A lexicographic approach to the study of copolysemy relations

The crucial notion of lexical cluster being introduced, we can proceed with the presentation of copolysemy relations. All copolysemy relations that have been identified in the fr-LN until now are listed in Table 1 below according to four descriptive parameters (the table's four columns).

1. Weight. The (semantic) weight of a copolysemy relation indicates to what extent this relation can participate in structuring the semantic lexical cluster of individual lexical units. We conceptualize the weight as a measurement of the semantic cohesiveness of copolysemy relations within the lexical network of the language. The weight can take three values, from the highest to the lowest degree of cohesiveness: Tight, Loose and Non-cohesive. (Copolysemy relations are listed in this order in Table 1.) To illustrate the notion of semantic weight of copolysemy relations, let us contrast Metonymy and Metaphor. Metonymy is a tight relation because the two copolysemes it connects belong to the same semantic space or to two closely related semantic spaces: e.g., by virtue of their definitions, neck I [of a person] and neck II [of a shirt] must have intersecting semantic lexical clusters. By contrast, Metaphor is a non- cohesive relation with respect to semantic space: there is no reason to expect neck I [of a person] and neck III [of a bottle] to have intersecting semantic lexical clusters.

2. Typ^e. The type of a copolysemy relation is the central (and often unique) element of its denomination. Types (or names) of copolysemy relations are systematically written with an initial capital letter and formatted in a non-proportional font in order to clearly distinguish them from various notions that may exist in linguistics. For instance, Metaphor designates a copolysemy relation in our model and not the rhetorical figure of metaphor. The same kind of remark applies to Conversion, Causation, etc.

3. Subtype. Some polysemy relation types are too general to allow for a description with sufficient level of granularity, even at this initial stage of elaboration of our model. In such cases, a subtype (or sub-name) is provided. The subtypes that appear in bold in Table 1 are compulsory.

4. Derivation. For each copolysemy relation L₁ ^ L₂, it is specified in Table 1 whether this relation corresponds to a true polysemy derivation or not, i.e. whether the meaning of L₂ can be considered as being derived from the meaning of L₁. Only three copolysemy relations are not actual polysemy derivations: Intersection, Grammaticalization and Coderivation. This means that, for such relations, we do not expect the lexicographic definitions of both lexical units to directly reflect their connection as copolysemes, and this will be explained for each individual relation in Subsections 3.2 to 3.4. We are fully aware though that the very notion of polysemy derivation would call for some in-depth discussion, that we cannot undertake here -- see, for instance, the discussion of the distinction between deductibily and motivatedness in Zalizniak (2007).

Table 1 Copolysemy relations in the French Lexical Network (fr-LN)

Weight	Type	Subtype	Derivation
Tight	Conversion		Yes
Tight	Causation		Yes
Tight	Result		Yes
Tight	Specialization	Subsense	Yes
Tight	Generalization		Yes
Tight	Metonymy	Set of, Part of	Yes
Loose	Extension		Yes
Loose	Antiphrasis		Yes
Loose	Intersection		No
Non-cohesive	Metaphor	As if, Meton as if, Behavior, Function, Functioning, Form, Position, Structure, Usage	Yes
Non-cohesive	Grammaticalization		No
Non-cohesive	Coderivation		No

Each copolysemy relation listed in Table 1 is described in Subsections 3.2 to 3.4 according to the following pattern:

¦ general characterization of the relation;

¦ illustration borrowed from the fr-LN -- therefore, from the French language;

¦ additional comments -- these comments are often minimal, due to lack of space, and are detailed only when it appears to be absolutely required.

Note that the illustration of a given L₁ ^ L₂ relation in presented in a table that has the following structure:

Table 2

L1	<Lexicographic name of L1>	<Short French example of use of Lj> <English translation of the example>
L2	<Lexicographic name of L2>	<Short French example of use of L2> <English translation of the example>

English translations of examples for L₂ are either “valid” translations, when the same corresponding L₁ ^ L₂ copolysemy exists in English (e.g. illustration table in Subsection 3.2.1 below), or literal with the indication of the correct lexical equivalent for L₂ between square brackets, when the corresponding copolysemy is absent from English (e.g. illustration table in Subsection 3.2.3).

When characterizing copolysemy relations, we often make use of the notion of denotation of a lexical unit. It can be defined as follows.

Definition 7. The denotation of a lexical unit is the (potentially infinite) set of facts or entities this lexical unit can designate strictly as function of its meaning.

