A theoretical model of dynamical grammatical gender shifting based on set-valued set function

Mohamed El Idrissi

cs.CLMar 3, 2026

A theoretical model of dynamical grammatical gender shifting based on set-valued set function

Authors: Mohamed El Idrissi

Organizations: ENS Paris-Saclay

Abstract

This study investigates the diverse characteristics of nouns, focusing on both semantic (e.g., countable/uncountable) and morphosyntactic (e.g., masculine/feminine) distinctions. We explore inter-word variations for gender markers in noun morphology. Grammatical gender shift is a widespread phenomenon in languages around the world. The aim is to uncover the underlying patterns governing the variation of lexemes. To this end, we propose a new computational component dedicated to pairing items with morphological templates (e.g., the result of a generated item-template pair: (funas, $\{N, +SG, -PL, -M, +F, -COL, +SING\}$ ), with its spell-out form: $ð$ a-funast 'cow'). This process is formally represented by the Template-Based and Modular Cognitive model. This proposed model, defined by a set-valued set function $h : \mathscr{P}(M) \rightarrow \mathscr{P}(M)$ , predicts the nonlinear dynamic mapping of lexical items onto morphological templates. By applying this formalism, we present a unified framework for understanding the complexities of morphological markings across languages. Through empirical observations, we demonstrate how these shifts, as well as non-gender shifts, arise during lexical changes, especially in Riffian. Our model posits that these variant markings emerge due to template shifts occurring during word and meaning formation. This study achieves two primary objectives. First, on the formal side, we prove the model's representational completeness in learning and prediction. Second, on the linguistic side, we challenge and broaden the conventional view of word formation by formally demonstrating that conversion is applicable to noun-to-noun derivation. This data-driven mathematical model not only contributes to a deeper understanding of morphosyntactic variation but also offers potential applications in other fields requiring precise modelling of linguistic patterns.

Figures & tables

	French			Riffian
	Gender
Non-animate	M	le port	port		a-X:am	chamber
	F	la valise	suitcase		Ta-zeQbutS	crossbody bag
Uncountable	M	le beurre	butter		a-nzaR	rain
	F	la farine	flour		Ta-Rgazt	courage

Table 1: Morphosyntactic gender contrasts in non-animate versus uncountable nouns

Item-template pair	Spell-out form	Gloss
( qzin , $\{N,+SG,-PL,+M,-F,-COL,+SING\}$ )	aqzin	dog.SG.M
( qzin , $\{N,+SG,-PL,-M,+F,-COL,+SING\}$ )	ð-aqzin-t	dog.SG.F
( qzin , $\{N,-SG,+PL,+M,-F,-COL,+SING\}$ )	iqzin-en	dog.PL.M
( qzin , $\{N,-SG,+PL,-M,+F,-COL,+SING\}$ )	ð-iqzin-in	dog.PL.F

Table 2: Nominal inflection for number and gender

Figure 1: The structure of the linguistic system from meanings to sentences

Figure 2: Conceptual illustration of the proposed subgroup optimisation methodology.

	Grammatical templates
Semantic features	$T_{1}$	$T_{2}$	$T_{3}$	$T_{4}$	$T_{5}$	$T_{6}$	$T_{8}$	$T_{9}$	Total
Countable	81	52	0	0	14	17	0	0	164
Countable/Uncountable	0	3	0	1	2	8	0	0	14
Noun of action	150	3	0	1	3	3	0	1	161
Noun of action/Countable	0	2	0	0	0	1	0	0	3
Noun of action/Uncountable	4	1	0	1	1	0	0	0	7

Table 3: Semantic features by grammatical templates

Semantic features	$N$	$k$	$\chi^{2}$	$df$	$p$
Countable	164	4	73.805	3	$<.001^{***}$
Noun of action	161	6	678.59	5	$<.001^{***}$
Uncountable	110	8	70.364	7	$<.001^{***}$
Countable/Uncountable	14	4	8.286	3	$.04^{*}$
Noun of action/Countable	3	2	0.333	1	$.564$ ns
Noun of action/Uncountable	7	4	3.857	3	$.277$ ns

