agreement mapping system approach to...

Journal of Language and Linguistics Vol. 3 No. 1 2004 ISSN 1475 - 8989

Agreement Mapping System Approach to Language

László DrienkóELTE University, Budapest

0. Abstract

The most fundamental idea behind generative linguistics – as evident from the very beginning (see Chomsky (1957)) – is closely connected with the basic property of natural languages that longer sequences of linguistic elements can behave like shorter sequences, or, in actuality, like a single element. This is trivially expressed in the form of production rules of generative grammars. Rule ‘A B C’ reflects that the linguistic behaviour of a sequence of elements (words) representable as ‘B C’ is similar to the behaviour of a single element represented as ‘A’. In other words, ‘B C’ can be substituted for ‘A’. Thus the key idea behind generative linguistics is SUBSTITUTION.

Nevertheless, there is another property of NLs which, we propose, seems to be equally important. It is related to the capacity of NLs to express correlations of linguistic elements and to encode information through such correlations. We refer to this capacity as AGREEMENT, and to such linguistic correlations as agreement relations. The notion of agreement lends itself naturally not only to conjugation or inflection paradigms but – we believe – many phenomena in linguistics –syntax, phonology , or morphology - can be interpreted in terms of it. Our approach does not hinge on ‘classical’ notions of generative grammars, thus non-regular or non-context-free cases such as e.g. cross-serial dependencies (Shieber, 1985), Bambara vocabulary (Culy, 1985), vowel harmonies, or phenomena in Arabic morphology can be accounted for by using the same framework. Our model incorporates a reconstruction mechanism to handle unidentified input.

In this paper we give a formal definition of our mapping system and relate it to such notions as perception-production, competence-performance, learning, implementation, parsing, grammaticality judgements, openness of language. To demonstrate the usability of the model, we apply it to the problematic cases named above.

1. Introduction

The most fundamental idea behind generative linguistics – as evident from the very beginning

(see Chomsky (1957)) – is closely connected with the basic property of natural languages that

longer sequences of linguistic elements can behave like shorter sequences, or, in actuality,

like a single element. This is trivially expressed in the form of production rules of generative

grammars. Rule ‘A B C’ reflects that the linguistic behaviour of a sequence of elements

(words) representable as ‘B C’ is quite similar to the behaviour of a single element

represented as ‘A’. In other words, ‘B C’ can be substituted for ‘A’. Thus the key idea behind

generative linguistics is SUBSTITUTION.

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Nevertheless, there is another property of NLs which, we propose, seems to be equally

important. It is related to the capacity of NLs to express correlations of linguistic elements

and to encode information through such correlations. We refer to this capacity as

AGREEMENT, and to such linguistic correlations as agreement relations.

In the following part of Section 1 we outline our approach. In section 2 the model will be

applied to ‘problematic’ issues like cross-serial dependency, Bambara vocabulary, Arabic

morphology, and vowel harmony.

1.1 Agreement relations

Most agreement relations are expressed morphologically. Consider e.g. the Russian sentence

in (1.1):

(1.1) Krasivaya d’evushka rabotayetbeautiful-FEM-NOM girl-FEM-NOM work-PRES-3rd-singThe/a beautiful girl works/is_working

The linguistic correlation of the adjective ‘krasivaya’ and the noun ‘d’evushka’ is expressed

through the shared feminine-nominative feature.

However, there may be correlation between elements which does not seem to have explicit

manifestation. In (1.2),

(1.2) The beautiful girl works,

no morphologically expressed correlation can be detected between the adjective and the

noun. Then, we may either say that the adjective and the noun share a nominative feature

represented by zero morphemes, or we may posit that the adjective-noun correlation is built

into the sequence configurationally, i.e., the environment for the adjective determines that it

must be the modifier of the noun. Thus it seems reasonable to infer that configurationality and

explicit agreement conditions should both be incorporated into our agreement model.

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Note how the notions ‘substitution’ and ‘agreement’ relate to each other. The right-hand

side of any production rule can be thought of as being a configurational agreement relation.

Intuitively, the left-hand side gives non-configurational information on the agreement relation

on the right. More specifically, consider rules (1.3) - (1.4)

(1.3) A B C(1.4) A B E D

We can say that there is a relationship between B and C in (1.3) characterised, on the one

hand, by the very fact that B and C can somehow belong together (and in the given order),

and, on the other hand, by the fact that, linked to each other, they can be substituted for

element A. The difference between (1.3) and (1.4) is that different elements are linked

together on the right-hand side, i.e they differ in configurational properties. The similarity is

that both right-hand sides can substitute for A, i.e. (1.3) and (1.4) share a feature related to

substitution properties.

