Evolution, Optimization, and Language Change: the Case of Bengali Verb Inﬂections

Evolution, Optimization, and Language Change: The Case of Bengali Verb Inﬂections

Monojit Choudhury1, Vaibhav Jalan2, Sudeshna Sarkar1, Anupam Basu1 1 Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur, India {monojit,sudeshna,anupam}@cse.iitkgp.ernet.in 2 Department of Computer Engineering Malaviya National Institute of Technology, Jaipur, India [email protected]

Abstract (e.g., Hare and Elman (1995); Dras et al. (2003); Ke et al. (2003); Choudhury et al. (2006b)), all the The verb inflections of Bengali underwent mathematical and computational models developed a series of phonological change between for explaining language change are built for artifi- 10th and 18th centuries, which gave rise cial toy languages. This has led several researchers to several modern dialects of the language. to cast a doubt on the validity of the current compu- In this paper, we offer a functional ex- tational models as well as the general applicability planation for this change by quantifying of computational techniques in diachronic explana- the functional pressures of ease of artic- tions (Hauser et al., 2002; Poibeau, 2006). ulation, perceptual contrast and learnabil- In this paper, we offer a functional explanation1 ity through objective functions or con- of a real world language change – the morpho- straints, or both. The multi-objective and phonological change affecting the Bengali verb multi-constraint optimization problem has inflections (BVI). We model the problem as a been solved through genetic algorithm, multi-objective and multi-constraint optimization whereby we have observed the emergence and solve the same using Multi-Objective Genetic of Pareto-optimal dialects in the system Algorithm2 (MOGA). We show that the different that closely resemble some of the real forms of the BVIs, as found in the several modern ones. dialects, automatically emerge in the MOGA framework under suitable modeling of the objective and 1 Introduction constraint functions. The model also predicts several

Numerous theories have been proposed to explain 1Functionalist accounts of language change invoke the basic the phenomenon of linguistic change, which, of late, function of language, i.e. communication, as the driving force behind linguistic change (Boersma, 1998). Stated differently, are also being supported by allied mathematical or languages change in a way to optimize their function, such that computational models. See (Steels, 1997; Perfors, speakers can communicate maximum information with min- 2002) for surveys on computational models of lan- imum effort (ease of articulation) and ambiguity (perceptual contrast). Often, ease of learnability is also considered a func- guage evolution, and (Wang et al., 2005; Niyogi, tional benefit. For an overview of different explanations in di- 2006) for reviews of works on language change. achronic linguistics see (Kroch, 2001) and Ch. 3 of (Blevins, The aim of these models is to explain why and how 2004). 2Genetic algorithm was initially proposed by Hol- languages change under specific socio-cognitive as- land (1975) as a self-organizing adaptation process mimicking sumptions. Although computational modeling is a the biological evolution. They are also used for optimization and machine learning purposes, especially when the nature of useful tool in exploring linguistic change (Cangelosi the solution space is unknown or there are more than one objec- and Parisi, 2002), due to the inherent complexi- tive functions. See Goldberg (1989) for an accessible introduc- ties of our linguistic and social structures, modeling tion to single and multi-objective Genetic algorithms. Note that in case of a multi-objective optimization problem, MOGA gives of real language change turns out to be extremely a set of Pareto-optimal solutions rather than a single optimum. hard. Consequently, with the exception of a few The concept of Pareto-optimality is defined later.