Note that some lexical units do not have a denotation because they do not possess a meaning that allows for the designation of facts or entities; such is the case of auxiliary verbs or purely structural prepositions, such as of in to think of something.

Subsections 3.2 to 3.4 below present copolysemy relations in three groups, according to their cohesiveness (i.e. their semantic weight). This presentation is inevitably a bit enumerative as it accounts for preliminary results of an inductive approach to the identification of copolysemy relations. Much work remains to be done on testing the validity of the description before an actual theorization of copolysemy relations can be elaborated and before a better mode of presentation can be found.

3.2 Tight Copolysemy Relations

Tight L₁ ^ L₂ relations are characterized by the fact that L₂ possesses roughly the same denotation as L₁ -- Conversion --, a narrower or broader denotation -- Causation, Result, Specialization, Generalization -- or a somehow “orthogonal” denotation -- Metonymy.

In terms of network structuring of the lexicon, if L₂ is in a tight copolysemy relation with L₁, its lexical cluster is almost identical to, or largely overlaps with L₁'s.

3.2.1 Conversion

An L₁ Conversion ^ L₂ relation is such that L₂ is an exact or approximate lexical conversive of L₁: it possesses (roughly) the same denotation as L₁ but its active valency displays a permutation of L₁'s syntactic actants. For instance, in the fr-LN:

Table 3

L1	COMMENCER I.2a	Le roman commence par un meurtre. 'The novel begins with a murder'
L2	COMMENCER I.2b	Un meurtre commence le roman. 'A murder begins the novel'

Conversion is a marginal copolysemy relation in the fr-LN -- and probably in French and in most languages as well: it represents barely more than 0.5% of the relations currently encoded in the fr-LN.

Note that Conversion possesses a counterpart among Meaning-Text paradigmatic lexical functions, namely Convoi. The relationship that some copolysemy relations entertain with paradigmatic or syntagmatic lexical functions is clearly an important topic, which calls for further study.

3.2.2 Causation

An L_j Causation ^ L₂ relation is such that L₂ means approximately `to cause <cause of> L_j'. In the fr-LN:

Table 4

L1	APPRENDRE I.1	Elle apprend la boxe. 'She learns boxing'
L2	APPRENDRE I.2	Je lui apprends la boxe. 'I teach her boxing'

Causation has Caus as syntagmatic lexical function counterpart and is directly related to the next copolysemy relation: Result.

3.2.3 Result

An Lj Result ^ L₂ relation is such that the denotation of L₂ is a set of facts or entities that can be considered as being prototypical results of the facts that make up the denotation of L_j. Semantically, L₂ is the de-causative counterpart of L_j; Causation, above, and Result are therefore symmetrical. In the fr-LN:

Table 5

L1	HUMILIATION 1	Comment peut-il supporter les humiliations infligйes par son patron ? 'How can he cope with humiliations inflicted by his boss?'
L2	HUMILIATION 2	Nous ressentons une profonde humiliation. 'We feel a deep humiliation'

Both Causation and Result are weakly present in the fr-LN: not even 1% each. Note that Causation and Result may be exceptionally rare for verbs in the fr-LN as French possesses de-causative reflexive verbs -- e.g. dissoudre `X dissolves Y in Z' vs. SE DISSOUDRE `Y dissolves in Z'. The reflexive counterpart of a non-reflexive verb is considered to belong to a separate vocable; therefore, the relation between the two verbs cannot be one of copolysemy.

Result has two paradigmatic lexical function counterparts, either S_res or Resulti, depending on the semantico-syntactic ratio between L₁ and L₂. In the above example, humiliation 2 is an S_res for humiliation 1. Below, salir 2 is a Result₂ for salir 1:

Table 6

L1	SALIR 1	Elle a sali sa chemise avec de la sauce tomate. 'She dirtied her shirt with tomato sauce'
L2	SALIR 2	Elle frotte la sauce tomate qui salit sa chemise. Lit. 'She rubs the tomato sauce that *dirties [= stains] her shirt'

3.2.4 Specialization

An L₁ Specialization ^ L₂ relation is such that L₂ is a richer synonym of L₁, cf. the Syn₃ lexical function, or at least contains L₁ as central (generic) component of its definition. In the fr-LN:



Table 7

L1	BAGUETTE I.1	Elle a utilisй des baguettes de bois pour fabriquer un cheval miniature. 'She used wooden sticks to make a miniature horse'
L2	baguette I.2a	Elle mange son riz avec des baguettes. Lit. 'She eats her rice with *sticks [= chopsticks]'

Specialization is not common in the fr-LN: less than 2.5%. It is directly related to the even less common Generalization relation (Subsection 3.2.5 below).

