ERROR DIAGNOSING AND SELECTION IN A, TRAINING SYSTEM 
FOR SECOND LANGUAGE LEARNING 
Wolfgang Menzel 
Zentralinstitut fur Sprachwissensehaft 
Akademie der Wissensehaften der DDR 
Pren~lauer Promenade 149-152 
Berlin, 1100, DDR 
Abstract 
A diagnosing procedure to be used in intelli- 
gent systems for language instruction is 
presented. Based on a knowledge representa- 
tion scheme for a certain class of syntactic 
correctness conditions the system carries out 
a thorough analysis of possible error hypoth- 
eses and their consequences. A comparison 
with earlier attempts shows a clearly im- 
proved precision of diagnostic results. First 
of all, the procedure concentrate s on an 
exact localization of rule violations, but - 
if desired - is able to infer information 
about factual faults as well. 
I. INTRODUCTION 
Error anticipation is a key issue so far, 
as systems for computeP assisted language 
learning are to be enhanced with diagnostic 
and explanatory capabilities. Traditional 
approaches do always rely on the central 
assumption that any mistake possibly done by 
a student can be foreseen by the author of a 
teaching exercise in order to supply the 
tutoring system with a collection of ade- 
quate responses to all the different errors 
and error combinations which might occur in 
real training sessions. 
Considering the enormous flexibility of 
natural language, however, this assumption is 
only justified for small classes of very 
simple .type exercises, and most efforts are 
spent into devising sensible teaching aids 
despite the absence of appropriate diagnostic 
techniques. The author is forced to concen- 
trate on single teaching programs without 
almost any chance to generalise from his 
results and to reuse parts of it in other 
contexts later. 
More ambitious solutions certainly can be 
expected, if it becomes feasible to derive 
the diagnostic and explanatory abilities of 
the desired system directly from r u 1 e s 
for what is considered to be a correct con- 
struction in a sensible restricted subset of 
natural language, instead of using pre- 
selected lists of possibly occurring answers. 
In this respect, research in intelligent 
systems for second language learning sooner 
or later will follow similar lines as a par- 
allel development in the field of expert 
systems, where a drastically improved diagno- 
stic behaviour is attempted by modelling 
structure and function of the application 
domain (yielding so called "deep modelled" 
expert systems, which then are able to inves- 
tigate faults by simulating them) rather than 
collecting huge amounts of symptom-oriented 
regularities to be used in a straightforward 
inference procedure on a surface level (c. f. 
for instance Davis 1984). 
By including semantic, syntactic and 
morpho-syntactie regularities into a single 
solution Weischedel et al. (1978) proposed a 
system fop intelligent language instruction 
that likewise turned out to be the most ambi- 
tious approach so far. Even today, almost 
exactly ten years.later, its main pPemises 
and challenging predictions obviously do not 
fully match the real pPospects in the field. 
~ven worse, this as well as more recent at- 
tempts (Barehan et al. 1985, Schwind 1986) 
are strongly oriented on the notion of a 
"typical error". Thus they clearly fall short 
of the deep-modelling ideal and ape connected 
with a number of critical shortcomings. These 
shortcomings can be avoided, if it becomes 
possible to identify limited application 
domains within the area of natural language 
instruction which allow a training system to 
be strictly based on the following basic 
prieiples: 
(I) Supply the system with only knowledge 
about correctness. 
(2) Devise a diagnosis procedure which is 
independent of the content of the knowl- 
edge base. 
Currently used semantic representation 
schemes in general seem much too rough to 
capture all the rather subtle distinctions 
414 
between an acceptable natural language ex- 
pression and a deviant one in a sufficientl~ 
systematic way. Even if the necessary means 
would be available the problem of actually 
coding the desired information for a realis- 
tic domain remains to be solved. 
Better prospects for a successful imple- 
mentation of these two principles can cer- 
tainly be expected on the syntactic level. 
Nevertheless, in order to diagnose structural 
errors ~lll currently known solutions rely 
exclusiw~ly on the use of "marked" rules, 
representing typical mistakes and being in- 
tended to invoke appropriate error messages. 