65 Proceedings of Ninth Meeting of the ACL Special Interest Group in Computational Morphology and Phonology, pages 65–74, Prague, June 2007. c 2007 Association for Computational Linguistics other possible dialectal forms of Bengali that seems Attributes Classical (Λ0) SCB ACB Sylheti PrS1 kari kori kori kori linguistically plausible and might exist or have ex- PrS2 kara karo kara kara isted in the past, present or future. Note that the PrS3 kare kare kare kare evolutionary algorithm (i.e., MOGA) has been used PrSF karen karen karen karoin here as a tool for optimization, and has no relevance PrC1 kariteChi korChi kartAsi koirtAsi to the evolution of the dialects as such. PrC2 kariteCha korCho kartAsa koirtAsae Previously, Redford et al. (2001) has modeled the PrC3 kariteChe korChe kartAse koirtAse PrCF kariteChen korChen kartAsen kortAsoin emergence of syllable systems in a multi-constraint and multi-objective framework using Genetic al- PrP1 kariAChi koreChi korsi koirsi gorithms. Since the model fuses the individual PrP2 kariACha koreCho karsa koirsae PrP3 kariAChe koreChe karse koirse objectives into a single objective function through PrPF kariAChen koreChen karsen korsoin a weighted linear combination, it is not a multi- objective optimization in its true sense and nei- Table 1: The different inflected verb forms of Clas- ther does it use MOGA for the optimization pro- sical Bengali and three other modern dialects. All cess. Nevertheless, the present work draws heavily the forms are in the phonetic forms and for the verb from the quantitative formulation of the objectives root kar. Legend: (tense) Pr – present; (aspects) S and constraints described in (Redford, 1999; Red- – simple, C – continuous, P – perfect, ; (person) 1 ford and Diehl, 1999; Redford et al., 2001). Ke et – first, 2 – second normal, 3 – third, F – formal in al. (2003) has demonstrated the applicability and ad- second and third persons. See (Bhattacharya et al., vantages of MOGA in the context of the vowel and 2005) for list of all the forms. tonal systems, but the model is not explicit about the process of change that could give rise to the optimal vowel systems. As we shall see that the conception verb root in Bengali, which are obtained through af- of the genotype, which is arguably the most impor- fixation of one of the 52 inflectional suffixes, option- tant part of any MOGA model, is a novel and signif- ally followed by the emphasizers. The suffixes mark icant contribution of this work. The present formu- for the tense, aspect, modality, person and polarity lation of the genotype not only captures a snapshot information (Bhattacharya et al., 2005). The ori- of the linguistic system, but also explicitly models gin of modern Bengali can be traced back to Vedic the course of change that has given rise to the partic- Sanskrit (circa 1500 BC 600 BC), which during ular system. Thus, we believe that the current model the middle Indo-Aryan period gave rise to the di- ¯ ¯ is more suitable in explaining a case of linguistic alects like Magadh¯ i, and Ardhamagadh¯ i (circa ¯ change. 600 BC 200 AD), followed by the Magadh¯ i − The paper is organized as follows: Sec. 2 intro- apabhramsha, and finally crystallizing to Bengali duces the problem of historical change affecting the (circa 10th century AD) (Chatterji, 1926). The ver- BVIs and presents a mathematical formulation of the bal inflections underwent a series of phonological same; Sec. 3 describes the MOGA model; Sec. 4 changes during the middle Bengali period (1200 - reports the experiments, observations and their in- 1800 AD), which gave rise to the several dialectal terpretations; Sec. 5 concludes the paper by sum- forms of Bengali, including the standard form – the marizing the contributions. In this paper, Bengali Standard Colloquial Bengali (SCB). th graphemes are represented in Roman script follow- The Bengali literature of the 19 century was ing the ITRANS notation (Chopde, 2001). Since written in the Classical Bengali dialect or the Bengali uses a phonemic orthography, the phonemes sadhubh¯ ash¯ a¯ that used the older verb forms and are also transcribed using ITRANS within two /s. drew heavily from the Sanskrit vocabulary, even though the forms had disappeared from the spoken th 2 The Problem dialects by 17 century. Here, we shall take the lib- erty to use the terms “classical forms” and “Classi- Bengali is an agglutinative language. There are cal Bengali” to refer to the dialectal forms of middle more than 150 different inflected forms of a single Bengali and not Classical Bengali of the 19th cen-

66 tury literature. Table 1 enlists some of the corre- APO Semantics sponding verb forms of classical Bengali and SCB. Del(p, LC, RC) p → φ/LC—RC Table 3 shows the derivation of some of the current Met(pipj, LC, RC) pipj → pjpi/LC—RC verb inﬂections of SCB from its classical counter- Asm(p, LC, RC) p → p0/LC—RC parts as reported in (Chatterji, 1926). Mut(p, p0, LC, RC) p → p0/LC—RC

