A Grammatical View of Language Evolution

Gemma Bel-Enguix

, Henning Christiansen

and M. Dolores Jim´enez-L´opez

Research Group on Mathematical Linguistics, Universitat Rovira i Virgili

Avd. Catalunya 35, 43002 Tarragona, Spain

Research Group on Programming, Logic and Intelligent Systems

Roskilde University, P.O.Box 260, DK-4000 Roskilde, Denmark

Abstract. Language evolves gradually through its use: over time, new forms

come into fashion and others become obsolete. While traditionally a grammar

provides a snapshot of an individual’s or a society’s linguistic competence at a

given point in time, our aim is to extend grammars to incorporate competences

related to evolution. This paper shows how language evolution can be modeled

using Adaptable Grammars, which may be deﬁned as logically based transfor-

mational grammars in which the grammar itself may be affected in a derivation

step.

1 Introduction

During the last decade, approaches to natural language have undergone a deep transfor-

mation thanks to a new interdisciplinary paradigm that integrates artiﬁcial intelligence,

physics, evolutionary biology and computer science [1,2]. Under such inﬂuences, a new

interest has arisen for diachronic change of natural language, based on the understand-

ing of language as a complex adaptive system [3] and evolutionary system [4]. This

interest is supported by computational models that provide simulations to understand

the dynamics of human language and its adaptation to the environment [5]. However,

grammatical and formal approaches, as we suggest in the present paper, are still to be

applied. The main problems approached in language evolution are the origins and emer-

gence of language [6], language acquisition [2], and language change [7]. Moreover, in

the broad area of formal languages, there exists from the sixties a growing interest in

grammatical inference or grammar induction [8, 9]. This is a specialized subﬁeld of

machine learning that deals with the learning of formal languages from a set of data.

Grammar induction refers, therefore, to the process of learning grammars and languages

from a given corpora. In order to solve a grammar induction problem we require, on one

hand, a teacher that provides data to a learner, and on the other hand, a learner that from

that data must identify the underlying language. In the ﬁeld of grammatical inference,

it is worth noting the contribution of [10], who introduces algorithms for inferring re-

versible languages from positive data, [11] who developed a grammar induction method

that produces stochastic context-free grammars, and [12] presenting an algorithm that

generates grammars from positive and negative examples in an incremental way; the

relation between this and our work is discussed in more details below.

Bel-Enguix G., Christiansen H. and Dolores Jiménez-López M..

A Grammatical View of Language Evolution.

DOI: 10.5220/0003309200570066

In Proceedings of the 1st International Workshop on AI Methods for Interdisciplinary Research in Language and Biology (BILC-2011), pages 57-66

ISBN: 978-989-8425-42-3

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

Our approach is related to both natural language evolution and grammatical infer-

ence. Roughly speaking, we search for a mechanism able to infer the grammar of a

system that is constantly changing. We apply a logically based transformational gram-

mar formalism in which the grammar itself may be affected in a derivation step. We

intend to model the linguistic competences of a silent listener having the reﬂective ca-

pability of being able to inspect and revise its competences according to current usages.

In contrast to some of the models mentioned above, it is not based on neither artiﬁcial

intelligence nor simulation of communicating agents. Instead we propose a strictly for-

mal approach to the problem of language evolution, showing how a grammar can adapt

to new words and ways of building phrases without any external means.

In order to reach this objective, we apply a formalism called Adaptable Grammars,

based on an earlier proposal of [13–15]. This grammar formalism was invented in the

1980ies, originally for describing phenomena in software systems and programming

languages. Later, it has been known under the name Christiansen grammars in work

by [16, 17]. It has been applied to formal linguistics only recently [18]. The work of [16]

have applied these grammars for grammatical, evolutionary programming; the authors

motivate their approach by the observation that with such grammars they can do with

shorter derivations of target programs.

In [18], such grammars are demonstrated to capture standard non-context-free lan-

guages used in the literature, that represent the central natural language properties of

reduplication, crossed dependencies, and multiple agreements. In the present work, we

take this a step further considering language evolution. A surprisingly simple imple-

mentation of Adaptable Grammars in Prolog was shown in [18], which, with a few

extensions, have been used for the experiments shown in the present paper.

The Adaptive Grammars of the present paper, explained as extensions to Deﬁnite

Clause Grammars (DCGs) [19], are inherently related to Abductive Logic Program-

ming (ALP); see, e.g., [21] for an overview. Normally, the process of ﬁnding new rules

(logical, grammatical, ...) is associated with induction and, in our context, Inductive

Logic Programming (ILP); see, e.g., [22] for overview. ILP differs from ALP by con-

sidering a larger set of observations, and use powerful machine learning techniques,

including generalization steps and statistics to produce rules that cover as many cases

as possible. The work by [12] can be seen as an algorithmic counterpart to our work.

