An RP is said to be applicable to an r-graph G i f f EDGES~EDGES G and the values in N~sare subsets 6f corresponding values in NPofor each node in LS... AFTER: Node properties as above
Trang 1A MULIIDIMENSIONAL APPROACH TO PARSING HIGHLY INFLECTIONAL LANGUAGES
Eero Hyv~nen He]sJnkJ I J n i v e r s i t y o f TechnoloQy
D i a J t a l SysLems L a b o r a t o r y
O t a k a a r J 5A n215n Espoo 15 FINLAND
A B S T R A C T
The s t r u c t u r e of many languages with
"free" word order and r i c h morphology l i k e
Finnish is rather c o n f i g u r a t i o n a l than
l i n e a r Although n o n - l i n e a r s t r u c t u r e s
can be represented by l i n e a r formalisms i t
is often more natural to study
multidimensional arrangement of symbols
Graph grammars are a multidimensional
g e n e r a l i z a t i o n of l i n e a r s t r i n g grammars
In graph grammars s t r i n g r e w r i t e rules are
generalized i n t o g r a p h r e w r i t e r u l e s
This p a p e r presents a g r a p h grammar
formalism and parsing scheme f o r parsing
languages with inherent c o n f i g u r a t i o n a l
f l a v o r A small experimental Finnish
parsing system has b e e n implemented
(Hyv6nen 1983)
A SIMPLE GRAPH GRAMMAR FORMALISM
WITH A CONTROL FACILITY
In applying s t r i n g grammars to parsing
natural Finnish several problems arise in
representing c o m p l e x w o r d s t r u c t u r e s ,
argeements, " f r e e " w o r d ordering,
d i s c o n t i n u i t y , and intermediate depencies
between morphology, syntax and semantics
A strong, multidimensional formalism that
can cope with d i f f e r e n t l e v e l s of language
seems necessary In t h i s chapter a graph
grammar formalism based on the notions of
r e l a t i o n a l graph grammars ( R a j l i c h 1975)
and a t t r i b u t e d programmed graph grammars
(Bunke 1982) is developed f o r parsing
languages with c o n f i g u r a t i o n a l s t r u c t u r e
D e f i n i t i o n 1.1 ( r e l a t i o n a l graph, r-graph)
Let ARCS, NODES, and PROPS be f i n i t e sets
of symbols A r e l a t i o n a l graph (r-graph)
RG i s pair RG = (EDGES, NP) c o n s i s t i n g of
a set of edges
EDGES, ARCSxNODESxNODES
and a f u n c t i o n liP t h a t associates each
node in EDGES to a set of labeled
property values:
tJP: NODESxPROPS -> PVALUES
PVALUES is the set of possible node
property values T h e y are represented as sets of symbols or l i s t s
Example: Figure I 1 depicts the morphological r-graph representation of Finnish word "ihmisten" (the humans') and
i t s edges as a l i s t EXT-property expresses the set of symbols the node
c u r r e n t l y r e f e r s to ( e x t e n s i o n ) ; CAT
t e l l s the syntactico-semantic category of the node
C~L~£ NR [XT.(PL)
[XT- {IHNINEN) CAT- (SUBST- I HHINEN)
((NOUN N1 N2) (C#3E NI N3) (NR Nl N4) (PERS Nl N5) (PS Nl N6) (EP Nl N7))
Fig 1.1 Morphological r-graph representation of w o r d "ihmisten" (the humans)
D e f i n i t i o n 1.2 ( r - p r o d u c t i o n )
An r - p r o d u c t i o n RP i s a p a i r :
RP = (LS, RS)
LS ( l e f t side) and RS ( r i g h t side) are r-graphs An RP is said to be applicable
to an r-graph G i f f EDGES~EDGES G and the values in N~sare subsets 6f corresponding values in NPofor each node in LS