This practice is clearly inconsistent with 
prineipl,~ (I) and comes out as nothing more 
than a simple shift of the necessity to 
anticipate student behaviour onto a new - not 
necessarily more perspicuous - level. 
Moreover, it leaves the system with all the 
consequences of a parsing grammar bloated 
with numbers Of fault-specific rules. 
The domain I believe is currently ripest 
for a strictly deep-modelled prototype is the 
area of morpho-syntactie correctness condi- 
tions which have to be satisfied in a given 
(if nec(!ssary artificially fixed) syntactic 
environm~nt. These consistency constraints 
fop well-formed syntactic trees comprise 
agreement relations as well as case govern- 
ment and, as Weischedel st al. (1978) 
acknowledge, constitute at least for lan- 
guages like German a major error source. They 
can easily be expressed as predicates over 
structured sets of morpho-syntactic features 
and, if taken together, form simple networks. 
Here again, all current approaches fall 
back on either short-cut solutions (e.g. take 
the fir~t predicate evaluating to false) or 
simple h~uristic guesses when trying to diag- 
nose (esp. to locate) consistency errors. 
Heuristics (or the use of rules-of-thumb) 
typically is the method of one's choice when 
being f~ced with a, by its nature, ill- 
defined ¢,r extremely complex problem. Obvi- 
ously the domain of. morpho--syntactie regular- 
ities belongs to neither the one nor the 
other category. 
Accordingly, an investigation into the 
problem of diagnosing consistency violations 
has shown that an efficient and extremely 
precise diagnostic procedure can be devised, 
which provides a sound basis for the genera- 
tion of comprehensible explanations (includ- 
ing proposals for a proper solution), for a 
valuation of the learning progress and for an 
adaptive determination of the further train- 
inq strategy. Moreover, it turned out that 
non-trivial training exercises based exclu-- 
sively on simple morpho-syntaetic correctness 
conditions can well be used independently of 
an error sensitive • parser and additionally 
are connected with a number of pedagogical 
and performane~ gains (for a detailed discus- 
sion see Menzel, 1987 and 1988). In this ease 
the student can be guided by an appropriate 
sentence context in a smooth and uncon- 
strained way to exactly produce those frag- 
mentary utterances which have the desired 
fixed syntactic structure. 
II. CONSISTENCY CONSTRAINTS 
Consistency constraints to be used as a 
basis for diagnosing students' faults are 
expressed in a quite common way as binary 
predicates which hold over structured feature 
sets of syntactically related word forms 
(source and destination). Feature sets, as 
usual, are attached to word forms via the 
dictionary or a morphological analysis. To 
specify the part of a feature set relevant 
to a specific correctness condition correct- 
ness predicates are augmented by a third 
argument, a category: 
agree\[<souree>,<destination>,<eategory>\]. 
Simple examples of correctness predicates 
define symmetrical relations between equiva- 
lent parts of the two involved feature sets, 
as does the number agreement between the 
determiner and the governing noun in a German 
noun phrase: 
agree(det, noun, number\]. 
Other predicates are needed to account for 
agreement between different parts of two 
feature sets. One example are selectional 
demands of a source to be matched with the 
corresponding properties of a destination, 
another is given by predicates coping with 
the distinction between e.g. different gender 
values belonging to stem or ending of German 
possessive pronouns. 
A basically different type of predicates 
does not specify a source but instead gives a 
condition to be fulfilled by the destination: 
satisfy\[ <destination>, <condition>\]. 
This type is always used in one of the 
following eases: 
(I) Conditions of pure structural origin so 
that no particular source can be given, e.g. 
the nominative of the subject: 
satisfy\[ noun-of-subject, ease=nora). 
(2) Case government of verbs, e.g. : 
satisfy\[ noun-of-dative-object, ease=dat\]. 
(3) Ordinary' agreement relations where, 
because of the limits of a specific exercise, 
it is not necessary or not possible to speci- 
fy the source of the condition explicitly 
(cut-off ares in the constraint network). 
(4) Word class restrictions, e.g. a noun 
phrase determiner can be an article as well 
as a possessive or demonstrative pronoun: 
415 
satisfy\[det, oat=(art, poss-p, dem-p)\]. 