They describe an algorithm for induction of context free grammars which is incremen-

tal in the sense that it takes one sample of a time and presents a well-deﬁned grammar

after each step. It is explained as an extension of the classical CYK parsing algorithm

that it works bottom-up in a breadth-ﬁrst way. In case it gives up, an induction step

inspects the store of unreduced items to suggest reductions which then are collected

to new grammar rules. Obviously such methods must be tested out for any practical

application of Adaptable Grammars for larger corpora, although they have not, to our

knowledge, been tested for natural language corpora.

In section 2 we give an introduction to adaptable grammars and indicate the fun-

damental principles for how they may be used for describing language evolution. Sec-

tion 3 introduces additional notation, which is applied in section 4 that demonstrates

grammars for evolution in simpliﬁed natural language setting. Finally, section 5 gives

some concluding remarks and ideas for future work.

2 Adaptable Grammars or Christiansen Grammars

A grammar formalism is adaptablewhen it allows a grammar to mutate dynamically ac-

cording to context. Thus, the selection of available grammar rules may change through-

out a discourse and that the formalism must provide a way to specify these grammar

changes. Intuitively, the notion of discourse may refer also to linguistic samples col-

lected over centuries, or even longer when language development is seen in a biological

evolution perspective.We may compare with DCGswhich encode context in dynami-

cally changing attributes that determine the set of available context-free instances of a

ﬁxed set of parameterized rules. Adaptable grammars go one step further, treating the

current grammar itself as an attribute that can be elaborated in arbitrary ways.

We have developedan adaptable version of the Prolog based DCGs, which give sev-

eral advantages: they provide a direct representation of grammar rules as data and an-

ticipate straightforward implementations based on well-understood meta-interpretation

techniques (see, e.g., [20]). The terminology of logic programs and ﬁrst-order logic is

assumed, including logical variables, terms and their (ground) instances. We use the

notion of a denotation function [[−]], which is a partial mapping from ground terms into

grammars. At this level, we do not need to specify the actual denotation function. The

formalism includes also a reiﬁcation of syntactic derivation; this is merely a practical

device which is not essential for grammar adaptation.

Deﬁnition 1. An adaptable grammar is a quintuple hΣ, N, Π, [[−]], Ri where Σ is a

ﬁnite alphabet of terminals, N a set of nonterminals which are function symbols of arity

at least 1, Π a logic program, [[−]] the denotation function, and R is a set of grammar

rules (below). As a convenient usage, the notion of a nonterminal applies also for a

term whose top symbol belongs to N.

A nonterminal has a distinguished argument called its grammar argument. We dis-

tinguish reﬂexive predicates of the forms

deriv

(N, S) and

nderiv

(N, S), where N is a

nonterminal and S a term. A grammar rule is of the form lhs → rhs, where lhs is a

nonterminal and rhs a ﬁnite sequence of terminal and nonterminal symbols, reﬂexive

predicates, and ﬁrst-order predicates of Π.

The meaning of

deriv

(N, S) (deﬁnition 2 below) is that a string S is derivable from

the nonterminal N;

nderiv

(N, S) represents the opposite, namely that no derivation is

possible. The use of an explicit denotation function eliminates any potential confusion

of variables at the different levels [20]. The program component Π is included for con-

venience only, as it can be embedded as a set of grammar rules producing the empty

string. For clarity, the grammar argument is moved outside the standard parentheses

and attach by a hyphen, e.g., instead of n(x, y, G), we write n(x, y)-G when n is a

nonterminal of arity 3 with grammar argument G. The reﬂexive predicates represent

a version of the general derivation relation, limited to a non-adaptable fragment. To

this end, we deﬁne a static rule as one without reﬂexive predicates and in which all

grammar arguments coincide with the same logical variable e.g., p-G → q-G, but not

p-G

→ {t(G

, G

)}, q-G

. The static restriction of a grammar G, written σ(G), co-

incides with G except that any non-static rule is removed. The following simultaneous

deﬁnition of derivation and meaning of reﬂexive predicates is sound as the latter are

characterized by derivation in statically restricted grammars that do not it turn contain

reﬂexive predicates.

Deﬁnition 2. A production instance of rule r of hΣ, N, Π, [[−]], Ri is found by

1. selecting a ground instance r

′

of r in which any reﬂexive predicate is satisﬁed

(def. below) and Π ⊢ A for any other logical predicate A in r

′

2. removing any such predicates from r

′

, so that only grammar symbols remain.

