Proceedings of the Second Workshop on Psychocomputational Models of Human Language Acquisition, pages 45–52,
Ann Arbor, June 2005. c©2005 Association for Computational Linguistics
A Second Language Acquisition Model Using  
Example Generalization and Concept Categories 
 
Ari Rappoport Vera Sheinman 
Institute of Computer Science Institute of Computer Science 
The Hebrew University The Hebrew University 
Jerusalem, Israel Jerusalem, Israel 
arir@cs.huji.ac.il vera46@cl.cs.titech.ac.jp 
 
Abstract 
We present a computational model of ac-
quiring a second language from example 
sentences. Our learning algorithms build a 
construction grammar language model, 
and generalize using form-based patterns 
and the learner’s conceptual system. We 
use a unique professional language learn-
ing corpus, and show that substantial reli-
able learning can be achieved even though 
the corpus is very small. The model is ap-
plied to assisting the authoring of Japa-
nese language learning corpora. 
1 Introduction 
Second Language Acquisition (SLA) is a central 
topic in many of the fields of activity related to 
human languages. SLA is studied in cognitive sci-
ence and theoretical linguistics in order to gain a 
better understanding of our general cognitive abili-
ties and of first language acquisition (FLA)
1
. Gov-
ernments, enterprises and individuals invest 
heavily in foreign language learning due to busi-
ness, cultural, and leisure time considerations. SLA 
is thus vital for both theory and practice and should 
be seriously examined in computational linguistics 
(CL), especially when considering the close rela-
tionship to FLA and the growing attention devoted 
to the latter by the CL community. 
In this paper we present a computational model 
of SLA. As far as we could determine, this is the 
first model that simulates the learning process 
 
1
Note that the F stands here for ‘First’, not ‘Foreign’.  
computationally. Learning is done from examples, 
with no reliance on explicit rules. The model is 
unique in the usage of a conceptual system by the 
learning algorithms. We use a unique professional 
language learning corpus, showing effective learn-
ing from a very small number of examples. We 
evaluate the model by applying it to assisting the 
authoring of Japanese language learning corpora.   
We focus here on basic linguistic aspects of 
SLA, leaving other aspects to future papers. In par-
ticular, we assume that the learner possesses per-
fect memory and is capable of invoking the 
provided learning algorithms without errors.  
In sections 2 and 3 we provide relevant back-
ground and discuss previous work. Our input, 
learner and language models are presented in sec-
tion 4, and the learning algorithms in section 5. 
Section 6 discusses the authoring application. 
2 Background 
We use the term ‘second language acquisition’ to 
refer to any situation in which adults learn a new 
language
2
. A major concept in SLA theory 
[Gass01, Mitchell03] is that of interlanguage:
when learning a new language (L2), at any given 
point in time the learner has a valid partial L2 lan-
guage system that differs from his/her native lan-
guage(s) (L1) and from the L2. The SLA process is 
that of progressive enhancement and refinement of 
interlanguage. The main trigger for interlanguage 
modification is when the learner notices a gap be-
tween interlanguage and L2 forms. In order for this 
to happen, the learner must be provided with com-
 
2
Some SLA texts distinguish between ‘second’ and ‘foreign’ 
and between ‘acquisition’ and ‘learning’. We will not make 
those distinctions here.   
45
prehensible input. Our model directly supports all 
of these notions.  
A central, debated issue in language acquisition 
is whether FLA mechanisms [Clark03] are avail-
able in SLA. What is clear is that SL learners al-
ready possess a mature conceptual system and are 
capable of explicit symbolic reasoning and abstrac-
tion. In addition, the amount of input and time 
available for FLA are usually orders of magnitude 
larger than those for SLA. 
The general linguistic framework that we utilize 
in this paper is that of Construction Grammar 
(CG) [Goldberg95, Croft01], in which the building 
blocks of language are words, phrases and phrase 
templates that carry meanings. [Tomasello03] pre-
sents a CG theory of FLA in which children learn 
whole constructions as ‘islands’ that are gradually 
generalized and merged. Our SLA model is quite 
similar to this process. 