Using agreement-relation terminology, we will say that elements B, C, D, and E share a

feature, or attribute, – say, S_FOR – whose value is the same for these elements, i.e.

B: S_FOR = A C: S_FOR = A D: S_FOR = A E: S_FOR = A.

Thus, a production rule can be viewed as an agreement relation: the right side of the rule

specifies which elements have to agree on a certain feature, the left side determines the value

for that feature.

The forgoing lines serve only demonstrative purposes. In our agreement approach we need

not make any reference to production rules.

1.2 Phrase, sentence: Pattern

Now we can say that any given phrase is representable as an agreement relation, i.e., as a

sequence of elements which satisfies the agreement conditions/constraints for that relation.

We shall call a sequence – or more generally, a set - of elements , together with its agreement

constraints a PATTERN. Graphically, we represent a pattern as in (1.5)

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(1.5) B C D

ATTR

where B, C, and D represent the elements which are configurationally linked together, and

the line connecting B and C indicates the explicit agreement constraint that B and C should

have the same values for attribute ATTR. For instance, the pattern for (1.3) could look like

(1.6).

(1.6)B C

S_FOR

The agreement constraint in (1.6) is satisfied if elements B and C have the necessary feature,

i.e.:

B: S_FOR = A C: S_FOR = A

The pattern for ‘krasivaya d’evushka’ may be given as (1.7).

(1.7)A N

S_FOR

and it is satisfied by elements

KRASIVAYA: CAT = A D’EVUSHKA: CAT = N S_FOR=N S_FOR=N

(1.7) corresponds to the production-rule interpretation of (1.3), namely, that the adjective-

noun sequence can be substituted for a noun. However, we may choose to abandon that

interpretation and refer to agreement features which are more convenient or useful. E.g., (1.7)

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does not express the requirement that the adjective and the noun must agree in gender and

case. Pattern (1.8) straightforwardly incorporates such an agreement relation, and it is still

possible to view the Adjective-Noun sequence as a single grammatical unit – a gender-case

complex.

(1.8)A N

GENDER CASE1

Insofar as a phrase can be viewed as made up by (configurational and explicit) agreement

relations, obviously, the grammaticality of a sentence will be determined by the agreement

relations holding for its ‘phrasal’ subparts. In (1.1), for instance, besides the A-N gender-case

correlation, person and number agreement is also required between the noun and the verb.

Consequently, a pattern for (1.1) should incorporate both agreement relations. Cf. (1.9).

(1.9)A N V

GENDER PERS CASE NUM

The agreement-approach counterpart of the generative sentence as made out of phrasal

CONSTITUENTS is the sentence pattern incorporating SUBPATTERNS.

1.3 The mapping system

After the forgoing introductory bunch of information in this section we set the scene for our

model more formally.

Basically, we consider the operation of the language faculty to be a mapping from input

elements to patterns.

1 Since there are two features/attributes that must be checked (GENDER , CASE), arguably, there are two agreement relations between the adjective and the noun. It is also possible to think of a single GENDER-CASE attribute whose values could be fem-nom, fem-acc,…masc-nom, masc-acc, …neutr-nom, neutr-acc,… (corresponding to the respective suffixes. Cf. our discussion of conjunctions of constraints below.)

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Patterns are ordered finite sets – sequences – of (symbolic or representational) elements..

Each pattern is associated with a finite (possibly empty) set of agreement

conditions/constraints. The set PAT of all patterns should be finite.

The set ALLREP of all possible representational elements is not finite. The finite number of

patterns is built out of elements in REPEL, a finite subset of ALLREP.The actual contents

of REPEL must be specified by linguistic research.

Input elements are simple attribute-value structures (AVS) consisting of a finite number of

attribute-value pairs. (1.10) exemplifies such an AVS.

(1.10)PHFORM dogCAT nPERS 3rdNUM sing

Known input elements are a finite set KEL. Elements in KEL are AVSs whose attribute

values are fully specified, i.e. each attribute has a value. (1.10), for instance, is a known

element.

Unknown input elements, i.e. AVSs with unspecified attribute values, constitute a nonfinite

set UEL.

Attributes constitute a non-finite set ALLATTR. The actual contents of ATTR, a subset of

ALLATTR to be used in an agreement model, must be specified by linguistic research. The

values for the attributes can also be arbitrarily chosen so that they best satisfy linguistic needs.

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The set ALLVAL of all attribute values need not be finite. Representational elements in

REPEL refer to elements of ATTR and VAL. VAL is a finite subset of ALLVAL. 2,3

The connection between attributes and their values is established by the mapping process.