To achieve a Uniform treatment, internally 
the satisfy-predicates are converted into 
ordinary agreement-predicates between an 
artificially created feature expression at a 
nowhere source (indicated by ***\] and the 
desired destination: 
satisfy\[ noun, case=ace\] 
==> 
agree\[ ***, noun, ease\] . 
A single training exercise usually is de- 
scribed by a number of correctness predicates 
which can be combined to form a simple con- 
straint network. The arcs in this network 
represent correctness predicates and the 
connected nodes ape identified by the source 
and destination arguments. A rather simple 
type exercise is, for example, the correct 
insertion of a German possessive pronoun into 
a carefully generated context like: 
"lob habe Schal und Mutze verloren. 
Hat jemand ... Sachen gesehen?" 
The exercise asks the student to have regard 
to the agreement of the pronoun with both, 
the subsequent noun ("Sachen") and the corre- 
sponding antecedent ("Ich"\]. It results in a 
constraint network consisting of three nodes 
and nine arcs. Two of the nodes (antece- 
dent and noun\] are associated with the con- 
text whereas ~the third (possessive\] repre- 
sents the student's response. The network is 
equivalent to the following list of correct- 
ness predicates: 
satisfy\[ possessive, cat=pose-p\] 
satisfy\[ noun, cat=noun\] 
satisfy\[ antecedent, cat=( noun, peps-p\] \] 
agree\[ antecedent, possessive, stem-number\] 
agree\[ antecedent, possessive, stem-gender\] 
agree\[ antecedent, possessive, stem-person\] 
agree\[ noun, possessive, case\] 
agree\[ noun, possessive, number\] 
agree\[ noun, possessive, gender\]. 
As a slightly more ambitious example 
serve the formation of a German local 
according to the fixed structural pattern 
may 
PP~ 
(preposition determiner adjective noun\] 
to be inserted into sentences like 
"Des Gold habe ich ... gelegt." 
This time the network consists of five nodes 
and 16 edges. All the nodes correspond to 
word forms in the student's response, but 
depending on the sentence context only a 
subset of exaetly four nodes (e.g. (prep-4 
dot adj noun\]\] is instantiated to the 
incoming word forms: 
satisfy\[ prep-3, cat=prep\] 
satisfy\[ prep-3, select=location\] 
satisfy\[ prep-4, cat=prep\] 
satisfy\[ prep-4, select=direction\] 
416 
satisfy\[ noun, cat=noun\] 
satisfy\[ det, cat=( art, pose-p, des-p\]\] 
satisfy\[ adj, oat=adj\] 
agree\[ prep-3, noun, ease\] 
agree\[ prep-4, noun, ease\] 
agree\[ noun, dot, case\] 
agree\[ noun, dot, number\] 
agree\[ noun, dot, gender\] 
agree\[ noun, adj, case\] 
agree\[ noun, adj, number\] 
agree\[ noun, adj, gender\] 
agree\[ det, adj, inflectional-degree\]. 
III. DIAGNOSIS 
Diagnosis is mainly based on constraint 
propagation techniques. The nodes in the 
constraint network are treated as variables 
which receive their values (feature sets) by 
means of a pattern matching procedure on the 
student's input. 
The procedure consists of four parts being 
invoked sequentially. Two of them (the hard 
core of diagnosis\] are intended to detect and 
- if desired to locate errors in the 
student's response. The other two refine 
diagnostic results by applying transforma- 
tional rules and preference criteria in order 
to provide a sound basis for th@ generation 
of appropriate explanations. 
The reason to draw a clear distinction 
between the error detection and localization 
components is one of mere technical nature. 
The separation has been introduced to consid- 
erably speed up the handling of error-free 
utterances, since it allows the time expen- 
sive localization procedure to be activated 
only if indeed an error ocurred and the 
student actually did ask for an explanation 
of his mistake. 