There exists a special subtype of Specialization that we termed Subsense, following Cruse (1995: 39--40). In an L₁ Specialization.Subsense ^ L₂ relation, L₂ possesses the exact same denotation as L₁ except for parameters linked to a specific domain of functioning, usage, etc. In the fr-LN:

Table 8

L1	ABEILLE I.a	Elle йtudie les abeilles, les guкpes, les fourmis et autres insectes sociaux. 'She studies bees, wasps, ants and other social insects'
L2	ABEILLE I.b	Administrativement, l'йlevage des abeilles relиve des activitйs agricoles. 'Administratively, raising bees falls within agricultural activities'

Clearly, Specialization.Subsense is a very borderline case of copolysemy, one where L₂ is not a distinctly separate lexical unit from L₁. All lexical information associated to L₁ is also associated to L₂: L₂, as a lexical unit, is L₁ “from a given viewpoint”. However, the converse is not true. L₂, because it is associated with a specific domain, controls a much richer lexical cluster than L₁. In point of fact, the same L₁ can have multiple L₂ subsenses, each one of them controlling its own specific lexical clusterThe English vocable KNIFE is a classic example for such copolysemy configuration. Its basic lexical unit is connected to a series of subsenses; at least: `knife as a weapon', `knife as a kitchen instrument' and `knife as tableware'..

Because they are borderline cases, subsenses are often used in the literature when debating such existential questions as: Does polysemy really exist?; Can it be systematically handled?; Do dictionaries over-generate senses in their entries? A good illustration of this is the case of the English vocable LOVE^ -- together with LOVE^ -- discussed by Goddard (2011: 40--42) in the context of his criticism of the proliferation of polysemy in dictionaries“Although lexical polysemy is a fact of life, dictionaries generally speaking posit excessive polysemy” (Goddard 2011: 40).. The central question Goddard examines is the distinction made by most dictionaries between a sex-free and a sex-related sense of LOVE(_V/N). Goddard's claim is that it is impossible to circumscribe everything that can go with love and that love can take multiple forms and manifestations. Consequently, he proposes a Natural Semantic Metalanguage explanation for one single sense of love_(v), that is supposed to encompass all forms of love:

“Someone X loves someone Y: X feels something good towards Y, thinks good things about Y, wants to do good things for Y, and wants good things to happen to Y” (Goddard 2011: 41)

If this is the definition for a one and unique sense of LOVE^, our main problem with it is: but where is the sex? There exist in the English language many traces of a lexicalization of the love-sex association; e.g. idioms such as make love or love making, and the separate sense of LOVE(_N) that means `love making' and that has to be derived from another sense containing `sexual desire' in its definition:

(7) Was there a need for the rest after love?

The problem with Goddard's argument is that it is based on a purely conceptual reasoning, which can lead lexicographers either way. If we look at the lexical cluster of LOVE(_V/N) in the English lexicon, on the other hand, and if we want to account for it in a simple manner, there is no other solution but to postulate a specialized sense of LOVE(_V/N), one that is a subsense (= a manifestation) of the more neutral basic sense and is at the center of a very specific network of lexical relations (lover, in love, puppy love, platonic love, etc.). It is mainly this systemic positioning in the global lexical network of English that gives this subsense a relative autonomy and, hence, a true existence in the English language. If this lexical cluster were not present in English, on the other hand, we would fully agree that there is no need to consider a separate sense.

We have discussed at length Specialization.Subsense because we believe that this apparently marginal relation plays in reality a crucial role in the development and structuring of the lexicon as regards to specialized vocabularies (i.e. terminologies). It often comes into play in association with technical/scientific terms that are inextricably embedded within general language -- see, e.g., BOND(_N) as a general language lexical unit vs. as a chemistry term (Ingrosso and Polguere 2015).