Formally, algorithm VALA(a(X)) returns a value4 for attribute X of input element ‘a’ by

(1.11)

1. looking up the value for elements in KEL (known elements)2. selecting values that yield successful mapping for elements in UEL (unknown

elements)

Agreement constraints are finite sets of symbolic representations of requirements for

agreement relations. Basically, they have three parts. Cf. (1.12).

(1.12)

1 3 4 PERS FIRST-TO-FIRST

The first part specifies the elements that take part in the agreement relation. The second part

specifies which attribute must have the same value for all the elements taking part in the

agreement relation.5 The third part, the recursive agreement strategy, is relevant only for

recursive cases. See below. Thus an agreement constraint is fulfilled, iff the elements enlisted

in the first part of the constraint have the attribute in the second part specified, and its value is

the same for all the elements (while using the necessary agreement strategy in the recursive

case). CONSTR, the set of constraints is a finite subset of ALLCONSTR, the set of all

possible constraints. (Cf. Footnote 2).

2 ALLREP, ALLATTR, and ALLVAL can be non-finite because PAT is finite. For our model to be operational it is enough to have a finite set of patterns onto which all possible inputs can be mapped. I.e., it is not important which representational elements and attributes we use of the non-finitely many to build patterns providing PAT remains finite. ALLVAL need not be finite, on the one hand, for the same reasons: values that can be used to build a finite number of patterns are restricted to a finite subset of ALLVAL. On the other hand, any number of values can be tackled by agreement. For an agreement constraint to be fulfilled it is irrelevant what actual values the attributes have. What matters is that values must be the same. The identity of values can be detected by the mapping algorithm independently of what the values are. The set of all possible input elements need not be finite, either, because we let the mapping algorithm gather information about unspecified features of input. (This may solve problems similar to those discussed in (Drienkó, L. 2004 The alphabet paradox. To appear in Linguistics and Philosophy). See below.).3 We assume that all sets in our model have elements of finite length only.4 Or it may return several values for ambiguous elements.5 We use the word ’element’ both for input elements and for symbolic or representational elements constituting patterns. In the general case it will cause no problem, but it should be kept in mind that the elements of patterns are representations of features of input elements.

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Agreement constraints may be (finite-length) conjunctions or disjunctions of other

constraints. Requiring that all ‘subconstraints’ of a constraint be satisfied can be interpreted

as a logical AND relationship. Our default interpretation of the relationship between

constraints is conjunction, since we require that all constraints of a pattern should be fulfilled.

In this respect, (1.13) and (1.14), for instance, are equivalent, so graphically we will use only

one line for several (AND) agreement relations between the same elements.

(1.13)

B C D

PERSNUM

C1 : 1 2 PERS FIRST-TO-FIRST C2 : 1 2 NUM FIRST-TO-FIRST

(1.14)B C D

PERS, NUM

C: C1 C2 = (1 2 PERS FIRST-TO-FIRST ) (1 2 NUM FIRST-TO-FIRST)

Agreement constraints can be applied disjunctively, as well. This means that, given e.g.

constraint C: C1 C2 , either C1 or C2 should be satisfied. In the examples below our OR

relations will not be exclusive. Disjunctive agreement relations will be indicated with dotted

lines. In (1.15) for instance either the person or the number value must be the same for B and

C.

(1.15)B C D

PERS, NUM

Non-graphically, we may refer to patterns as sets of attribute-value specifications. For

instance, (CAT = noun), or (X = x) represent such attribute-value specifications: they are

atomic or non-recursive elements of ALLREP ( and of REPEL, if we choose to use them in

our model).

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We will say that a representational element is saturated, if an input element is mapped on it.

That is, representational element Re: (X = x) is saturated if there is an input element

i( ..., X, ... ) such that VALA(i( X )) = x. Re can be saturated by unknown input element

iu(?). since our VALA function may ‘suppose’ X=x for iu(?)

Patterns can contain recursive elements. Recursive representational elements are sequences

of non-recursive elements. While atomic representational elements can be saturated only once

in a pattern, recursive ones can be saturated any times. ((Xi = x i) (Yi = yi)) may symbolise a

recursive representational element Rei consisting of two atomic elements.

A recursive element is n-saturated if all of its atomic elements are saturated n times, n 0.

The mapping algorithm can be sketched in the following way.