In language education, current classroom meth-
ods use a combination of formal rules and commu-
nicative situations. Radically different is the 
Pimsleur method [Pimsleur05], an audio-based 
self-study method in which rules and explanations 
are kept to a minimum and most learning occurs by 
letting the learner infer L2 constructs from transla-
tions of contextual L1 sentences. Substantial anec-
dotal evidence (as manifested by learner comments 
and our own experience) suggests that the method 
is highly effective. We have used a Pimsleur cor-
pus in our experiments. One of the goals of our 
model is to assist the authoring of such corpora. 
3 Previous Work 
There is almost no previous CL work explicitly 
addressing SLA. The only one of which we are 
aware is [Maritxalar97], which represents interlan-
guage levels using manually defined symbolic 
rules. No language model (in the CL sense) or 
automatic learning are provided.   
Many aspects of SLA are similar to first lan-
guage acquisition. Unsupervised grammar induc-
tion from corpora is a growing CL research area 
([Clark01, Klein05] and references there), mostly 
using statistical learning of model parameters or 
pattern identification by distributional criteria. The 
resulting models are not easily presentable to hu-
mans, and do not utilize semantics.  
[Edelman04] presents an elegant FLA system in 
which constructions and word categories are iden-
tified iteratively using a graph. [Chang04] presents 
an FLA system that truly supports construction 
grammar and is unique in its incorporation of gen-
eral cognitive concepts and embodied semantics.  
SLA is related to machine translation (MT), 
since learning how to translate is a kind of acquisi-
tion of the L2. Most relevant to us here is modern 
example-based machine translation (EBMT) [So-
mers01, Carl03], due to its explicit computation of 
translation templates and to the naturalness of 
learning from a small number of examples 
[Brown00, Cicekli01]. 
The Computer Assisted Language Learning 
(CALL) literature [Levy97, Chapelle01] is rich in 
project descriptions, and there are several commer-
cial CALL software applications. In general, 
CALL applications focus on teacher, environment, 
memory and automatization aspects, and are thus 
complementary to the goals that we address here. 
4 Input, Learner and Language Knowl-
edge Models  
Our ultimate goal is a comprehensive computa-
tional model of SLA that covers all aspects of the 
phenomenon. The present paper is a first step in 
that direction. Our goals here are to:  
 
 Explore what can be learned from exam-
ple-based, small, beginner-level input 
corpora tailored for SLA; 
 Model a learner having a mature concep-
tual system;
 Use an L2 language knowledge model 
that supports sentence enumeration; 
 Identify cognitively plausible and effective 
SL learning algorithms;
 Apply the model in assisting the author-
ing of corpora tailored for SLA.  
In this section we present the first three compo-
nents; the learning algorithms and the application 
are presented in the next two sections. 
4.1 Input Model 
The input potentially available for SL learners is of 
high variability, consisting of meta-linguistic rules, 
usage examples isolated for learning purposes, us-
age examples partially or fully understood in con-
text, dictionary-like word definitions, free-form 
explanations, and more.  
46
One of our major goals is to explore the rela-
tionship between first and second language acqui-
sition. Methodologically, it therefore makes sense 
to first study input that is the most similar linguis-
tically to that available during FLA, usage exam-
ples. As noted in section 2, a fundamental property 
of SLA is that learners are capable of mature un-
derstanding. Input in our model will thus consist of 
an ordered set of comprehensible usage exam-
ples, where an example is a pair of L1, L2 sen-
tences such that the former is a translation of the 
latter in a certain understood context.  
We focus here on modeling beginner-level pro-
ficiency, which is qualitatively different from na-
tive-like fluency [Gass01] and should be studied 
before the latter. 
We are interested in relatively small input cor-
pora (thousands of examples at most), because this 
is an essential part of SLA modeling. In addition, it 
is of great importance, in both theoretical and 
computational linguistics, to explore the limits of 
what can be learned from meager input.  
One of the main goals of SLA modeling is to 
discover which input is most effective for SLA, 
because a substantial part of learners’ input can be 
controlled, while their time capacity is small. We 
thus allow our input to be optimized for SLA, by 
containing examples that are sub-parts of other 
examples and whose sole purpose is to facilitate 
learning those (our corpus is also optimized in the 
sense of covering simpler constructs and words 
first, but this issue is orthogonal to our model). We 
utilize two types of such sub-examples. First, we 
require that new words are always presented first 
on their own. This is easy to achieve in controlled 
teaching, and is actually very frequent in FLA as 
well [Clark03]. In the present paper we will as-
sume that this completely solves the task of seg-
menting a sentence into words, which is reasonable 
for a beginner level corpus where the total number 
of words is relatively small. Word boundaries are 
thus explicitly and consistently marked.  