3.2.5 Generalization

An L₁ Generalization ^ L₂ relation is such that L₂ is a poorer synonym of L₁, cf. the Syn_c lexical function; its definition is identical to that of L₁ except for some missing components. In the fr-LN:

Table 9

L1	CHAMP1 I.l	Les paysans labourent les champs. 'Farmers are plowing the fields [= piece of land for growing crop]'
L2	champ1 I.2	Les vaches sont dйjа au champ. 'Cows are already in the field [= piece of agricultural land]'

Generalization is extremely marginal: only three occurrences in the fr-LN. Additionally, all cases we have identified are somehow controversial. For instance, the second sense of champ above, champ¹ I.2, could be fused with the first one, from the strict point of view of its definition. The reason we keep both senses separated is that champ¹ I.1 -- `open land for growing crops' -- controls a very specific lexical cluster that simply does not apply to the more general champ¹ I.2. But again, our analysis of the polysemy structure of champ in the fT-LN is debatable and it is safe to say that Generalization is more a logically plausible copolysemy relation than a truly attested oneAnother legitimate question is why choosing the semantically more specific CHAMP I.1 over the more general CHAMP I.2 as origin of the copolysemy relation. We have no better answer to offer than the fact that the use of the latter by French speakers is rather marginal and it is a rather elusive lexical unit from a lexicographic point of view..

3.2.6 Metonymy

An L₁ Metonymy ^ L₂ relation is such that the denotation of L₂ relates to the denotation of L_j through contiguity, in the broadest sense of the term. As a consequence, the meaning `L_j' necessarily appears in the lexicographic definition of L₂, though not as central component. In the fr-LN:

Table 10

L1	raisin a	Notre raisin est rйcoltй а la main. `Our grape is harvested by hand'
L2	RAISIN b	Dйcorez votre salade avec quelques raisins [= grains de raisin a]. `Decorate your salad with a few grapes [= grape berries]'

Metonymy is the first copolysemy relation examined here that is truly widespread in the fr-LN -- 18% of all relations --, and most probably in the lexicon of all natural languages as well. Metonymy, as characterized above by the very general notion of contiguity (whether physical, temporal, psychological, logical, etc.), is a heterogenous phenomenon. A complete modeling of Metonymy relations calls for a sub-classification of these relations. As indicated in Table 1 (Subsection 3.1 above), we have for now introduced only two subtypes of Metonymy: Set of and Part of. As our descriptive apparatus is still embryonic, the indication of a subtype is not obligatory for the time being when encoding Metonymy relations. In the future, all our currently encoded relations should be carefully analyzed in order to identify and encode new subtypes, so that all cases of Metonymy relations are made more specific.

3.3 Loose Copolysemy Relations

Loose L₁ ^ L₂ relations are characterized by the fact that lexicographic definitions of L₁ and L₂ share significant semantic content without having directly related denotation -- contrary to all cases of tight copolysemy relations we just examined.

In terms of network structuring of the lexicon, if L₂ is in a loose copolysemy relation with L₁, its lexical cluster marginally intersects with L₁'s, as opposed to cases of tight copolysemy relations (Subsection 3.2 above).

3.3.1 Extension

An L₁ Extension ^ L₂ relation is such that the denotation of L₂ is relatively close to the denotation of L_j while it is clear that no (quasi-)synonymy relation holds between these two lexical units. It is as if the meaning `L<sub>j</sub>' had been doctored in order to construct the meaning `L₂'. In the fr-LN:

Table 11

L1	GATEAU a	Nous devons trouver des bougies pour le gвteau d'anniversaire. `We have to find candles for the birthday cake'
L2	GATEAU b	Je prends un paquet de gвteaux au cas oщ on a faim dans l'aprиs-midi. Lit. `I bring a pack of * cakes [= cookies] in case we feel hungry in the afternoon'

Note that in many instances -- such as for the bras I.1a vs. bras I.3 pair presented below -- an Extension relation could be argued to be in reality a Metaphor relation (Subsection 3.4.1 below).

Table 12

L1	BRAS I.1a	Elle a failli se casser le bras en tombant dans l'escalier. `She almost broke her arm falling in the stairs'
L2	BRAS I.3	Les pieuvres possиdent huit bras munis de ventouses. `Octopuses have eight arms equipped with suckers'

One could say that octopus arms are called bras `arms' in French by analogy, as if they were indeed (human) arms. As always in the lexical network approach to lexicology/lexicography, our decision will be guided, not by some form of purely conceptual/semantic reasoning, but rather by considering the individual cluster of each lexical unit. In this particular case, our perception is that bras I.3 controls a lexical cluster that is not sufficiently apart from the cluster controlled by bras I.1a to be considered as being a metaphor of bras I.1a: we will see in 3.4.1 below that the autonomy of the clusters controlled by the two copolysemes is a characteristic of a Metaphor relation.