2.1 Dialect Data Table 2: Semantics of the basic APOs in terms of Presently, there are several dialects of Bengali that rewrite rules. LC and RC are regular expressions vary mainly in terms of the verb inflections and in- specifying the left and right contexts respectively. p, 0 tonation, but rarely over syntax or semantics. We do p , pi and pj represent phonemes. not know of any previous study, during which the Rule APO Example Derivations different dialectal forms for BVI were collected and No. kar − iteChe kar − iten kar − iAChi systematically listed. Therefore, we have collected 1 Del(e, φ, Ch) kar − itChe NA NA 2 Del(t, φ, Ch) kar − iChe NA NA dialectal data for the following three modern dialects 3 Met(ri, φ, φ) kair − Che kair − ten kair − AChi of Bengali by enquiring the näive informants. 5 Mut(A, e, φ, Ch) NA NA kair-eChi 6 Asm(a, i, φ, φ) koir − Che koir − ten koir − eChi • Standard Colloquial Bengali (SCB) spoken in a 7 Del(i, o, φ) kor − Che kor − ten kor − eChi region around Kolkata, the capital of West Ben- Table 3: Derivations of the verb forms of SCB from gal, classical Bengali using APOs. “NA” means the rule • Agartala Colloquial Bengali (ACB) spoken in is not applicable for the form. See (Choudhury et and around Agartala, the capital of Tripura, and al., 2006a) for the complete list of APOs involved in the derivation of SCB and ACB forms • Sylheti, the dialect of the Sylhet region of Bangladesh. RC. Also, we do not consider epenthesis or inser- Some of the dialectal forms are listed in Table 1. tion as an APO, because epenthesis is not observed The scope of the current study is restricted to 28 in- for the case of the change affecting BVI. flected forms (12 present tense forms + 12 past tense The motivation behind defining APOs rather than forms + 4 forms of habitual past) of a single verb representing the change in terms of rewrite rules is root, i.e., kar. as follows. Rewrite rules are quite expressive and therefore, it is possible to represent complex phono- 2.2 Problem Formulation logical changes using a single rewrite rule. On the Choudhury et al. (2006a) has shown that a sequence other hand, APOs are simple phonological changes of simple phonological changes, which we shall that can be explained independently in terms of pho- call the Atomic Phonological Operators or APO for netic factors (Ohala, 1993). In fact, there are also short, when applied to the classical Bengali lexicon, computational models satisfactorily accounting for gives rise to the modern dialects. We conceive of cases of vowel deletion (Choudhury et al., 2004; four basic types of APOs, namely Del or deletion, Choudhury et al., 2006b) and assimilation (Dras et Met or metathesis, Asm or assimilation, and Mut al., 2003). or mutation. The complete specification of an APO Table 3 shows the derivation of the SCB verb includes specification of its type, the phoneme(s) forms from classical Bengali in terms of APOs. The that is(are) affected by the operation and the left and derivations are constructed based on the data pro- right context of application of the operator specified vided in (Chatterji, 1926). as regular expressions on phonemes. The semantics of the basic APOs in terms of rewrite rules are 2.3 Functional Explanation for Change of BVI shown in Table 2.2. Since Bengali features assim- Let Λ0 be the lexicon of classical Bengali verb ilation only with respect to vowel height, here we forms. Let Θ: θ1, θ2, ··· θr be a sequence of r shall interpret Asm(p, LC, RC) as the height as- APOs. Application of an APO on a lexicon implies similation of the vowel p in the context of LC or the application of the operator on every word of the