Whenever α(N-G)γ is a sequence of ground grammar symbols and N -G → β a pro-

duction instance of a rule in [[G]], the following derivation step applies,

α(N-G)γ ⇒ αβγ.

The derivation relation ⇒

∗

refers to the reﬂexive, transitive closure of ⇒.

A ground reﬂexive predicate

deriv

(A-G, S) is satisﬁed whenever σ[[G]] ⇒

∗

nderiv

(A-G, S) is satisﬁed when

deriv

(A-G, S) is not satisﬁed. The language given

by a ground nonterminal N-G is the set of terminal strings S with N -G ⇒

∗

The available implementation in Prolog can analyze text in terms of queries posed as

follows, where G represents a grammar,

?- parse(N(Atts)-G,text).

The obtained answer may be either 1) a substitution for variables in Atts under which

the derivation succeeds, or 2) “no” if parsing is not possible.

Example 1. General grammar induction is not the main focus of the present paper, but

we can use it to illustrate the power of adaptable grammars. Grammar induction is the

problem of ﬁnding a good grammar that can recognize a given discourse. This can be

speciﬁed in terms of an adaptable grammar as shown in ﬁgure 1. The predicate good-

grammar speciﬁes a class of grammars in which the induced grammar is to be found.

Thus the rule speciﬁes that variable G

new

should be instantiated to a grammar that

makes it possible to parse the given input as discourse.

hΣ, N

, Π

, [[−]], R

i, where

= {induce/2}

= {good-grammar(G):- . . . , . . .}

= {induce(G

new

)-G →

{good-grammar(G

new

)},

discourse-G

new

}

Fig.1. Grammar induction formulated as an adaptable grammar.

We do not intend to present an implementation capable of handling example 1; this

would require more advanced techniques (e.g., of Inductive Logic Programming) that

those we introduce below for an incremental adaptation. For grammars with explicit

synthesis of new grammar rules, it is straightforward to extend a general DCG parser

written in Prolog for adaptable grammars, cf. [18]; the following “constructive” gram-

mar represents the essence of our approach to characterize language evolution.

Example 2. Consider sequences of letters in which the letter a is the only one known

by the initial grammar. Instead of failing for an unknown letter, a new rule should

be added. Let Gram

= hΣ

, N

, ∅, [[−]]

, R

i be a grammar with Σ = {a, b, . . .},

= {d/2, s/2} (for discourse and sentence) and R

the rules shown in ﬁgure 2; the

denotation function [[−]]

represents a grammar as a list of terms for each rule; each

symbol stands for itself except variables where

X denotes variable X. The reﬂexive

predicate in the last rule ensures that new rules are only considered when necessary.

The answer to a query ?- parse(d(G)-Gram

, [a, b , c]) should provide a value for

G that denotes a grammar whose static restriction is isomorphic to a CFG for sequences

of exactly the letters a, b and c.

d(G)-G → [ ]

d(G

)-G → s(G

)-G, d(G

)-G

s(G)-G → [a]

s(G

)-G → [X], nderiv(s( )-G, [X]), {G

= [(s(

G))-

G → [X])|G]}

Fig.2. The rules of an adaptable grammar for a single letter sentence language.

3 Adaptable Grammars for Language Evolution

A specialized notation for Adaptable Grammars has been implemented in Prolog for

experiments with language evolution; the implementation is a straightforward extension

of the 10 line Prolog program given in [18] and is not described further.

Grammars are given a more conventional appearance, having the grammars argu-

ments implicit, so that language changes appear as side-effect on a “current” grammar.

A weighting of each rule is introduced for measuring how recently it has been applied.

With this we can model both how new forms come into fashion and obsolete forms dis-

appear from the language user’s memory. Furthermore, the grammar notation allows to

indicate which syntactic categories can be changed and which can be used in the right

hand side of new rules. The new notation is introduced by the following example.

(structural categories --d) //

(lexical categories ++s) //

[ (d --> []):null,

(d --> s,

forget, d):null,

(s --> [a]):1,

(s --> [X], d \=> [X], +(s-->[X]):1):null ]

Fig.3. Adaptable grammar for a single letter sentence with rule weights.