Extension is a very common copolysemy relation in the fr-LN -- 26.5% of all copolysemy relations. It can be considered as being the default relation among loose copolysemy relations within the fr-LN. At this stage, it would be adventurous to state that this is an actual characteristic of the polysemic organization of the French lexicon, or of the lexicon of natural languages in general. Much lexicographic work remains to be performed on the fr-LN -- and undertaken on networks for other languages -- before we can venture to propose this type of theoretical generalization.

3.3.2 Antiphrasis

An L₁ Antiphrasis ^ L₂ relation is such that the meaning of L₂ is in a quasi- antithetical relation with the meaning of L₁. This relation generally entails an ironic stylistic charge in L₂. In the fr-LN:

Table 13

L1	JOYEUX I.1a	Je vois des enfants joyeux qui jouent dans le parc. `I see cheerful children playing in the park'
L2	JOYEUX III	Les enfants ont mis une joyeuse pagaille dans leur chambre. Lit. `Kids have made a *cheerful [= real niceironic] mess in their bedroom'

L_j Antiphrasis si L₂ was added quite recently to our list of copolysemy relations We are grateful to Veronika Lux-Pogodalla for this. and it seems to be very marginal: only five cases identified so far in the fT-LN. It is our conjecture, however, that Antiphrasis may be more present in the polysemy of French than it appears to be as it is the lexicalized manifestation of a rhetorical figure commonly used in oral speech (Henault 2008: 297).



3.3.3 Intersection

An L_j Intersection s L₂ relation is such that there is a perceived semantic relation between L_j and L₂, but one that seems impossible to truly specify by contrasting these units' lexicographic definitions and by identifying a clear Extension, Metaphor, etc. relation. In other words, the term Intersection is used here to mean `semantic intersection only, of undetermined nature'. The Intersection relation is therefore some kind of joker relation, for lack of a better characterization of the copolysemy relation under consideration. Because of the tenuous and synchronically unexplained nature of L_j Intersection s L₂ relations, L₂ cannot be considered synchronically as being the product of an actual polysemy derivation. In the fr-LN:

Table 14

L1	DISPOSER I	Elle a disposй artistiquement des groseilles autour du gвteau. 'She artistically placed red currants around the cake'
L2	DISPOSER II	Paris dispose d'un rйseau de mйtro extrкmement dйveloppй. Lit. 'Paris *places [= possesses] an extremely developed underground network'

Intersection is rare in the fr-LN: less than 0.5% of all copolysemy relations. As can be seen with the above example, cases of L_j Intersections L₂ relations are generally good candidates for homonymy rather than polysemy. It is only the intuitive perception by many native speakers of French of a semantic connection between DISPOSER I and DISPOSER II that justifies a non-homonymic description in this case The semantic connection, in this particular case, seems extremely tenuous: something like the vague semanteme `presence [of something]'. This pair of lexemes may very well be treated as homonyms as well..

It is not clear that the Intersection relation should be kept in the model and a simple drastic solution would be to have recourse to homonymy instead. In general, it is our opinion that there is nothing to gain and everything to lose by maintaining copolysemy links when they are not supported by clear evidence.



3.4 Non-cohesive Copolysemy Relations

Non-cohesive L_j s L₂ relations are characterized by the fact that L₂'s denotation is, in principle, totally disconnected from that of L_j. There are three types of such relations: Metaphor, Grammaticalization and Coderivation. For this latter case, note that two lexical units linked by a Coderivation relation could very well have intersecting denotations, but this would be purely coincidental and would not be a consequence of the characteristics of Coderivation as such (see 3.4.3 below).

In terms of network structuring of the lexicon, if L₂ is in a non-cohesive copolysemy relation with L_j, their lexical clusters can be expected to be largely distinct.