(1.16) Given:

a sequence S of N input elements: S = {i1(I11, ... , I1m(1)), ... , iN(IN1, ... , INm(N))}, where 0 < N, m(i) is a function that returns the number of attributes input element i has; I11, ..., INm(N) ATTR,i1(I11, ... , I1m(1)) KEL UEL, ... , iN(IN1, ... , INm(N)), KEL UEL

pattern P = {((X1 = x1)…) ... ((XL(P) = xL(P))…)}= {Re1 ... ReL(P)}, L(P) is a function that returns the length of a pattern, i.e, how many representational elements the pattern consists of;x1, ... , xL(P) VAL; X1, ..., XL(P) ATTR; Re1 ... ReL(P) REPELP PAT

C(P), the set of constraints for P:C(P) = {c1, c2, ... ch}, > h 0 , c1, c2, ... ch CONSTR

iorder(S): a function that returns a list containing input elements in the ‘original’ order, i.e. in the order they are given to the mapping systemmorder(S,P): a function that returns a list containing input elements in the order they are mapped onto representational elements of P

For each input element i S find a representational element Rej P such that i saturates Rej.

S is successfully mapped on P /input is licensed by pattern/input is ‘grammatical’ iff

(1.17)

1. a.) random-access/non-linear case:

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all elements of P are n-saturated and N, the number of input elements, or the cardinality of S is

L(P) N = len(Rej)st(Rej)

j=1

where L(P) is the function that returns the length of a pattern,len(Rej) is a function that returns the length of representational element Rej of P, its value is 1 for an atomic element, and it returns the number of atomic elements that a recursive element consists of for recursive elementsst(Rej) is a function that computes how many times a recursive element has been saturated. Its value is 1 for atomic elements, since they can be saturated only once. We say that representational element Rej is n-saturated, where n= st(Rej). represents algebraic multiplication

b.) linear case:

saturation is monotonic, i.e.all representational elements are n-saturated, where n is specified by st(Rej)iorder(S) = morder(S, P), i.e, input elements are mapped in the order they are presented to the mapping system representational element Rej of P is saturated by input elements if , where

f(j, k, pos(j)) = start(j) + klen(Rej) +Pos(j),

j-1

start(j) = len(Reg)st(Reg), g=0

0 < pos(j) len(Rej), 0 k < st(Rej), len(Re0) = 0, st(Re0) = 0.

2. Constraints c1, c2, ... ch are satisfied.

The graphical representation in (1.9), repeated here as (1.18) is a shorthand notation for the

more detailed (1.19).

(1.18) A N V


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(1.19) CAT=Adj CAT=Noun Cat=Verb


That is, we omit the attribute specifications when they are self-evident.

Elements can be mapped onto patterns recursively. It may be specified for a pattern where

recursion is allowed to occur. Such specification may be incorporated in the actual patterns.

We will use arrows to show recursion.

(1.20) A N V


Pattern (1.20) licenses sentences like (1.21).

(1.21)

Krasivaya mal’en’kaya russkaya ... d’evushka rabotayetBeautiful little Russian ... girl works/is working.

In pattern (1.20) recursion is restricted to a single element represented by (CAT = A). It is a

recursive representational element – as the arrow indicates. Generally, we will use arrows to

mark recursive representational elements. The staring point of the arrow is the last atomic

representational element of a recursive element. The arrow points to the first atomic element

of the recursive element. In (1.22), e.g. the arrow indicates that the first element of the

pattern is recursive representational element ((CAT = Adv) (CAT =A)) consisting of the two

atomic elements (CAT=Adv) and (CAT=A).

(1.22)

Adv A N V

GENDER PERS CASE

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However, in recursive cases it may not be straightforward how to check agreement since

several input elements can be mapped on a single representational element. Given i.e. pattern

(1.23)

(1.23)

A N

GENDER

and input elements

i1: PHFORM = krasivaya, i2: PHFORM = malen’kiy CAT = A CAT = A GENDER = fem GENDER = masc

i3: PHFORM = devushka i4: PHFORM = malchik CAT = N CAT = N GENDER = fem GENDER = masc

and morder(S,P)= (i1 i3, i2, i4) – i.e: krasivaya devushka malen’kiy malchik – it should be

desirable that i1 agree with i3 and i2 with i4. This type of agreement strategy will be called

FIRST-TO-FIRST since agreement checking observes the order in which elements are

mapped.

Another possibility – absurd for our current example, but useful in other cases – is checking

agreement in semi-reverse order, that is the checking process observes mapping order for one

atomic element, but input elements mapped on the other atomic element are taken in reversed

order. Such a strategy may be called LAST-TO-FIRST. Imagine that mapping order is

morder(S,P)= (i1 i2, i4, i3), i.e krasivaya malen’kiy malchik devushka. Then strategy LAST-

TO-FIRST guarantees that malen’kiy malchik and krasivaya devushka be checked.