67 lexicon. The sequence of operators Θ, thus, repre- 3.1 Phenotype and Genotype sent a dialect obtained through the process of change We define the phenotype of a dialect d to be the lex- from Λ0, which can be represented as follows. icon of the dialect, Λd, consisting of the 28 inflected forms of the root verb kar. This choice of phenotype Θ(Λ0) = θr(··· θ2(θ1(Λ0)) ···) = Λd is justified because, at the end of the optimization process, we would like to obtain the Pareto-optimal The derivation of the dialect Λd from Λ0 can be con- dialects of Bengali and compare them with their real structed by following the APOs in the sequence of counterparts. their application. The genotype of a dialect d could also be defined We propose the following functional explanation as Λd, where the word forms are the genes. How- for the change of BVI. ever, for such a choice of genotype, crossover and A sequence of APOs, Θ is preferred if Θ(Λ0) has mutation lead to counter-intuitive results. For ex- some functional benefit over Λ0. Thus, the modern ample, mutation would affect only a single word in Bengali dialects are those, which have some func- the lexicon, which is against the regularity principle tional advantage over the classical dialect. of sound change (see Bhat (2001) for explanation). We would like to emphasize the word “some” in Similarly, exchanging a set of words between a pair the aforementioned statements, because the modern of lexica, as crossover would lead to, seems insensi- dialects are not better than the classical one (i.e., the ble. ancestor language) in an absolute sense. Rather, the Therefore, considering the basic properties of classical dialect is suboptimal compared to the mod- sound change as well as the genetic operators used ern dialects only with respect to “some” of the func- in MOGA, we define a chromosome (and thus the tional forces and is better than the them with respect genotype) as a sequence of APOs. The salient fea- to “some other” forces. Stated differently, we expect tures of the genotype are described below. both the classical as well as the modern dialects of • Gene: A gene is defined as an APO. Since in 3 Bengali to be Pareto-optimal with respect to the set order to implement the MOGA, every gene must be of functional forces. mapped to a number, we have chosen an 8-bit binary In order to validate the aforementioned hypoth- representation for a gene. This allows us to spec- esis, we carry out a multi-objective and multi- ify 256 distinct genes or APOs. However, for rea- constraint optimization over the possible dialectal sons described below, we use the first bit of a gene forms of Bengali, thereby obtaining the Pareto- to denote whether the gene (i.e., the APO) is active optimal set, which has been achieved through (the bit is set to 1) or not. Thus, we are left with MOGA. 128 distinct choices for APOs. Since the number of words in the lexicon is only 28, the APOs for Del, 3 The MOGA Model Asm and Met are limited, even after accounting for the various contexts in which an APO is applicable. Specification of a problem within the MOGA frame- Nevertheless, there are numerous choices for Mut. work requires the definition of the genotype, phe- To restrain the possible repertoire of APOs to 128, notype and genotype-to-phenotype mapping plus the we avoided any APO related to the mutation of con- objective functions and constraints. In this section, sonants. This allowed us to design a comprehensive we discuss the design choices explored for the prob- set of APOs that are applicable on the classical Ben- lem of BVI. gali lexicon and its derivatives. • Chromosome: A chromosome is a sequence of 3 Consider an optimization problem with n objective func- 15 genes. The number 15 has been arrived through tions f1 to fn, where we want to minimize all the objectives. Let S be the solution space, representing the set of all possible experimentation, where we have observed that in- solutions. A soulution sinS is said to be Pareto-optimal with re- creasing the length of a chromosome beyond 15 spect to the objective functions f1 to fn, if and only if there does 0 0 does not yield richer results for the current choice not exist any other solution s ∈ S such that fi(s ) ≤ fi(s) for 0 all 1 ≤ i ≤ n and fi(s ) < fi(s) for at least one i. of APOs and Λ0. Since the probability of any gene

68 of articulation, perceptual contrast and learnability, which can be expressed as functions or constraints. Several models have been proposed in the past for estimating the articulatory effort (Boersma (1998), Ch. 2, 5 and 7) and perceptual distance between phonemes and/or syllables (Boersma (1998), Ch. 3, 4 and 8). Nevertheless, as we are interested in modeling the effort and perceptual contrast of the whole lexicon rather than a syllable, we have chosen to work with simpler formulations of the objective functions. Due to paucity of space, we are not Figure 1: Schematic of genotype, phenotype and able to provide adequate details and justiﬁcation for genotype-to-phenotype mapping. the choices made.