Table 4: Chi-square goodness-of-fit results per cognitive set (H 0 : uniform distribution across templates).

k

= number of non-zero templates;

N

= total item count. Significance codes:

{}^{***}p<.001

;

{}^{*}p<.05

; ns

p\geq.05

Cognitive set	Pair	$\hat{p}_{i}$	$\hat{p}_{j}$	$z$	$p$
Countable ( $N=164$ , $k=6$ , $\alpha_{\text{adj}}=0.0083$ )
	$T_{1}$ vs $T_{2}$	0.494	0.317	3.261	$.001$	∗∗
	$T_{1}$ vs $T_{5}$	0.494	0.085	8.156	$<.001$	∗∗∗
	$T_{1}$ vs $T_{6}$	0.494	0.104	7.72	$<.001$	∗∗∗
	$T_{2}$ vs $T_{5}$	0.317	0.085	5.234	$<.001$	∗∗∗
	$T_{2}$ vs $T_{6}$	0.317	0.104	4.742	$<.001$	∗∗∗

Table 5: Significant pairwise two-proportion

z

-tests with Bonferroni correction for the three prototypical cognitive sets. Only pairs that survive correction (

p<\alpha_{\text{adj}}

) are reported; all remaining pairs were non-significant.

\hat{p}

= observed proportion within the cognitive set;

\alpha_{\text{adj}}=0.05/k

, where

k

is the total number of pairs per set. Full results are provided in the Supplementary Appendix C1.

Cognitive set	$N$	$k$	$\chi^{2}$	$df$	$p$
Countable	73	4	30.726	3	$<.001^{***}$
Noun of action	159	5	540.025	4	$<.001^{***}$
Uncountable	52	7	79.654	6	$<.001^{***}$

Table 6: Chi-square goodness-of-fit results for the deverbal sub-sample, per cognitive set (H 0 : uniform distribution across templates).

k

= number of non-zero templates;

N

= total item count. Significance:

{}^{***}p<.001

Cognitive set	Pair	$\hat{p}_{i}$	$\hat{p}_{j}$	$z$	$p$
Countable ( $N=73$ , $k=6$ , $\alpha_{\text{adj}}=0.0083$ )
	$T_{1}$ vs $T_{2}$	0.301	0.493	-2.368	$.02$	ns
	$T_{1}$ vs $T_{5}$	0.301	0.096	3.112	$.002$	∗∗
	$T_{1}$ vs $T_{6}$	0.301	0.11	2.868	$.004$	∗∗
	$T_{2}$ vs $T_{5}$	0.493	0.096	5.265	$<.001$	∗∗∗
	$T_{2}$ vs $T_{6}$	0.493	0.11	5.05	$<.001$	∗∗∗

Table 7: Significant pairwise two-proportion

z

-tests with Bonferroni correction for the deverbal sub-sample. Only pairs surviving correction (

p<\alpha_{\text{adj}}

) are shown (except for

T_{1}

T_{2}

\hat{p}

= observed proportion within the cognitive set;

\alpha_{\text{adj}}=0.05/k

. Full results are provided in the Supplementary Appendix C2.

Variable	Description
Data variables
Noun	Riffian noun in orthographic notation
Type	Grammatical gender and number: nfp. (fem. plural), nfs. (fem. sing.), nmp. (masc. plural), nms. (masc. sing.)
Pages	Page number(s) in the source dictionary ( Serhoual, 2002 ) where the noun appears
Feature variables
Formula arguments

Table 8: Description of the dataset.

Filter	$n_{C}$	$n_{T_{2}}$	$P(T_{2}\|C)$	$n_{U}$	$n_{T_{6}}$	$P(T_{6}\|U)$	$H$	$\mathrm{Lift}_{C}$	$\mathrm{Lift}_{U}$	$\mathrm{WRAcc}_{\Sigma}$	$\min(P)$
$\varphi_{1}$	29	22	0.759	25	15	0.6	0.67	2.393	1.648	0.128	0.6
$\varphi_{2}$	17	16	0.941	15	9	0.6	0.733	2.968	1.648	0.099	0.6
$\varphi_{3}$	12	6	0.5	11	7	0.636	0.56	1.577	1.747	0.041	0.5
$\varphi_{4}$	66	36	0.545	52	29	0.558	0.552	1.72	1.532	0.184	0.545
Baseline	164	52	0.317	110	40	0.364	—	—	—	—	0.317

Table 9: Joint optimisation of

P(T_{2}\mid C)

and

P(T_{6}\mid U)

. Bold marks the leading value per criterion column.