Of course, there are many more strategies to check agreement for recursive cases. It is for

linguistic research to determine which strategy is optimal for which case.

Recall we view the language faculty as the operation of a mapping mechanism. We assume

that the same – or similar - mechanisms may be involved for both language production

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(‘generation’) and perception (recognition). The difference lies in the selection of input

elements for the mapping system. In the case of recognition linguistic input is provided by

the environment more directly, i.e. linguistic stimuli from the speaker’s environment activate

representations of input elements in the speaker’s internal linguistic system (elements of

KEL). In the case of production, input elements for the linguistic mapping system are

activated by other internal cognitive modules.

For both cases – production and perception – the mapping system is equipped with a

reconstruction mechanism to handle unknown6 elements (elements of UEL, see (1.11)).This

reconstruction mechanism can make guesses as to the status of unknown input elements.

Basically, it is done by finding a pattern into which the unknown input element can fit

together with the other (known) elements of the input and supposing that the unknown input

element has the features required by the pattern.

We distinguish between linear and random-access ways of mapping. Arguably, the choice of

the concrete mapping mode may depend on the particular linguistic task, i.e., on the particular

circumstances under which linguistic input is available. The basic difference between linear

and random-access mapping is analogous to the difference between ‘on-line’ and ‘off-line’

processing. Our terminology, however, attempts to emphasise that in the random-access case

all elements of the input set are available for the mapping system at the same time – input is

considered an unordered set – , while in the linear case only one input element - the next

one – is available at a time – input is regarded as a sequence. Accordingly, linear mapping

may play an important role in syntactic processing – parsing – where the temporal order of

words is relevant, while random-access mapping should be supposed to be at work in cases

where the temporal order of input elements is irrelevant or cannot be detected. The latter case

is exemplified by phonetic processing where the temporal aspect of setting phonetic feature

values seems to be irrelevant or unmanageable suggesting the alternative that phonetic

features of an individual phoneme be considered collectively, i.e. the order of input elements

– phonetic features – should not be taken into consideration when mapping onto phonetic

patterns.

6 Note we can let the contents of KEL vary in time. This allows us to interpret ’unknown’ , besides ’unidentified’ , as ’temporarily inaccessible’.

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Note we do not exclude the possibility that saturated patterns have representations in REPEL.

This entails that it is possible to think of patterns as built out of representational elements

corresponding to patterns. For instance, a pattern corresponding to a word can be regarded as

a sequence of patterns corresponding to the respective phonemes of that word. In the same

fashion, sentence patterns can be viewed as sequences of word or phrase patterns, or

phoneme patterns can be seen as sets of phonetic feature patterns. In this way, a pattern can

be interpreted as a superposition of other patterns. Such superpositions are effected

configurationally and by explicit agreement constraints in our model.

So far we have been speaking of mapping in a theoretical or ‘abstract’ sense. We believe that

the issue of how the actual mapping should be carried out is equally important. Utilising

automata may be a straightforward option. The agreement automaton (AA) was designed in

Drienkó (2003) to incorporate agreement facilities. Linear mapping can be done by the

agreement automaton in time linear in the length of the input sequence – the number of input

elements – providing no reconstruction mechanism is involved and recursive agreement

strategies are ‘not very complicated’7. Reconstruction requires a backtracking mechanism

which searches the whole pattern space – PAT – and needs time proportional to the size of

the search space – the number of patterns. Random-access mapping requires the modification

of the agreement automaton so that it be a state-memory automaton (SMA). Every state of a

SMA has a memory whose size is proportional to the length of the input. 8. Mapping with

SMA – without reconstruction - may require time of the order n2 , where n is the number of

input elements. Reconstruction, again, increases time requirements by a factor proportional to

the size of the search space. The same holds for a state-memory agreement automaton

(SMAA), plus the SMAA – just like the AA – needs additional time for agreement checking.

In a commonsense way, we may argue that our theoretical outlining of the mapping system is

related to the hypothetical capacities of the speaker of the language – linguistic competence

–, whereas the choice of the particular mapping mechanism influences performance.