Second, the sub-example mechanism is also use-
ful when learning a construction. For example, if 
the L2 sentence is ‘the boy went to school’ (where 
the L2 here is English), it could help learning algo-
rithms if it were preceded by ‘to school’ or ‘the 
boy’. Hence we do not require examples to be 
complete sentences.  
In this paper we do not deal with phonetics or 
writing systems, assuming L2 speech has been 
consistently transcribed using a quasi-phonetic 
writing system. Learning L2 phonemes is certainly 
an important task in SLA, but most linguistic and 
cognitive theories view it as separable from the rest 
of language acquisition [Fromkin02, Medin05].  
The input corpus we have used is a transcribed 
Pimsleur Japanese course, which fits the input 
specification above. 
4.2 Learner Model 
A major aspect of SLA is that learners already pos-
sess a mature conceptual system (CS), influenced 
by their life experience (including languages they 
know). Our learning algorithms utilize a CS model. 
We opted for being conservative: the model is only 
allowed to contain concepts that are clearly pos-
sessed by the learner before learning starts. Con-
cepts that are particular to the L2 (e.g., ‘noun 
gender’ for English speakers learning Spanish) are 
not allowed. Examples for concept classes include 
fruits, colors, human-made objects, physical activi-
ties and emotions, as well as meta-linguistic con-
cepts such as pronouns and prepositions. A single 
concept is simply represented by a prototypical 
English word denoting it (e.g., ‘child’, ‘school’). A 
concept class is represented by the concepts it con-
tains and is conveniently named using an English 
word or phrase (e.g., ‘types of people’, ‘buildings’, 
‘language names’).  
Our learners can explicitly reason about concept 
inter-relationships. Is-a relationships between 
classes are represented when they are beyond any 
doubt (e.g., ‘buildings’ and ‘people’ are both 
‘physical things’).  
A basic conceptual system is assumed to exist 
before the SLA process starts. When the input is 
controlled and small, as in our case, it is both 
methodologically valid and practical to prepare the 
CS manually. CS design is discussed in detail in 
section 6.  
In the model described in the present  paper we 
do not automatically modify the CS during the 
learning process; CS evolution will be addressed in 
future models.  
As stated in section 1, in this paper we focus on 
linguistic SLA aspects and do not address issues 
such as human errors, motivation and attention. 
We thus assume that our learner possesses perfect 
memory and can invoke our learning algorithms 
without any mistakes.   
47
4.3 Language Knowledge Model 
We require our model to support a basic capability 
of a grammar: enumeration of language sentences 
(parsing will be reported in other papers). In addi-
tion, we provide a degree of certainty for each. The 
model’s quality is evaluated by its applicability for 
learning corpora authoring assistance (section 6).   
The representation is based on construction 
grammar (CG), explicitly storing a set of construc-
tions and their inter-relationships. CG is ideally 
suited for SLA interlanguage because it enables the 
representation of partial knowledge: every lan-
guage form, from concrete words and sentences to 
the most abstract constructs, counts as a construc-
tion. The generative capacity of language is ob-
tained by allowing constructions to replace 
arguments. For example, (child), (the child goes to 
school), (<x> goes to school), (<x> <v> to school) 
and (X goes Z) are all constructions, where <x>, 
<v> denote word classes and X, Z denote other 
constructions.  
SL learners can make explicit judgments as to 
their level of confidence in the grammaticality of 
utterances. To model this, our learning algorithms 
assign a degree of certainty (DOC) to each con-
struction and to the possibility of it being an argu-
ment of another construction. The certainty of a 
sentence is a function (e.g., sum or maximum) of 
the DOCs present in its derivation path. 
Our representation is equivalent to a graph 
whose nodes are constructions and whose directed, 
labeled arcs denote the possibility of a node filling 
a particular argument of another node. When the 
graph is a-cyclic the resulting language contains a 
finite number of concrete sentences, easily com-
puted by graph traversal. This is similar to [Edel-
man04]; we differ in our partial support for 
semantics through a conceptual system (section 5) 
and in the notion of a degree of certainty.   