(A\] error detection 
Error detection, in fact, is a direct 
proof procedure for the correctness of the 
utterance. Trying to show the absence of 
errors, it evaluates the relevant predicates 
of the constraint network, taking into con- 
sideration all the morpho-syntactic readings 
of the word forms concerned. The values of 
the network variables ape constantly updated 
according to the results of an ordinary fea- 
ture set unification until finally a state is 
reached which satifies all relevant predi- 
cates simultaneously. 
Given the ease this proof cannot be estab- 
lished, one or possibly several mistakes of: 
the student have to be assumed and upon 
request a detailed analysis of the error 
reasons may become necessary. 
( B\] error localization 
Error localization is carried out by a 
simulation of constraint violations. For 
e a c h predicate in the network the proce- 
dure fol:Lows up the consequences of assuming 
the student did ignore the existence of 
exactly this particular regularity. This 
assumption is modelled by temporarily adding 
the negated predicate to the knowledge base 
and following up its consequences around the 
network. Theoretically such a modification of 
the knowledge base is equivalent to reasoning 
based on Re(tar' s famous "closed world as- 
sumption" (Re(tar, 1978): If you cannot proof 
P, add not(P) to the set of premises. 
By adding it as a premise the diagnosis 
procedur~ treats a negated predicate as no- 
thing more than merely an error hypothesis. 
It can be raised to the level of a confirmed 
error description only after its consequences 
for othc~r predicates in the network have 
carefully been investigated and properly 
recorded. In contrast to a typical short-cut 
solution or a heuristics-based approach the 
diagnosi~ procedure thus carries out a 
thorough analysis of all possible error hypo- 
theses. Hence, it is particularly qualified 
to diagnose multiple faults as well as errors 
with an ambiguous interpretation. 
Technically this kind of reasoning is 
achieved by simply resuming error detection 
with just the logical complement of the usual 
feature unification results• Error detection 
provides for this purpose and collects all 
necessary data on a separate stack. 
Despite the rather' tiny size of a typical 
constraint network, the simulation of con- 
straint violations results in a procedure of 
high complexity and effective measures are 
required to keep the size of the search space 
limited• Hence, in a widely accepted way 
error localization is restricted to the 
search of minimal diagnoses (that is, results 
including only a minimum number of constraint 
violation hypotheses)• 
(C) error transformation 
According to the fundamental distinction 
between rules and facts in a knowledge base 
two different types of misconceptions have to 
be distinguished in the diagnostic results: 
(a) rule violations: the ignorance of cor- 
rectness conditions ( expressed by predicates 
Jn the network) and 
(b) faetual faults: the lack of knowledge 
about specific morpho~syntactic properties of 
a word form (expressed by a feature set in 
the dictionary. 
An integration of both types of misconcep- 
tions into a single diagnosing procedure 
neither yields an efficient solution nor 
turns out to be really necessary. In print(- 
. ple, rule violations and factual faults re- 
pr'esent different views on one and the same 
phenomenon and .a particular error can equally 
well he explained in terms of rules or in 
terms of facts. Both types should be convert- 
ible into each other without much difficulty. 
Accordingly, error localization has been 
designed to exclusively concentrate on the 
analysis of rule violations and to leave open 
the problem of factual faults. A total igno- 
rance of factual faults, of course, would be 
an intolerable restriction on the diagnostic 
capabilities of the system, since then it 
interprets errors of whatever kind in terms 
of rule violations only. 
Hence, a transformational component has 
been added which is able to infer factual 
faults from the hitherto obtained diagnostic 
results. The necessary information is usually 
contained in typical structural error config- 
urations involving the violation of adjoining 
predicates for one and the same morpho- 
syntactic category. One or several simulta- 
neous constraint violations 
and\[ not\[ agree\[ Xi~ Y, C\] \] , 
not\[ agree\[ Xn, Y, C\] \] \] 
or 
and\[ not\[ agree\[ Y, Xi, C\] \], 
not\[ agree\[ Y, Xn, C\] \] \] 
can be transformed into a factual fault 
description, iff 
(i) the set of constraint violations is com- 
plete with respect to Y, i.e. there is no 
other X which appears as source or destina- 
tion argument of a predicate agree\[ X~ Y, C\] or 
agree\[ Y,X, C\] within the knowledge base, and 
(2) consistency holds for all neigbouring 
nodes of Y: agree\[Xi,Xj,C\]. 