7 The agreement strategies that we adopt in this work are ’not very complicated’, so that they do not spoil linearity. As a matter of fact, more complicated strategies could only spoil linearity of the time needed for agreement checking since the checking of constraints is done after the final state has been reached.8 Or it can be of any size practical for the actual computing task. ’Practical’ involves that it should be finite.See (Drienkó, L. 2000. Egy keresésre épülő rekonstrukciós nyelvi modell alapjai. Ms.) for more information about the use of SMA’s

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Our model is compatible with a ‘mental(language/linguistic) organ’ attitude to language. Our

patterns can be thought of as having direct neurological representations in the brain, just like

reconstruction mechanisms symbolised by VALA(a(X)) may represent cognitive processes

effected by neural activation. In such a setting, updating the mapping system could model

language learning. Basically, updating the mapping system means that new patterns can be

added to PAT and new input elements can be added to KEL. This may be done in the

following way. Any implemented version of an agreement mapping system should provide

means of including new elements in any – or at least most - of its components. For instance,

if patterns are represented as pathways in a graph, it should mean no problem for the system

to accommodate new nodes – corresponding to new patterns - anytime it is necessary, i.e.

anytime the ‘learner’, or more probably the ‘teacher’, judges it desirable. The learning

process may be guided by VALA(a(X)). VALA(a(X)) gathers information about the relevant

features of the unknown input element on the basis of what the system has already ‘learnt’. If

it fits into an already existing pattern the ‘learner’ may infer that the unknown input element

has the properties prescribed by that pattern and may choose to include it in KEL, or it may

choose to build a new pattern if unknown input does not go with any existing pattern, or it

may ask for the teacher’s help

Suppose now, that an ‘agreement child’ has been born. Its brain contains no information

about the language it will have to learn. What is given is a computing apparatus capable of

building patterns, a reconstruction mechanism capable of making guesses, and a memory

capable of storing patterns, input elements, and results of ‘mental computations’. Since

initially the child’s PAT and KEL are empty, he will start to build patterns and store them in

his memory together with the input elements that triggered the constructions of patterns. The

construction of patterns will be guided by the reconstruction mechanisms of her innate

mapping system and by teachers around her. After a number of patterns have been built and a

number of input elements have become familiar, pattern-building slows down since most

linguistic input can be mapped on patterns in her PAT. The learning of new input – storing

new words, phrases, etc. in KEL – also becomes less intensive as the acquiring of her

language and her knowledge of the word proceeds. However, the reconstruction mechanisms

will always be there to be resorted to in ‘times of trouble’.

Integrating reconstruction mechanisms in our mapping system offers a solution to paradoxical

problems related to the ‘openness’ of natural languages, in particular to the question of

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finiteness or non-finiteness of generative alphabets/vocabularies/lexicons. Consider sentences

(1.24)-(1.26).9

(1.24) Mr Zaxvul is a linguist.(1.25) The three sisters was written by Chekhov.(1.26) Be do he is nonsense.

These sentences are paradoxical in the sense that they are grammatical despite the fact that

they are built out of elements that are not legal sequences of the language (English): ‘zaxvul‘

is an unknown word for speakers of English – unlike, hopefully, Chekhov or Bartók - , ‘the

three sisters was’ and ‘be do he’ are also illegal sequences of English. Suppose now, that

PAT contains patterns10 (1.27)-(1.29).

(1.27) Mr N BE Det N (e.g. Mr Smith is a teacher.)(1.28) Det N BE PP by N (e.g. The job was done by Jack)(1.29) N(pro) BE N (e.g. It is water.)

When our system processes e.g. (1.24) VALA(a(X)) may return the following values:

(1.30) VALA(mr(CAT)) = mr(1.31) VALA(zaxvul(CAT)) = ?(1.32) VALA(is(CAT)) = be(1.33) VALA(a(CAT)) = det(1.34) VALA(linguist(CAT)) = n

The question mark indicates that the word ‘zaxvul’ is unknown, i.e. it is not in KEL. Next the

system tries to find a matching pattern. Ideally, (1.27) is chosen, with the condition, or

‘guess’, that ‘zaxvul’ be a noun (3rd person singular, since agreement constraints are checked).

Thus the not fully known input (1.24) can be mapped onto an already familiar pattern. The

analysis for (1.25) or (1.26) differs in that we may extend the notion of ‘input element’ to

units larger than a word. Thus the value for ‘the three sisters’ is either ‘n’ representing a 3rd

person singular nominal entity referring to a book, or a play – ‘the three sisters’ is in KEL – or

VALA(the_three_sisters(CAT)) = ?, i.e. input element ‘the three sisters’ is unknown. In the

latter case reconstruction will select (1.28) for (1.25) with the proviso that

VALA(the_three_sisters(CAT)) = n, VALA(the_three_sisters(PERS)) =3rd , VALA(the_three_sisters(NUM)) =sing. Sentence (1.26) can be treated similarly. 9 See Drienkó (2004) for further paradoxical cases.10 We omit agreement relations here for simplicity.