5 Learning Algorithms 
Our general SLA scheme is that of incremental 
learning – examples are given one by one, each 
causing an update to the model. A major goal of 
our model is to identify effective, cognitively plau-
sible learning algorithms. In this section we present 
a concrete set of such algorithms. 
Structured categorization is a major driving 
force in perception and other cognitive processes 
[Medin05]. Our learners are thus driven by the de-
sire to form useful generalizations over the input. 
A generalization of two or more examples is possi-
ble when there is sufficient similarity of form and 
meaning between them. Hence, the basic ingredi-
ent of our learning algorithms is identifying such 
similarities. 
To identify concrete effective learning algo-
rithms, we have followed our own inference proc-
esses when learning a foreign language from an 
example-based corpus (section 6). The set of algo-
rithms described below are the result of this study.  
The basic form similarity algorithm is Single 
Word Difference (SWD). When two examples 
share all but a single word, a construction is 
formed in which that word is replaced by an argu-
ment class containing those words. For example, 
given ‘eigo ga wakari mas’ and ‘nihongo ga wakari 
mas’, the construction (<eigo, nihongo> ga wakari 
mas) (‘I understand English/Japanese’), containing 
one argument class, is created. In itself, SWD only 
compresses the input, so its degree of certainty is 
maximal. It does not create new sentences, but it 
organizes knowledge in a form suitable for gener-
alization.  
The basic meaning-based similarity algorithm is 
Extension by Conceptual Categories (ECC). For 
an argument class W in a construction C, ECC at-
tempts to find the smallest concept category U’ 
that contains W’, the set of concepts corresponding 
to the words in W. If no such U’ exists, C is re-
moved from the model. If U’ was found, W is re-
placed by U, which contains the L2 words 
corresponding to the concepts in U’. When the re-
placement occurs, it is possible that not all such 
words have already been taught; when a new word 
is taught, we add it to all such classes U (easily 
implemented using the new word’s translation, 
which is given when it is introduced.) 
In the above example, the words in W are ‘eigo‘ 
and ‘nihongo’, with corresponding concepts ‘Eng-
lish’ and ‘Japanese’. Both are contained in W’, the 
‘language names’ category, so in this case U’ 
equals W’. The language names category contains 
concepts for many other language names, includ-
ing Korean, so it suffices to teach our learner the 
Japanese word for Korean (‘kankokugo’) at some 
point in the future in order to update the construc-
tion to be (<eigo, nihongo, kankokugo> ga wakari 
mas). This creates a new sentence ‘kankokugo ga 
wakari mas’ meaning ‘I understand Korean’. An 
48
example in which U’ does not equal W’ is given in 
Table 1 by ‘child’ and ‘car’.  
L2 words might be ambiguous – several con-
cepts might correspond to a single word. Because 
example semantics are not explicitly represented, 
our system has no way of knowing which concept 
is the correct one for a given construction, so it 
considers all possibilities. For example, the Japa-
nese ‘ni’ means both ‘two’ and ‘at/in’, so when 
attempting to generalize a construction in which 
‘ni’ appears in an argument class, ECC would con-
sider both the ‘numbers’ and ‘prepositions’ con-
cepts.  
The degree of certainty assigned to the new con-
struction by ECC is a function of the quality of the 
match between W and U’. The more abstract is U, 
the lower the certainty. 
The main form-based induction algorithm is 
Shared Prefix, Generated Suffix (SPGS). Given 
an example ‘x y’ (x, y are word sequences), if there 
exist (1) an example of the form ‘x z’, (2) an ex-
ample ‘x’, and (3) a construction K that derives ‘z’ 
or ‘y’, we create the construction (x K) having a 
degree of certainty lower than that of K. A Shared 
Suffix version can be defined similarly. Require-
ment (2) ensures that the cut after the prefix will 
not be arbitrary, and assumes that the lesson author 
presents constituents as partial examples before-
hand (as indeed is the case in our corpus).  
SPGS utilizes the learner’s current generative 
capacity. Assume input ‘watashi wa biru o nomi 
mas’ (‘I drink beer’), previous inputs ‘watashi wa 
america jin des’ (‘I am American’), ‘watashi wa’ 
(‘as to me...’) and an existing construction K = 
(<biru, wain> o nomi mas). SPGS would create the 
construction (watashi wa K), yielding the new sen-
tence ‘watashi wa wain o nomi mas’ (‘I drink 
wine’). 