Example 3. The grammar of ﬁgure 3 is identical to the one of example 2, with the dif-

ference that some rules that have not been used, may be removed. A grammar has three

parts, structural and lexical nonterminals and the set of rules. The distinction between

structural and lexical categories (or nonterminals) may be utilized in more advanced

patterns for creation of new rules and has no inﬂuence for this grammar. The pluses and

minuses in front of a nonterminal determine how it may be used in when forming new

rules. The ﬁrst sign determines whether it can appear in the left-hand side of new rules,

i.e., whether or not this category can be extended with new rules; the second whether

the nonterminal can be applied in right-hand sides in new rules. The “:n” is the current

weight assigned to each rule; the special value null indicates that the given rule is not

degraded by not being used. The

forget operation degrades each rule (with non null

weight) multiplying its weight by 0.99, and deleting those with a weight < 0.5.

New

rules are added to the current grammar using the preﬁx plus operator as shown in the

last rule. Finally, reﬂexive predicates

deriv

and

nderiv

are represented by the operators

=> and \=>, referring to (non-) derivation in the current grammar.

When the grammar of example 3 is applied for the discourse [a,b], the ﬁnal grammar

has rules for sentences ‘a’ and ‘b’; for [a,b,c,b,c,. . .,b,c] with ‘b,c’ repeated

sufﬁciently many times, there will be rules ‘b’ and ‘c’ for but not for ‘a’ .

For the examples below, the distinction between lexical and structural categories is

made as follows. A lexical category C allows only rules of the form C-->[Terminal]

that we refer to as lexical rules. Structural categories can have rules whose right-hand

side is composed of one or more nonterminals.

4 Modeling Language Evolution by Adaptable Grammars

Example 3 above demonstrated the overall principles of how a grammar may adapt

to current usages. Here we show two linguistically inspired examples. The grammar

shown in ﬁgure 4 shows how new rules can created be by a naive oracle to cope with

new usages in very simple Catalan sentences. The period symbol serves here as a unique

demarkation of where a sentence can end, and thus reduces the search space drastically.

We allow, for simplicity of writing, that structural rules of the initial grammar may

contain terminals (such as “.”), although this is not allowed in automatically generated

rules. Nonterminal d stands for discourse, p for period s for sentence and to period

for arbitrary sequences until and including the period symbol. The device

new rules

generates rules in a nondeterministic fashion according to the following heuristics.

– A ﬁrst attempt is made adding lexical rules only.

– If this is not sufﬁcient, combinations of structural and (perhaps) lexical rules are

tried out.

– Only a limited number of rules can be introduced in one go and only a limited

number of nonterminals are allowed in the right-hand side of a structural rule; here

both are arbitrarily limited to a maximum of two.

– Grammar extensions are not allowed to introduce left-recursion.

– A rule already in the grammar will not be created again.

– Any word belongs to at most one lexical category (admittedly too simple for real-

istic applications).

The indicated degradation factor and threshold are arbitrary and should of course be reﬁned

for any practical applications.

At the level of implementation, our Prolog implementation works in a generate-and-test man-

ner,

new rules generating candidates until one is accepted by p=>Tokens.

Due the inherent top-down parsing strategy, a left recursive grammar will lead to inﬁnite loops.

(structural categories --d, +-s, ++np, ++vp) //

(lexical categories ++a, ++pr, ++n, ++v) //

[ ( np --> pr):1,

( np --> a, n):1,

( pr --> [ella]):1,

( a --> [una]):1,

( n --> [poma]):1,

( v --> [menja]):1,

( vp --> v):1,

( vp --> v, np):1,

( s --> np, vp):1,

( d --> p,d):null,

( d --> []):null,

( p --> s,[’.’],

forget):null,

( p --> to_period(Tokens), period \=> Tokens,

new_rules(Tokens,R), +R, p => Tokens):null,

(to_period([T|Ts]) --> [T], {T \= ’.’}, to_period(Ts)):null,

(to_period([’.’]) --> [’.’] ):null]

Fig.4. An adaptable grammar for a simple language evolution problem.

Sentence(s) New rule(s)

(1) ella menja una poma. (no new rules)

(2) blabla menja una poma. pr-->[blabla]

(3) la blabla menja una poma. a-->[la]

n-->[blabla]

(4) menja una poma. s-->vp

(5) ella una poma menja. vp-->np,vp

(6) menja. s-->vp

(7) beu. s-->a

a-->[beu]

(8) menja. beu. s-->vp

v-->[beu]

Fig.5. Sample sentences and discourse plus the rules created to accommodation.

In the section for future work below, we discuss possible improvements of this strategy.