Filter	$n_{C}$	$n_{T_{1}}$	$P(T_{1}\|C)$	$n_{U}$	$n_{T_{6}}$	$P(T_{6}\|U)$	$H$	$\mathrm{Lift}_{C}$	$\mathrm{Lift}_{U}$	$\mathrm{WRAcc}_{\Sigma}$	$\min(P)$
$\varphi_{1}$	29	4	0.138	25	15	0.6	0.224	0.279	1.65	$-0.013$	0.138
$\varphi_{2}$	17	1	0.059	15	9	0.6	0.107	0.119	1.65	$-0.011$	0.059
$\varphi_{3}$	12	3	0.25	11	7	0.636	0.359	0.506	1.75	0.009	0.25
$\varphi_{4}$	66	16	0.242	52	29	0.558	0.338	0.491	1.534	$-0.01$	0.242
Baseline	164	81	0.494	110	40	0.364	—	—	—	—	0.364

Table 10: Joint optimisation of

P(T_{1}\mid C)

and

P(T_{6}\mid U)

. Same filter subgroups as Table 9 ; only the Countable target template changes from

T_{2}

T_{1}

. Bold marks the leading value per criterion column.

Deverbal countable noun	1-2	1-3	Deverbal uncountable noun	1-6	1-7
BuR ‘to micturate’	$\looparrowright$	Da-Bew:aRt ‘bladder’	dhen ‘to grease’	$\looparrowright$	dduhneT ‘unctuousness’
feSfeS ‘to be effervescent’	$\looparrowright$	Da-feSfaSt ‘spray’	lul:eS ‘to sparkle’	$\rightarrow$	t-lul:eSt ‘toy’
ij:es ‘to be muddy’	$\looparrowright$	Da-ij:ast ‘mire’	bumbes ‘to get dark’	$\looparrowright$	t-bambast ‘twilight’
new:eR ‘to bloom’	$\looparrowright$	Da-new:aRt ‘flower’	d:aa ‘to be proud’	$\looparrowright$	d:aiT ‘pride’
sef:aR ‘to whistle’	$\rightarrow$	Da-sef:aRt ‘whistle’	fTeR ‘to roll semolina’	$\looparrowright$	T-faTaRt ‘semolina’
sij:eq ‘to mop the floor’	$\looparrowright$	Da-sij:aqt ‘squeegee’	dek: ‘to sip’	$\rightarrow$	dek:eT ‘sip’

Table 11: Subset of the subspace for obtaining initial templates of C and U

Cognitive set	Initial template
Countable	$T_{2}$ : $\{N,+SG,-PL,-M,+F,-COL,+SING\}$
Uncountable	$T_{6}$ : $\{N,+SG,-PL,-M,+F,+COL,-SING\}$
Noun of action	$T_{1}$ : $\{N,+SG,-PL,+M,-F,-COL,+SING\}$

Table 12: Initial templates of each cognitive set

$\alpha$ .	V	$\looparrowright$	NA	$\supseteq$	U
	R Ω aZa ‘to wait’		a- R Ω aZi ‘act of waiting’		a- R Ω aZi ‘wait’
			( R Ω aZi , $\{N,+SG,-PL,+M,-F,-COL,+SING\}$ )		( R Ω aZi , $\{N,+SG,-PL,+M,-F,-COL,+SING\}$ )
$\mu$ .	V	$\looparrowright$	NA	$\rightarrow$	U
	sendu ‘to churn’		a-sendu ‘act of churning’		Da-senduT ‘cream’
			( sendu , $\{N,+SG,-PL,+M,-F,-COL,+SING\}$ )		( sendu , $\{N,+SG,-PL,-M,+F,-COL,+SING\}$ )
$\gamma$ .	V	$\rightarrow$	NA

Figure 3: Formation model of gender in Riffian

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