3.4.1 Metaphor

An L₁ Metaphor .<Subtype> ^ L₂ relation is such that the denotation of L₂ relates to the denotation of L_j through analogy in the broadest sense of the term. Metaphor is a heterogenous relation and compulsory subtypes have been introduced in the fr-LN model of copolysemy (Table 1, Subsection 3.1 above): As if, Meton as if, Behavior, Function, Functioning, Form, Position, Structure and Usage. For instance, the following L₁ ^ L₂ pair, borrowed from the fr-LN, illustrates a case of L₁ Metaphor. Form ^ L₂ relation Reminder: baguette I.1 is also used in Subsection 3.2.4 as the source of a Specialization copolysemy relation.:

Table 15

L1	BAGUETTE I.1	Elle a utilisй des baguettes en bois pour fabriquer un cheval miniature. 'She used wooden sticks to make a miniature horse'
L2	BAGUETTE II	Elle a achetй deux baguettes au boulanger du coin. Lit. 'She bought two *sticks [= baguettes] from the neighborhood bakery'

As if is the default subtype; it simply indicates the presence of at least one component in the definition of L₂ which specifies the nature of the analogy that connects L₁ and L₂'s denotations. As lexicographic work progresses and descriptions become finer, all occurrences of the As if subtype should be replaced with more specific subtypes. All other current subtypes are self-explanatory, except for Meton as if which we examine now.

In the course of weaving copolysemy relations in the fr-LN, we noticed the recurrent apparition of a very special type of metaphor: one that is rooted in an underlying metonymy and that we termed metonymy-based metaphor -- cf. the Meton as if subtype. Let us explain this relation with an example borrowed from the fr-LN:

Table 16

L1	boire I.2a	Dйsolй, je ne bois pas. 'Sorry, I don't drink [= usually drink alcohol]'
L2	BOIRE II	Chaque mois, il boit son salaire. Lit. 'Each month, he *drinks [= drinks away] his salary'

Boire son salaire/ses йconomies/etc. (lit. `to drink [= drink away] one's salary/ savings/etc.') is undoubtedly a metaphor. This sense of the vocable boire is based on an analogy with BOIRE I.2a which means `to have the habit of drinking (in the basic sense) alcohol'. However, the actual semantic connection between boire I.2a and BOIRE II is quite complex as revealed by the following lexicographic definition of BOIRE II, written according to the principles of Explanatory Combinatorial Lexicology (Mel'cuk and Polguиre In press).

X boit II Y:X gaspille Y

'X drinks II Y''X wastes Y'

¦ Y йtant de l'argent 'Y being money'

¦ en dйpensant Y pour boire I.2.a de l'alcool de faзon excessive 'by spending Y on drinking I.2a alcohol in excess'

¦ comme si Y йtait des boissons alcoolisйes que X boit I.2a 'as if Y were alcoholic drinks that X drinks I.2a'

The above definition clearly shows that the semanteme `boire I.2a' is present twice in the definition of boire II: first, outside the metaphoric component `as if ...', in a component which explains that, in drinking II, there is indeed an act of drinking I.2a involved; second, in the metaphoric component `as if ...', which explains that an act of drinking II Y presents an analogy with an act of drinking I.2a alcohol -- in fact, it presents at the same time Y (salary, savings, ...) as analogous to alcoholic drinks, i.e. something that can be drunk I.2a. The first occurrence of `boire I.2a' implies that BOIRE II is, in part, in a metonymy relation with BOIRE I.2a (actual presence of an act of drinking I.2a on which the situation of drinking II is based). The second occurrence implies that BOIRE II is at the same time related to BOIRE I.2a by a relation of metaphor. With BOIRE II, we are faced with a clear case of metonymy-based metaphor.

To conclude on metonymy-based metaphors, it is important to highlight the fact that they are truly atypical in that they do not entail non-cohesive relations, as “normal” metaphors do: in an L₁ Metaphor.Meton as if ^ L₂ relation, L₂ is strongly connected to L₁ from the viewpoint of their denotations because of the embedded metonymy.

Metaphor is by far the most widespread copolysemy relation in the fT-LN: over 48% of all such relations! This is an unexpected outcome of our study. We somehow anticipated some form of equilibrium between Metonymy, Extension and Metaphor relations, and were apparently wrong. A note of caution is, however, warranted before drawing any general conclusion about metaphor and polysemy. Most vocables of the fr-LN have been subjected to only a partial polysemy analysis. It is quite possible that, in the process of building polysemy structures, lexicographers tend to pick first metaphorical copolysemes because they are more easily identifiable and often “look good” in a vocable structure. We anticipate that the importance of Metaphor relations in the overall polysemy of the fr-LN will gradually decrease as polysemy structures of vocables receive finer descriptions. In order to test this hypothesis, we conducted a little experiment. The four published volumes of the Explanatory Combinatorial Dictionary of French (Mel'cuk et al. 1984--1999) describe quite exhaustively the polysemy of a representative sample of the French lexicon. By analyzing lexicographic definitions, we systematically identified metaphorical senses in the fourth volume of this dictionary, which contains 180 vocables for a total of 587 senses. Based on the principle that the number of copolysemy relations in a vocable structure is equal to the number of senses it contains minus 1 -- because this structure is, by default, a tree graph --, The structure of a monosemous vocable is a minimal tree graph of only one node. The arithmetic for computing the number of copolysemy relations contained in its structure is therefore the same as for polysemous vocables: 1 sense minus 1 equals 0 copolysemy relation. we estimated the total number of copolysemy relations in the fourth volume of the dictionary to be 587 - 180 = 407. As we identified 133 lexicographic definitions embedding a metaphorical component, we concluded that a bit less than 33% of copolysemy relations in this small but representative sample of the French lexicon are metaphors, against 48% in the fr-LN. Though it is by no means a demonstration of the actual quantitative importance of Metaphor copolysemy relations in French, this experiment seems to corroborate our intuition that Metaphor is most probably overrepresented in the fr-LN in its current state.