Figure 5 shows the new rules that are created for sample sentences that contain new

words and usages. Example (1) illustrates that no rules are generated when the existing

ones are sufﬁcient; (2–4) shows examples of new usages that are accommodated by

means of the rules that we might expect; in (5), a new structural rule is created, which

may or may not be the desired one; in (6), the perfect rule for a new type of sentences

is created, whereas in (7), a new sort of sentence consisting of one new word gener-

ates some unnatural rules. We may relate the problem in (7) to the observation that any

competent and reﬂexive language user may have difﬁculties when too many novelties

are introduced at the same time; here both a new word and new sentence form is intro-

duced in a one word sentence. Sample (8) is perhaps the most interesting: it analyzes a

discourse consisting of two sentences, the ﬁrst one shows a new sentence form that is

accommodated by the rule s-->vp, which is feasible as menja is known to be a verb;

in the next sentence this rule is applied when accommodating the new word beu which

is now classiﬁed in an intuitively correct way.

For investigating the long-term behavior of the suggested adaptation mechanism,

an artiﬁcial corpus of 300 sentences has been generated in a probabilistic way from

two grammars, one (a) for simplistic English sentences and another (b) for a kind

of Yoda-like German. In the beginning of the corpus, only rules from grammar (a)

can be used, and gradually rules of (b) sneaks and replaces (a) via changing proba-

bilities so that only rules of (b) are used at the end. For example, grammar (a) al-

lows sentences such as [peter,and, mary,likes,pluto], grammar (b) for

example [peter,und,mary,pluto,liebst].

Midway, we ﬁnd hybrids such as

[peter,und,mary,liebst,pluto,and,mary]and [pluto,peter,and,

mary,liebst]Grammar (a) is then given as Adaptable Grammar; ﬁgure 6 shows the

language speciﬁc rules, and the those for periods, p, and to period are as in ﬁgure 4;

the lexical category of proper names pnare deﬁned to be ﬁxed throughout the discourse.

The ﬁnal grammar resulting from the successive adaptations is shown in ﬁgure 7.

s --> np,vp vp --> v,np pn --> [mary]

np --> pn vp --> v pn --> [pluto]

np --> pn,more_np con --> [and] v --> [eats]

more_np --> con,np pn --> [peter] v --> [likes]

Fig.6. Simplistic English grammar prior to adaptation.

s --> np,vp vp --> np,vp pn --> [mary]

np --> pn vp --> v pn --> [pluto]

np --> pn,more_np con --> [und] v --> [liebst]

more_np --> con,np pn --> [peter] v --> [isst]

Fig.7. The result of adapting the grammar of ﬁg. 6 via 300 sentences to Simplistic Yoda-like

German.

The verbs and the conjunctions have been replaced by German ones as expected,

and the change of order of object and verb is accommodated by the replacement of

vp-->v,npby vp-->np,vp. The last one of these rules is intuitively not the desired

one as it is too general; the best rule would, of course, be vp-->np,v.

5 Conclusions and Future Work

Language evolution is an aspect of natural language that is especially difﬁcult to model

by means of formal grammars. We have approached it by adaptable grammars, that can

evolve during the processing and modify their own rules, changing gradually in order

to adapt themselves to the evolving language.

If the main ideas collected here are shown to be expressive enough to be developed,

then a new system should be designed taking into account many aspects that have been

dismissed up to now, in order to approach language evolution in a more realistic way.

We characterize language evolution from the viewpoint of a passive listener, but it seems

As it appears, we ignore inﬂection for singular and plural; this is, however, trivial to add.

possible to apply these ideas also in the setting of communicating agents. An agent

may test a proposed grammar extension by generating sentences that are presented to

other agents for evaluation (a pattern often observed between children and parents). The

multi-agent perspective may also be used to model how different languages develop and

inﬂuence each other over time.

Summing up, the principle of having the grammar dynamically modifying or adapt-

ing itself along a discourse may be seen as a universal mechanism that may be incorpo-

rated in other grammatical frameworks as well. The advantage is that original and novel

language constructs are represented in an equal manner so that, at any stage, the current

grammar may be read out. In most traditional grammar formalisms, that are capable of

expressing some context-dependencies, this need to be modeled by highly over-general

rules whose application is controlled by an encoding of the linguistic context.

We are considering to improvethe adapt-to-one-sentence-at-a-timeprinciple by giv-

ing preference to least general rules when adapting to a single sentence, complemented

by a generalization step that groups often used rules into a more general rule when pos-

sible and judged suitable. It will also be interesting to apply the principle of Adaptable

Grammars to see if it can reveal new bits of knowledge of how different languages may

descent from each other or inﬂuence each other. There may be other and much faster

evolution processes that also may be interesting to characterize, for example to trace the

spreading of topics in electronic and social networks.

Acknowledgements

This work is supported by the Spanish Ministry of Science and Education, project

MTM2007-63422, and the NABIIT committee under the Danish Strategic Research

Council, project “Logic-statistic modelling and analysis of biological sequence data”.

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