of quite a few flower names, such as those that are metaphorical idioms alluding to a shape (and eventually color): e.g., bouton-d’or ‘buttercup’ (lit. ‘button made.of gold’) and gueule-de-loup ‘snapdragon’ (lit. ‘maw of wolf’).

This concludes our presentation of polysemy patterns activated in the Gener cluster of fleur I.2. Our description is informal as our main target was to experiment with an exploratory methodology for polysemy pattern extraction. A more rigorous approach is required at the descriptive level in order to formalize these patterns – see for instance proposals made by Barque (2008, ch. 4), also within the framework of Explanatory Combinatorial Lexicology.

We are convinced that lexical regularities have to be explored and modeled by considering them as part of a system, rather than in isolation. For regular polysemy, in particular, the analyses presented above show that this phenomenon should be studied in parallel with regularities one can find in the lexicographic definitions for semantic classes of lexical units (Section 3.2). Ultimately, all these regularities that are encapsulated in the language manifest themselves as regular combinatorial patterns in speech; this is illustrated by the epigraph to the present section.

4. Conclusion

The purpose of this study was not the “discovery” of patterns of regular polysemy, and the four patterns presented in Section 3.3 are hardly new. Our aim was to propose and experiment with a novel approach to regular polysemy identification/characterization that displays some degree of systematicity. The key feature of this approach is, firstly, to be lexicography-based and to use non-taxonomic network lexical models, namely Lexical Systems. Secondly, it makes systematic use of the lexical function Gener and the relations it weaves within Lexical Systems, avoiding the recourse to taxonomically organized semantic labels (such as in Barque et al., 2018). We strongly believe that the Mental Lexicon is not structured as a taxonomy and that lexicological studies that are based on or require a taxonomic structure for the lexicon are flawed in terms of cognitive adequacy (Polguère, 2014, 2016). For small-world models such as the fr-LN, we came to the conclusion that the extensive use of semantic labels to project a hierarchical structure onto the lexical graph is a dead-end, precisely because the lexicon resists semantic hierarchization – see non-nominal parts of speech and phenomena such as semantic ambivalence of lexical units (Milićević & Polguère, 2010; Smirnova & Tolochin, 2018). Therefore, semantic labels should be kept very coarse (to be used by grammar rules for instance) and the lexical function Gener should systematically be used instead.32

Finally, it is important to highlight the fact that, within our Gener-based approach, regular polysemy is dealt with not in isolation but as a phenomenon that interacts with other lexical regularities (mainly, patterns of lexicographic definitions). It is our opinion that the outcome of our experiment with the Gener cluster of fleur I.2 is conclusive and that the proposed methodology should be explored further on the fr-LN and, eventually, applied systematically to all main generic terms of the French language.