3.4.2 Grammaticalization

An L_j Grammaticalization ^ L₂ relation is such that L₂ is a grammatical or quasi-grammatical lexical unit that is (barely) related to L_j through extreme impoverishment of L_j's meaning. It is only this perceived creation of L₂ through semantic impoverishment from L_j that justifies considering a copolysemy relation instead of pure homonymy. Of course, Grammaticalization is a totally non- cohesive relation and, additionally, L₂ is not a copolysemy derivative of L_j in synchrony. There are two main cases of Grammaticalization, depending on the nature of L₂.

Firstly, L₂ can be a true grammatical lexical unit which participates in expressing either grammemes of the language (cf. auxiliary verbs) or syntactic dependencies (cf. valency-controlled empty prepositions such as in in to believe in something). In the fr-LN:

Table 17

L1	AVOIR I.1	Elle a un ordinateur trиs bruyant.
		'She has a very noisy computer'
L2	AVOIR V.2	Elle a visitй Barcelone.
		'She has visited Barcelona'

The French verb AVOIR possesses a very peculiar morphological behavior with unpredictable inflections (avoirinfiniti^ e«past parO aijst pers. sing. indic. pres^ »0 that is identical for both AVOIR I.1 and AVOIR V.2. It is this formal identity, rather than any semantic consideration, that justifies the grouping of both lexical units within the same vocable. Otherwise, from a strictly semantic viewpoint, AVOIR I.1 and AVOIR V.2 could, and probably should be considered as homonyms.

Secondly, L₂ can be a collocative lexical unit expressing the very basic and vague meaning of one of Meaning-Text lexical functions. Such is the case of the French support verb faire II.1, which expresses the Oper! lexical function.

Table 18

L1	FAIRE I	Elle fait des crкpes. 'She makes pancakes'
L2	FAIRE II.1	Elle fait du yoga quotidiennement. 'She makes some yoga daily'

Lexical units such as faire II.1 are not true grammatical units, but their meaning is so poor -- empty or close to empty in the case of support verbs -- that their connection to their source copolyseme can be assimilated to Grammaticalization. A word of caution though: in order for a collocative lexical unit to be considered as linked through Grammaticalization to its source, it has to express the “bare” meaning of its corresponding lexical function. For instance, heavy in heavy sigh expresses the meaning of intensification -- that is, of the Magn lexical function -- and nothing more. Therefore, the corresponding collocative sense of the heavy vocable should be considered as connected through Grammaticalization to its source copolyseme. Contrary to this, verbs of realization -- e.g. those corresponding to the Real lexical function -- are often standard full lexical units connected to their source copolyseme by a true polysemy derivation. For example, follow in to follow a lead in an inquiry -- a clear case of Real₂ collocate -- should be described as a Metaphor copolyseme of follow in to follow a person on the street, and absolutely not as a Grammaticalization.

From the viewpoint of diachrony and word creation, one could see both cases of Grammaticalization as results of preliminary polysemic derivations, such as metaphoric derivations. For instance, the intensifier heavy in heavy sigh most probably originates via some form of metaphor from heavy in heavy package. However, we believe that the lexicographic definition of the intensifier heavy should be extremely basic -- based on the `intense' semanteme which is the trigger for the Magn lexical function (Mel'cuk and Polguere in press); it should by no means develop a metaphor- based explanation of the collocate meaning.

Grammaticalization is minimally present in the fr-LN polysemy structures: only four cases. But this is a consequence of incomplete (and sometime erroneous) lexicographic description. At present, Grammaticalization is in all probability largely underrepresented in our data.