To enable faster learning of more abstract con-
structions, we use generalized versions of SWD 
and SPGS, which allow the differing or shared 
elements to be a construction rather than a word or 
a word sequence.  
The combined learning algorithm is: given a 
new example, iteratively invoke each of the above 
algorithms at the given order until nothing new can 
be learned. Our system is thus a kind of inductive 
programming system (see [Thompson99] for a sys-
tem using inductive logic programming for seman-
tic parsing).  
Note that the above algorithms treat words as 
atomic units, so they can only learn morphological 
rules if boundaries between morphemes are 
marked in the corpus. They are thus more useful 
for languages such as Japanese than, say, for Ro-
mance or Semitic languages. 
Our algorithms have been motivated by general 
cognitive considerations. It is possible to refine 
them even further, e.g. by assigning a higher cer-
tainty when the focus element is a prefix or a suf-
fix, which are more conspicuous cognitively. 
6 Results and Application to Authoring of 
Learning Corpora 
We have experimented with our model using the 
Pimsleur Japanese I (for English speakers) course, 
which comprises 30 half-hour lessons, 1823 differ-
ent examples, and about 350 words. We developed 
a simple set of tools to assist transcription, using an 
arbitrary, consistent Latin script transliteration 
based on how the Japanese phonemes are pre-
sented in the course, which differs at places from 
common transliterations (e.g., we use ‘mas’, not 
‘masu’). Word boundaries were marked during 
transliteration, as justified in section 4.  
Example sentences from the corpus are ‘nani o 
shi mas kaa ? / what are you going to do?’, ‘wa-
tashi ta chi wa koko ni i mas / we are here’, ‘kyo 
wa kaeri masen / today I am not going back’, 
‘demo hitori de kaeri mas / but I am going to return 
alone’, etc. Sentences are relatively short and ap-
propriate for a beginner level learner.  
Evaluating the quality of induced language 
models is notoriously difficult. Current FLA prac-
tice favors comparison of predicted parses with 
ones in human annotated corpora. We have fo-
cused on another basic task of a grammar, sentence 
enumeration, with the goal of showing that our 
model is useful for a real application, assistance for 
authoring of learning corpora. 
The algorithm has learned 113 constructions 
from the 1823 examples, generating 525 new sen-
tences. These numbers do not include construc-
tions that are subsumed by more abstract ones 
(generating a superset of their sentences) or those 
involving number words, which would distort the 
count upwards. The number of potential new sen-
tences is much higher: these numbers are based 
only on the 350 words present, organized in a 
rather flat CS. The constructions contain many 
49
placeholders for concepts whose words would be 
taught in the future, which could increase the num-
ber exponentially.  
In terms of precision, 514 of the 525 sentences 
were judged (by humans) to be syntactically cor-
rect (53 of those were problematic semantically). 
Regarding recall, it is very difficult to assess for-
mally. Our subjective impression is that the learned 
constructions do cover most of what a reasonable 
person would learn from the examples, but this is 
not highly informative – as indicated, the algo-
rithms were discovered by following our own in-
herence processes. In any case, our algorithms 
have been deliberately designed to be conservative 
to ensure precision, which we consider more im-
portant than recall for our model and application. 
There is no available standard benchmark to 
serve as a baseline, so we used a simpler version of 
our own system as a baseline. We modified ECC to 
not remove C in case of failure of concept match 
(see ECC’s definition in section 5). The number of 
constructions generated after seeing 1300 exam-
ples is 3,954 (yielding 35,429 sentences), almost 
all of which are incorrect.  
The applicative scenario we have in mind is the 
following. The corpus author initially specifies the 
desired target vocabulary and the desired syntacti-
cal constructs, by writing examples (the easiest 
interface for humans). Vocabulary is selected ac-
cording to linguistic or subject  (e.g., tourism, 
sports) considerations. The examples are fed one 
by one into the model (see Table 1). For a single 
word example, its corresponding concepts are first 
manually added to the CS. 
The system now lists the constructions learned. 
For a beginner level and the highest degree of cer-
tainty, the sentences licensed by the model can be 
easily grasped just by looking at the constructions. 