3.2.1 fe: Articulatory Effort being switched off (i.e., the first bit being 0) is 0.5, Articulatory effort of a lexicon Λ is a positive real the expected number of active APOs on a chromo- number that gives an estimate of the effort required some with 15 genes is 7.5. It is interesting to note to articulate the words in Λ in some unit. If fe de- that this value is almost equal to the number of APOs notes the effort function, then required (7 to be precise) for derivation of the SCB 1 X verb forms. f (Λ) = f (w) (1) e |Λ| e • Genotype to phenotype mapping: Let for a given w∈Λ chromosome, the set of active APOs (whose first bit The term fe(w) depends on three parameters: 1) is 1) in sequence be θ1, θ2, ··· , θr. Then the pheno- the length of w in terms of phonemes, 2) the struc- type corresponding to this chromosome is the lex- ture of the syllables, and 3) the features of adjacent icon Λd = θr(··· θ2(θ1(Λ0)) ···). In other words, phonemes, as they control the effort spent in co- the phenotype is the lexicon obtained by successive articulation. We define fe(w) to be a weighted sum application of the active APOs on the chromosome of these three. on the lexicon of classical Bengali. The concepts of gene, chromosome and the map- fe(w) = α1fe1(w) + α2fe2(w) + α3fe3(w) (2) ping from genotype to the phenotype are illustrated where, α = 1, α = 1 and α = 0.1 are the relative in Fig. 3.1. It is easy to see that the regularity hy- 1 2 3 weights. pothesis regarding the sound change holds good for The value of f is simply the length of the word, the aforementioned choice of genotype. Further- e1 that is more, crossover in this context can be interpreted as f (w) = |w| (3) a shift in the course of language change. Similarly, e1 mutation of the first bit turns a gene on or off, and of Suppose ψ = σ1σ2 ··· σk is the usual syllabifica- the other bits changes the APO. Note that according tion of w, where the usual or optimal syllabification to this formulation, a chromosome not only models for Bengali is defined similar to that of Hindi as de- a dialect, but also the steps of its evolution from the scribed in (Choudhury et al., 2004). Then, fe2 is classical forms. defined as follows. k X 3.2 Objectives and Constraints fe2(w) = hr(σi) (4) Formulation of the objective functions and con- i=1 straints are crucial to the model, because the linguis- hr(σ) measures the hardness of the syllable σ and is tic plausibility, computational tractability and the re- a function of the syllable structure (i.e. the CV pat- sults of the model are overtly dependent on them. tern) of σ. The values of hr(σ) for different syllable We shall define here three basic objectives of ease structures are taken from (Choudhury et al., 2004).

69 Since vowel height assimilation is the primary al., 2004), the PCs are defined at the level of sylla- co-articulation phenomenon observed across the di- ble onsets and codas and therefore, syllabification is alects of Bengali, we define fe3 so as to model a preprocessing step before evaluation of Cp. only the effort required due to the difference in the 3.2.4 f and C : Regularity heights of the adjacent vowels. r r Although learnability is a complex notion, one Let there be n vowels in w represented by Vi, can safely equate the learnability of a system to the where 1 ≤ i ≤ n. Then fe3 is defined by the following equation. regularity of the patterns within the system. In fact, in the context of morphology, it has been observed n−1 that the so called learning bottleneck has a regular- X fe3(w) = |ht(Vi) − ht(Vi+1)| (5) izing effect on the morphological structures, thereby i=1 leaving out only the most frequently used roots to behave irregularly (Hare and Elman, 1995; Kirby, The function ht(V ) is the tongue height associ- i 2001). ated with the vowel V . The value of the function i In the present context, we define the regularity ht(V ) for the vowels /A/, /a/, /E/ /o/, /e/, /i/ i of the verb forms in a lexicon as the predictability and /u/ are 0, 1, 1, 2, 2, 3, and 3 respectively. Note of the inflectional suffix on the basis of the mor- that the values are indicative of the ordering of the phological attributes. Brighton et al. (2005) discuss vowels with respect to tongue height, and do not re- the use of Pearson correlation between phonologi- flect the absolute height of the tongue in any sense. cal edit distance and semantic/morphological ham-

3.2.2 fd and Cd: Acoustic Distinctiveness ming distance measures as a metric for learnabil- We define the acoustic distinctiveness between ity. On a similar note, we define the regularity function fr as follows. For two words wi, wj ∈ Λ, the two words wi and wj as the edit distance between (dis)similarity between them is given by ed(wi, wj). them, which is denoted as ed(wi, wj). The cost of insertion and deletion of any phoneme is assumed to Let ma(wi, wj) be the number of morphological at- be 1; the cost of substitution of a vowel (consonant) tributes shared by wi and wj. We define the reg- for a vowel (consonant) is also 1, whereas that of a ularity of Λ, fr(Λ), as the Pearson correlation co- vowel (consonant) for a consonant (vowel) is 2, ir- efficient between ed(wi, wj) and ma(wi, wj) for respective of the phonemes being compared. Since all pairs of words in Λ. Note that for a regular languages are expected to increase the acoustic dis- lexicon, ed(wi, wj) decreases with an increase in tinctiveness between the words, we define a mini- ma(wi, wj). Therefore, fr(Λ) is negative for a regular lexicon and 0 or positive for an irregular one. mizing objective function fd over a lexicon Λ as the sum of the inverse of the edit distance between all In other words, fr(Λ) is also a minimizing objective pair of words in Λ. function. We also define a regularity constraint Cr, such 2 X that a lexicon Λ violates Cr if fr(Λ) > −0.8. f (Λ) = ed(w , w )−1 (6) d |Λ|(|Λ| − 1) i j ij,i6=j 4 Experiments and Observations