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Note that our model – like human speakers and unlike generative models – does not

necessarily specify a definite ‘yes’ or ‘no’ answer as to the grammaticality of a given input

sentence. The model either simply states that a given sentence can be mapped onto an already

familiar pattern (or patterns in the case of ambiguous sentences) if all of its elements are

identified as known, or gives a tentative answer that unfamiliar input can be mapped,

provided certain agreement conditions are fulfilled.

It was mentioned that our agreement approach need not make reference to production rules or

to the corresponding phrasal constituents. However, it is possible to obtain the ‘classical’

phrase structure of a sentence. Drienkó (2003) shows how agreement transducers can delimit

phrasal components.

2. Applications

2.1 Cross-serial dependency

Arguing against the context-freeness of Swiss German, Shieber (1985) cites cross-serial

dependency data like (2.1), (p.336).

(2.1)… mer d’chind em Hans es huus haend wele… we the children-ACC Hans-DAT the house-ACC have wanted

laa hälfe aastriichelet help paint‘… we have wanted to let the children help Hans paint the house’

Pattern (2.2) can license such sentences.

(2.2)

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N

N N haend wele V

ARG2CASE

PERS,NUMARG1CASE

Note, that the basic part here is played by ARG2CASE. The first noun - the first argument of

the verb – , the subject, has to agree in person and number with the auxiliary , plus the subject

must be in the nominative (ARG1CASE). On the other hand , agreement of ARG2CASE

means that the noun must have that case which the verb prescribes for it (as its second

argument). As the arrows indicate, infinitely many nouns and verbs can be agreed, in theory.

The recursive agreement strategy is (the default) FIRST-TO-FIRST.

2.2 Bambara reduplication

Culy (1985) reports data which prove that the vocabulary of the Bambara language cannot be

described by context-free machinery. There are two constructions which combine to rule out

context-freeness. First, Bambara has a

(2.3) noun + o + noun

pattern, where the two nouns are identical . For instance,

(2.4) wulu-o-wuludog dog

means “whichever dog”. Second, there is an agentive construction

(2.5) noun + transitive verb + la

for cases like (2.6)a-b

(2.6) a. wulu + file + ladog watch“dog watcher”

b. wulu + nyini + la11

dog search

11 For our purposes it is irrelevant that ’la’ becomes ’na’ after a syllable containing a nasal consonant, that is, that the actual word is wulunyinina.

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“dog searcher”

(2.5) can be used in a recursive fashion, as shown in (2.6).

(2.6) a. wulufilela + file + ladog watcher watch“dog-watcher watcher”

b. wulufilela + nyini + ladog watcher search“dog-watcher searcher”

Constructions (2.3) and (2.5) can be combined to yield words like (2.7).

(2.7) a. wulufilelafilela o wulufilelafileladog-watcher watcher dog-watcher watcher“whoever watches dog-watchers”

b. wulufilelanyinina o wulufilelanyininadog-watcher searcher dog-watcher searcher“whoever searches for dog-watchers”

Agreement pattern (2.8) below can account for the phenomena.

(2.8) V V

N V la o N V la

PHFORM

PHFORM

The agreement of PHFORM values expresses the identity of words, i.e. it prescribes that the

verbs and the nouns at the given points of the sequence must have the same phonological

forms. The PHFORM value, e.g., for the verb ‘file’ is straightforwardly ‘file’.12 Our default

FIRST-TO-FIRST strategy seems to suffice to check the agreement.

2.3 Arabic morphology

12 Of course, the PHFORM value could as well be anything, provided it exclusively specifies the word in question.

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Arabic verb forms are created in the following fashion.13 There is a basic stem of consonants,

say, ‘k-t-b’ (‘write’) and there are vowel sequences which determine grammatical properties

of the verb. Such vowel sequences are given in (2.9).

(2.9) a a perfective, activeu i perfective, passivea u imperfective, activeu a imperfective, passive

The verb form is the combination of the skeleton of consonants and the vowel sequence.

Accordingly, the four forms of ‘write’ as specified by (2.9) are (2.10)a-d.

(2.10) a) katabb) kutibc) aktubd) uktab

Further verbal forms - corresponding to modifications of the ‘basic’ meaning – can be

created by other combinations of consonants and vowels: e.g., ‘kattab-writeCAUSATIVE’,

‘kaatab-correspond with sb.’, etc.

There are a finite number of consonant-vowel skeletons (CV templates) in Arabic, onto which

templates all verb forms can be mapped. Such templates are given in (2.11).