The fact that our model’s representations can be 
easily communicated to people is also an advan-
tage from an SLA theory point of view, where ‘fo-
cus on form’ is a major topic [Gass01]. For 
advanced levels or lower certainties, viewing the 
sentences themselves (or a sample, when their 
number gets too large) might be necessary.  
The author can now check the learned items for 
errors. There are two basic error types, errors 
stemming from model deficiencies and errors that 
human learners would make too. As an example of 
the former, wrong generalizations may result from 
discrepancies between the modeled conceptual sys-
tem and that of a real person. In this case the au-
thor fixes the modeled CS. Discovering errors of 
the second kind is exactly the point where the 
model is useful. To address those, the author usu-
ally introduces new full or partial examples that 
would enable the learner to induce correct syntax. 
In extreme cases there is no other practical choice 
but to provide explicit linguistic explanations in 
order to clarify examples that are very far from the 
learner’s current knowledge. For example, English 
speakers might be confused by the variability of 
the Japanese counting system, so it might be useful 
to insert an explanation of the sort ‘X is usually 
used when counting long and thin objects, but be 
aware that there are exceptions’. In the scenario of 
Table 1, the author might eventually notice that the 
learner is not aware that when speaking of some-
body else’s child a more polite reference is in or-
der, which can be fixed by giving examples 
followed by an explanation. The DOC can be used 
to draw the author’s attention to potential prob-
lems.  
Preparation of the CS is a sensitive issue in our 
model, because it is done manually while it is not 
clear at all what kind of CS people have (WordNet 
is sometimes criticized for being arbitrary, too fine, 
and omitting concepts). We were highly conserva-
tive in that only concepts that are clearly part of the 
conceptual system of English speakers before any 
exposure to Japanese were included. Our task is 
made easier by the fact that it is guided by words 
actually appearing in the corpus, whose number is 
not large, so that it took only about one hour to 
produce a reasonable CS. Example categories are 
names (for languages, places and people), places 
(park, station, toilet, hotel, restaurant, shop, etc), 
people (person, friend, wife, husband, girl, boy), 
food, drink, feelings towards something (like, 
need, want), self motion activities (arrive, come, 
return), judgments of size, numbers, etc. We also 
included language-related categories such as pro-
nouns and prepositions. 
7 Discussion 
We have presented a computational model of sec-
ond language acquisition. SLA is a central subject 
in linguistics theory and practice, and our main 
contribution is in addressing it in computational 
linguistics. The model’s learning algorithms are 
unique in their usage of a conceptual system, and 
50
its generative capacity is unique in its support for 
degrees of certainty. The model was tested on a 
unique corpus. 
The dominant trend in CL in the last years has 
been the usage of ever growing corpora. We have 
shown that meaningful learning can be achieved 
from a small corpus when the corpus has been pre-
pared by a ‘good teacher’. Automatic identification 
(and ordering) of corpora subsets from which 
learning is effective should be a fruitful research 
direction for CL. 
We have shown that using a simple conceptual 
system can greatly assist language learning algo-
rithms. Previous FLA algorithms have in effect 
computed a CS simultaneously with the syntax; 
decoupling the two stages could be a promising 
direction for FLA.  
The model presented here is the first computa-
tional SLA model and obviously needs to be ex-
tended to address more SLA phenomena. It is clear 
that the powerful notion of certainty is only used in 
a rudimentary manner. Future research should also 
address constraints (e.g. for morphology and agree-
ment), recursion, explicit semantics (e.g. parsing 
into a semantic representation), word segmenta-
tion, statistics (e.g. collocations), and induction of 
new concept categories that result from the learned 
language itself (e.g. the Japanese counting system). 
An especially important SLA issue is L1 trans-
fer, which refers to the effect that the L1 has on the 
learning process. In this paper the only usage of the 
L1 part of the examples was for accessing a con-
ceptual system. Using the L1 sentences (and the 
existing conceptual system) to address transfer is 
an interesting direction for research, in addition to 
using the L1 sentences for modeling sentence se-
mantics.  
Many additional important SLA issues will be 
addressed in future research, including memory, 
errors, attention, noticing, explicit learning, and 
motivation. We also plan additional applications, 
such as automatic lesson generation. 
 
Acknowledgement. We would like to thank Dan 
Melamed for his comments on a related document.  

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