If for any pair of words wi and wj, ed(wi, wj) = In order to implement the MOGA model, we have −1 0, we redeﬁne ed(wi, wj) as 20 (a large penalty). used the Non-dominated Sorting GA-II or NSGA- We say that a lexicon Λ violates the acoustic dis- II (Deb et al., 2002), which is a multi-objective, tinctiveness constraint Cd, if there are more than two multi-constraint elitist GA. Different MOGA mod- pairs of words in Λ, which are identical. els have been incrementally constructed by intro- ducing the different objectives and constraints. The 3.2.3 Cp: Phonotactic constraints motivation behind the incorporation of a new ob- A lexicon Λ is said to violate the constraint Cp if jective or constraint comes from the observations any of the words in Λ violates the phonotactic con- made on the emergent dialects of the previous mod- straints of Bengali. As described in (Choudhury et els. For instance, with two objectives fe and fd,

70 and no constraints, we obtain dialects that violate phonotactic constraints or/and are highly irregular. One such example of an emergent dialect4 is Λ = { kor, kara, kar, kore, korea, kore, karA, karAa, karA, *korAlm, *korl, korla, *koreAlm, korel, ko- rela, *karAlm, karAl, karAla }. The * marked forms violate the phonotactic constraints. Also note that the forms are quite indistinct or close to each other. These observations led to the formulation of the constraints Cp and Cd. Through a series of similar experiments, finally we arrived at a model, where we could observe the emergence of dialects, some of which closely resemble the real dialects and others also seem linguisti- Figure 2: The Pareto-optimal front. The gray trian- cally plausible. In this final model, there are two gles (light blue in colored version available online) show the position of the real dialects: 0 – Classi- objectives, fe and fd, and 3 constraints, Cp, Cd and cal Bengali, 1 – SCB, 2 – ACB, 3 – Sylheti. The Cr. Table 4 lists the corresponding forms of some of the emergent dialects, whose real counterparts are top-most dot in the plot corresponds to the emergent shown in Table 1. dialect D0 shown in Table 4. Fig. 2 shows the Pareto-optimal front obtained for the aforementioned model after 500 generations, repertoire of APOs is 5.6. Second, at fe(Λ) = 6, with a population size of 1000. Since the objectives the slope of the front, i.e. dfd/dfe, is approximately 2 2 are minimizing in nature, the area on the plot below −2, and the second derivative d fd/dfe is around and left of the Pareto-optimal front represents im- 20. This implies that there is sharp transition be- possible languages, whereas the area to the right and tween the vertical and horizontal limbs at around top of the curve pertains to unstable or suboptimal fe(Λ) = 6. languages. It is interesting to note that the four real Interestingly, all the real dialects studied here lie dialects lie very close to the Pareto-optimal front. In on the horizontal limb of the Pareto-optimal front fact, ACB and SCB lie on the front, whereas clas- (i.e., fe(Λ) ≥ 6), classical Bengali being placed at sical Bengali and Sylheti appears to be slightly sub- the extreme right. We also note the negative corre- optimal. Nevertheless, one should always be aware lation between the value of fe for the real dialects, that impossibility and suboptimality are to be inter- and the number of APOs invoked during derivation preted in the context of the model and any general- of these dialects from classical Bengali. These facts ization or extrapolation of these concepts for the real together imply that the natural direction of language languages is controversial and better avoided. change in the case of BVIs has been along the hor- Several inferences can be drawn from the exper- izontal limb of the Pareto-optimal front, leading to iments with the MOGA models. We have observed the formation of dialects with higher and higher ar- that the Pareto-optimal fronts for all the MOGA ticulatory ease. Among the four dialects, SCB has Models look like rectangular hyperbola with a hori- the minimum value for fe(Λ) and it is positioned on zontal and vertical limb; the specific curve of Fig. 2 the horizontal limb of the front just before the begin- satisfies the equation: ning of the vertical limb. Therefore, it is natural to ask whether there are f (Λ)0.3(f (Λ) − 5.6) = 0.26 (7) d e any real dialects of modern Bengali that lie on the Several interesting facts, can be inferred from the vertical limb of the Pareto-optimal front; and if not, above equation. First, the minimum value of fe un- what may be the possible reasons behind their inex- der the constraints Cr and Cd, and for the given istence? In the absence of any comprehensive col- 4Due to space constraints, we intentionally omit the corre- lection of Bengali dialects, we do not have a clear sponding classical forms. answer to the above questions. Nevertheless, it may