Under these circumstances Y is said to be 
isolated with respect to C and without loss 
of generality a new description can be gener- 
ated, stating the student's misconception to 
assume a wrong feature value concerning cate- 
gory C at the word form Y: 
not\[ agree(~** Y, C\] \] 
resp. 
not( agree( Y, ~*, C\] \] 
again using *** to indicate a non-specified 
source or destination. In particular three 
types of structural configurations have to be 
distinguished: 
(I) A single constraint violation concerning 
two isolated nodes X and Y can be transformed 
into two alternative factua\] error 
descriptions: 
not\[ agree( X, Y, C\] \] 
==> 
exor( not\[ agree\[ ***, Y, C\] \] 
not\[ agree( X, **~, C} \] \] . 
(2) A single constraint violation with only. 
, 417 
one isolated node Y is equivalent to a single 
factual error description: 
not\[ agree\[ X, Y, C\] \] ==> not\[ agree{ ***, Y, C\] \] . 
(3) Several constraint violations for an 
isolated node Y can be summarized by a single 
factual error description (c. f. the general 
ease above). 
The decision whether to apply a transforma- 
tion or not is influenced by two criteria, 
the tolerable complexity of diagnostic 
results {it is raised by (I), maintained by 
{ 2) and reduced by (3)) and the intended 
teaehing strategy (e. f. section IV). 
(4) error generalization 
Error generalization aims at an as high as 
possible aggregation of elementary errors 
(constraint violations or factual faults) 
into a more concise description. Generaliza- 
tion schemata can be defined for all three 
argument positions of a violated correctness 
predieate~ e.g. for a category generaliza- 
tion: 
and{ not\[ agree\[X~ Y, CI\]\]~ 
not{ agree\[X,Y, C2\]\]\] 
==> 
not\[agree\[X,Y,(C1,C2)\]\] 
which for the purpose of explanation later 
might be paraphrased like 
"Missing CI and C2 agreement between X 
and Y." 
Other ~eneralization rules are intended to 
collapse alternative diagnostic readings 
which merely are artJ fi~et~ resulting from the 
technical layout of dictionary entries. 
Besides these stringent generalization 
schemes sometimes very weak ones turn out to 
be useful as well. They are partieularly 
suited to generate an at least partially 
comprehensible explanation which in an opaque 
error situation may give a rough indication 
of the error location instead of annoying the 
student with plenty of detail: 
and{ not{ agree\[XI,Y, CI\]\], 
\[ not{ agree{ X2, Y, C2\]\]\] 
==> 
not{ agreeE**x,Y,(C1~C2)\]\]. 
The result of a weak generalization then may 
be explained to the student perhaps in a 
sentence like: 
"There is something wrong with CI 
and C2 at Y." 
Since it is logically incomplete, however, a 
weak generalization can no longer serve as a 
reliable basis to derive repair suggestions 
from, neither for internal use nor for a 
presentation to the student. 
418 
There is some reason to assume the general 
four step scheme of diagnosis not being 
restricted to violations of consistency con- 
straints, but rather being adaptable to other 
types of errors, namely structural ones, as 
well. Again, the procedure has to be based on 
a detection and proper localization of ele- 
mentary error types with respect to a simple 
model of correctness, e.g. a recursion-free 
PSG. In this context the elementary error 
types are substitution, insertion and omis- 
sion of single word forms. Other types (e.g. 
extraposition or mutual interchange of forms) 
can later be inferred from the primary 
results by means of transformation rules. 
Generalization finally allows to condense 
error descriptions into more complex 
structural units (e.g. constituent based 
errors). 
IV. ERROR SELECTION 
Error selection is an integral part of 
several steps of the diagnosis procedure. It 
tries to keep the number of concurrent error 
descriptions as small as possible. Error 
localization selects on the number of primary 
errors per error description, but since 
transformation as well as generalization can 
influence the resulting complexity, their 
results in turn are subject to a decision 
with regard to a minimal number of errors. 