3.4.3 Coderivation

An L_j Coderivation ^ L₂ relation is such that instead of L₂ existing in the lexicon in reference to its copolyseme L_j, both lexical units are individually derived from a pair of copolysemes of another vocable. Let us exemplify this atypical case of copolysemy relation with the following pair of lexical units borrowed from the fr-LN.

Table 19

L1	APPLICABLE I	Cette crиme hydratante est applicable sur tous les types de peau. 'This moisturizing cream is applicable on all types of skin'
L2	APPLICABLE II	Cette rйglementation n'est pas applicable aux mineurs. 'This regulation is not applicable to minors'

The adjective applicable I is, first of all, a semantic (and morphological) derivative of the verb appliquer I `X puts/spreads Y on Z' and denotes the property of something to be a potential Y which can be put/spread on a Z. This corresponds to a standard paradigmatic lexical function called Able₂:

Able₂( APPLIQUER I ) = APPLICABLE I.

The same paradigmatic derivation holds for applicable II, derived from appliquer II `X makes Y be effective/relevant as regards to Z':

Able₂( APPLIQUER II ) = APPLICABLE II.

in other words, we are faced with the following apparent paradox:

¦ both adjectives applicable I and applicable II clearly belong to the same adjectival vocable applicable and should be connected by a copolysemy relation in its polysemy structure;

¦ the obvious lexical sources in the French lexicon of applicable I and applicable II are, respectively, the two copolysemes appliquer I and appliquer II of the verbal vocable appliquer, and the corresponding Able₂ semantic derivation clearly supersedes -- and even overrides -- in the network structure of the lexicon any type of copolysemy relation that may connect the two adjectives.

The solution we adopted is to introduce a copolysemy relation, namely Coderivation, which holds a very special status: it exists only in relation to another copolysemy relation present in another vocable of the language. Figure 3 below visualizes this lexical configuration for the applicable I vs. applicable II pair of copolysemes.

Figure 3. System of lexical relations involving a Coderivation

In an L_j Coderivation ^ L₂ copolysemy relation, whether the denotations of L_j and L₂ intersect is entirely dependent on the corresponding copolysemy relation in the source vocable. In the case examined above and visualized in Figure 3, the verbs appliquer I and appliquer II are connected by the non-cohesive relation of Metaphor; consequently, the resulting Coderivation relation between the adjectives applicable I and applicable II is equally non-cohesive (the denotations of the adjectives do not significantly intersect). Because of this lack of autonomy as regards its semantic weight, Coderivation is not considered as being inherently a case of polysemy derivation.

To conclude on this relation, note that Coderivation is not much present in the fr-LN, but is not that marginal either: it represents close to 2.2% of all copolysemy relations identified so far.



4. Concluding remarks

We hope that the present study -- as incomplete as it is -- offers useful preliminary results on what a lexical network approach to the modeling of polysemy can offer. The strategy that consists in systematically considering lexical relations controlled by copolysemes -- i.e. their individual lexical cluster (see Definition 6, Subsection 3.1) -- is a major characteristic of the lexical network approach. It is, in our opinion, more rigorous than pure intuitive conceptual and semantic reasoning on word senses, which often leads to non-falsifiable modeling. It is also a good way of accounting for lexical variation, e.g. diachronic or individual variation. For instance, the pair bras I.1a `arm of a person' vs. bras I.3 `arm of some animals [cf. octopuses]' examined in Subsection 3.3.1 may very well be considered by one individual as implicating an Extension relation because she/he perceives intuitively the presence of many shared lexical connections in the clusters of these two lexical units, whereas another individual may not have access to such information and, therefore, interpret the relation as one of Metaphor. In the case of a Lexical System type of model, such as the fr-LN, what matters is the consistency between the diagnosis of a given polysemy relation and the systems of lexical connections -- lexical clusters -- that position both copolysemes within the topology of the global lexical graph of the language.

Further work that remains to be done includes: (i) validation, refinement and extension of the description of French in the fr-LN; (ii) identical large-scale work on the networks of other languages (English and Russian are next on the list); (iii) extraction of general theoretical principles from these analyses, which will deepen our understanding of polysemy as a universal linguistic phenomenon.

One last word to mention Barque et al. (2018), published at the time of writing of the present paper. It describes a study of regular polysemy based on the extraction of copolysemy templates from the fr-LN and from the Wolf lexical database.



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