71 Attributes D0 D1 D2 D3 for the verbs, Hindi makes a distinction between the PrS1 kar kor kori kori genders (masculine and feminine) as well as num- PrS2 kara kora kora kora PrS3 kare kore kore korA bers (but only singular and plural), and Bengali has PrSF karen koren koren koren markers for neither gender nor number. Since both Hindi and Bengali are offshoots of Vedic Sanskrit, PrC1 kartA karChi karteChi kairteChi presumably the differences between the phonologi- PrC2 kartAa karCha karteCha kairteCha cal structure of the verb inflections of these two lan- PrC3 kartAe karChe karteChe kairteChA PrCF kartAen karChen karteChen kairteChen guages must have also been affected by the loss or addition of morphological attributes. It would be in- PrP1 karA korChi koriChi koriChAi teresting to study the precise nature of the interac- PrP2 karAa korCha koriCha koriACha tion between the inflections and attributes within the PrP3 karAe korChe koriChe koriAChA PrPF karAen korChen koriChen koriAChen current computational framework, which we deem to be a future extension of this work. Table 4: Examples of emergent dialects in the MOGA model. Note that the dialects D1, D2 and 5 Conclusions D3 resemble SCB, ACB and Sylheti, whereas D0 seems to be linguistically implausible. For legends, In this paper, we have described a MOGA based refer to Table 1 model for the morpho-phonological change of BVIs. The salient contributions of the work include: (1) the conception of the genotype as a sequence of APOs, be worthwhile to analyze the emergent dialects of whereby we have been able to capture not only the the MOGA models that lie on the vertical limb. We emergent dialects, but also the path towards their have observed that the vertical limb consists of di- emergence, and (2) a plausible functional explana- alects similar to D0 – the one shown in the first tion for the morpho-phonological changes affecting column of Table 4. Besides poor distinctiveness, the BVIs. Nevertheless, the results of the experi- D0 also features a large number of diphthongs that ments with the MOGA models must be interpreted might result in poorer perception or higher effort of with caution. This is because, the results are very articulation of the forms. Thus, in order to eliminate much dependent on the formulation of the fitness the emergence of such seemingly implausible cases functions and the choice of the constraints. The set in the model, the formulations of the objectives fe of APOs in the repertoire also play a major role in and fd require further refinements. shaping the Pareto-optimal front of the model. Similarly, it can also be argued that the structure Before we conclude, we would like to re- of the whole lexicon, which has not been modeled emphasize that the model proposed here is a func- here, has also a strong effect on the BVIs. This is tional one, and it does not tell us how the dialects because even though we have measured the acous- of Bengali have self-organized themselves to strike tic distinctiveness fd with respect to the 28 inflected a balance between the functional pressures, if at all forms of a single verb root kar, ideally fd should be this had been the case. The evolutionary algorithm computed with respect to the entire lexicon. Thus, (i.e., MOGA) has been used here as a tool for op- change in other lexical items (borrowing or extinc- timization, and has no relevance to the evolution of tion of words or change in the phonological struc- the dialects as such. Nevertheless, if it is possible tures) can trigger or restrain an event of change in to provide linguistically grounded accounts of the the BVIs. sources of variation and the process of selection, Furthermore, merging, extinction or appearence then the MOGA model could qualify as an evolu- of morphological attributes can also have significant tionary explanation of language change as well. Al- effects on the phonological change of inflections. It though such models have been proposed in the liter- is interesting to note that while Vedic Sanskrit had ature (Croft, 2000; Baxter et al., 2006), the fact, that different morphological markers for three numbers global optimization can be an outcome of local inter- (singular, dual and plural) and no gender markers actions between the speakers (e.g., Kirby (1999), de

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