(2.11) a) CVCVCb) CVCCVCc) CVVCVCd) CVCVCCVCe) CVCVVCCVCf) CCVCVCg) CCVVCVCh) CCVCCVCi) VCCVC

Thus, to obtain a grammatical form of a verb we need a CV-skeleton, a consonant sequence,

and a vowel sequence. This is quite compatible with our agreement approach. Licensing

‘katab’ or ‘kutib’ can be done with (2.12).

13 We thank Ferenc Kiefer for information on Arabic morphology.

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(2.12)

C V C V C

PHFORM = k t b, …

PHFORM = a aPHFORM = u i

Note how the notion of ‘agreement’ can be extended to prescribe the order of the elements in

a sequence. ‘A= val1 val2 ‘ in Condition (2.13) requires that the respective A values of

elements x and y should form the specified sequence ‘val1 val2’.

(2.13) x y A = val1 val2 STRATEGY

Thus ‘PHFORM = k t b’ requires the necessary order of consonants, while e.g., ‘PHFORM =

u i’ determines the desired sequence of the vowels for ‘kutib’. (The PHFORM value for ‘k’

is k, for ‘u’ it is u, etc.)

Dotted lines, as was pointed out earlier, indicate possible – disjunctive - alternatives for

agreement. In (2.12) not only is there a choice between perfective-active or perfective-

passive, but consonant sequences, other than ‘k-t-b’, corresponding to other verbs can also be

considered.

Note that (2.12) corresponds to template (2.11)a.

A similar analysis is available for Arabic broken plural. There are two plural-templates,

(2.14)a and (2.14)b.

(2.14) a) CVCVVCVCb) CVCVVCVVC

The plural vowel sequence is ‘a-i’. Thus, e.g., the plural form ‘jawaamiis’ of ‘jaamuus’,

‘buffalo’ is licensed by (2.15), corresponding to (2.14)b.

(2.15)

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C V C V V C V V C

PHFORM = j w m s, …

PHFORM = a a a i i

2.4 Vowel harmony

Consider the following data from Hungarian.

(2.16) szósznak (sauce-DAT) tíznek (ten-DAT)húsnak (meat-DAT) tűznek (fire-DAT)háznak (house-DAT) kéznek (hand-DAT)vasnak (iron-DAT) gőznek (steam-DAT)

The dative suffix is either ‘nak’ or ‘nek’. The vowel in the noun determines which allomorph

must follow. The vowel of the noun stem and the vowel in the suffix must have the same

high-or-low (HILO) value. We sketch the corresponding pattern in (2.17).

(2.17)

C V C C V C

HILOPHFORM= sz ó sz PHFORM= n a kPHFORM= h ú s PHFORM= n e kPHFORM= h á zPHFORM= v a sPHFORM= t í zPHFORM= t ű zPHFORM= k é zPHFORM= g ő z…Ó, Ú, Á, A: HILO = lowÍ, Ű, É, Ő, E: HILO = high

3. Conclusion

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In this work we outlined an approach towards modelling natural language phenomena. We

showed how the notion of ‘agreement’ can be useful for our system mapping input elements

onto patterns.

Our model states that a given phrase, or sentence is representable as an agreement relation,

i.e., as a sequence of elements which satisfies the agreement conditions/constraints for that

relation. We called a sequence – or more generally, a set - of elements, together with its

agreement constraints a pattern. The model considers the operation of the language faculty to

be a mapping from input elements to patterns and it incorporates a reconstruction mechanism

capable of handling unidentified input. The importance of ‘reconstruction’ was emphasised

with respect to the indeterminacy that natural languages incorporate.

As was suggested, specifying the ‘exact’ contents of several components of our model needs

extensive linguistic research. However , we believe that the model is widely applicable.

Possibly, it can also be useful in fields not mentioned in the present paper.

Acknowledgements

I thank the following people for their respective help: Ildikó Szabóné-Szommer, Béla Tóth,

Ágoston Orosz Jr., Kinga Gárdai, László Kálmán, Ferenc Kiefer, Gábor Prószéky,

Péter Rebrus, Huba Bartos, Zoltán Bánréti, Jenő Breyer

About the Author

Mr Drienko teaches at ELTE University, Budapest.

Email: [email protected]

References

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Chomsky, N. (1957) Syntactic Structures. Hungarian translation: Mondattani szerkezetek

Osiris Kiadó, Budapest. 1999.

Culy, Ch. (1985) The complexity of the vocabulary of Bambara. Linguistics and philosophy

8, pp. 345-351

Drienkó, L. (2003) A finite-state tool for nonfinite-state phenomena: the agreement

automaton. Journal of Language and Linguistics. Vol. 2. No. 2, 212-223

Shieber, S. M. (1985) Evidence against the context-freeness of natural language. Linguistics

and philosophy 8. 333-343

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