Although the side effect of further re- 
ducing the complexity of minimal diagnoses is 
normally welcomed, error transformations have 
to be sensitive to the intended teaching 
strategy. Diagnosing a constraint violation 
exactly pinpoints the conceptual mistake of 
the student but does not always give useful 
hints about where to correct the utterance. 
In these cases, despite being more complex, 
an indication of factual faults may sometimes 
be more helpful, since it better points out 
the existing possibilities for an improvement 
o~ the partially wrong solution. 
On the other hand, even less complex 
factual faults may be quite undesired if they 
result in doubtful correction proposals (e.g. 
in a given semantic context a gender-of-the- 
noun error can hardly be repaired by simply 
exchanging the noun in question). 
Despite the selection of minimal diagnoses 
on several levels, sometimes the diagnosing 
component provides a number of alternative 
minimal diagnoses. They finally are evaluated 
and weighted accordi"g to a number of prefer- 
ence criteria: 
(a) a structural measure which depending on 
whether a conceptual description or a repair 
suggestion is preferred may select errors 
higher up or deeper down in a hierarchical 
syntactic representation of the utterance, 
(b) the degree to which an error explanation 
can be assumed to be helpful for the student 
(if possible, certai, types of explanations 
are suppressed), 
(c) hints, resulting from an obstinate repe- 
tition of one and the same error type. 
V. CONCLUSIONS 
absolutely exact localization of an error 
either by pointing out the erroneous form 
(plus the categories and values involved) or 
by properly reflecting an ambiguous correc- 
tion possibility: 73 percent. 
approximative localization by only indi~ 
caring the violated constraint predicate 
without being able to decide between source 
or destination: 23 percent. 
Although it is connected with a number of 
interesting advantages, deep modelled reason- 
ing clearly should not be considered the sine 
qua non of future tools for language instruc- 
tion. Based on the very idea of a closed 
world, it is by definition limited to the 
rather narrow domains of knowledge about 
natural language which allow a highly relia- 
ble and complete description of the necessary 
correctness conditions. Unfortunately, nei- 
ther high precision nor completeness can well 
be attributed to major parts of currently 
available grammar models. 
Nevertheless, two possibilities for an 
advantageous application of the , presented 
diagnosis procedure can be identified even 
today: 
bad localization either by returning sev- 
eral rule violations or by ignoring an alter- 
native correction possibility: 4 percent. 
Notice that not a single instance of wrong, 
that is~ misleading diagnostic results 
occurred. 
The system currently runs on 16-bit-micros 
(with drastic reductions on 8-bit-micros, as 
well) and has been tested on a number of 
non-trivial exercises for German. Experience 
has shown that the approach allows diversi- 
fied and intensive training and supplies 
surprisingly precise explanations for most of 
the erroneous utterances. 
(I) "stand alone" use in simple 
exercises similar to the examples 
in section II. 
agreement 
presented 
References 
(2) integration of the procedure as a spe- 
cialized subroutine into an error sensitive 
parser (whether it be surface oriented or 
deep modelled) to replace currently used 
heuristics for consistency cheek. 
FolI.owing the first opening a prototype 
system has bean realized which integrates the 
diagnosing procedure into a learning environ- 
ment. Besides the guiding advice of the sen-- 
tential context additional measures have been 
taken to avoid the student feeling uneasy 
about the limitations of the fixed structural 
input pattern. Using a menu-ba~ed input mo~e 
it is possible not only to inspect the dic- 
tionary at run time but also to select appro- 
priate word forms from it. Thu~ a quick and 
convenient interaction facility is offered 
and the student is encouraged to construct 
his solution in a toy kit manner from the 
available stock of word forms. 
To valuate the diagnostic capabilities of 
the approach a quality measurement has been 
carried out using the constraint network of 
the second exercise sample of section II 
(formation of a local PP). The valuation has 
been based on the observation that for prac- 
tical purposes the ability to precisely io- 
. care single word form errors is of most im- 
portance. An exhaustive analysis of all in- 
stances of arti.ficially implanted single word 
form substitutions (including rather "exotic" 
ones as well) yielded the following results: 

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