D e f i n i t i o n 1.3 ( d i r e c t r - d e r i v a t i o n ) The d i r e c t r - d e r i v a t i o n of r-graph H from r-graph G via an r - p r o d u c t i o n RP = (LS, RS) i s defined by the f o l l o w i n g algorithm: Algorithm 1.1 ( D i r e c t r - d e r i v a t i o n )
I n p u t : An r-graph G and
an r - p r o d u c t i o n RP = (LS, RS) Output: An r-graph H derived via RP
from G
Trang 2PROCEDURE Di rect-r-deri vation :
BEGIN
IF RP is applicable to G (see text)
THEN
EDGES G := EDGES G - EDGESLs
H :=GURS
RETURN H
ELSE
RETURN "Not applicable"
END
Here U is an operation defined f o r two
r-graphs RGI and RG2 as f o l l o w s :
H = RGI I~ RG2
i f f
EDGES H = EDGESRG 1 U EDGESRG 2 a n d
NPw(ni, propj) = NPDr.~(ni, propj) for any
priJperty propj in every node ni in RG2
Time complexity: D i r e c t r - d e r i v a t i o n s are
e s s e n t i a l l y set operations and can be
performed e f f i c i e n t l y By using a hash
table the expected time complexity i s O(n)
w i t h respect to the size of the production
( i t d o e s not depend on the size of the
object graph) The worst c a s e complexity
i s O(n**2)
Example: Figure 1.2 represents an
r - p r o d u c t i o n and f i g u r e 1.3 i t s
a p p l i c a t i o n to an r-graph We have
designed a meta-production d e s c r i p t i o n
f a c i l i t y f o r r - p r o d u c t i o n s by which
match-predicates can be attached to nodes
and arcs in order to t e s t and modify node
properies The i n s t a n t i a t i o n of a
context-dependently w h i l e matching the
production l e f t side I t i s also possible
to specify some special m o d i f i c a t i o n s to
the d e r i v a t i o n graph by meta-productions
)
Fig 1.2 Production ADJ-ATTR
i d e n t i f y a d j e c t i v e a t t r i b u t e s
to
D e f i n i t i o n 1.4 (r-graph gralnmar and
r-graph language)
An r-graph grammar (RGG) i s a p a i r :
RGG = (PROD, START)
PROD i s a set of r - p r o d u c t i o n s and START
i s a set of r-graphs
An r-graph language (RGL) generated by an r-graph grammar i s the set of a l l derivable r-graphs f r o m any r-graph in START by any sequence of a p p l i c a b l e
r - p r o d u c t i o n s of PROD:
RGL ={R-graphISTART =,~R-graph!
EXT-fPL) EXT-{~ PL)
• ~T~U~T I F CM.ANECilVE CM-IIOUtt-ABST EXT=(eO~-ALL) EXT.{BIG) [XT=(PRCG
AFTER:
(Node properties as above)
Fig 1.3 The e f f e c t of applying production ADJ-ATTK ( f i g 1.2) to an r-graph
D e f i n i t i o n 1.5 ( c o n t r o l l e d r-graph grammar)
A c o n t r o l l e d r-graph grammar (CRG) is a
p a i r : CRG = (CG, RGG)
CG i s an r-graph c a l l e d control graph ( c - g r a p h ) I t s i n t e r p r e t a t i o n is defined very much in the same way as w i t h ATN-networks The actions associated to arcs are d i r e c t r - d e r i v a t i o n s ( d e f 1.3) RGG i s an r-graph grammar ( d e f 1 4 ) Example: Figure 1.4 i l l u s t r a t e s a c-graph expressing p o t e n t i a l a t t r i b u t e
c o n f i g u r a t i o n s of n o u n s belonging to category !JOUN-HUMAN A d j e c t i v e , pronoun and genetive a t t r i b u t e s and a q u a n t i f i e r may be i d e n t i f i e d hy corresponding
r - p r o d u c t i o n s (the meaning of (READWORD)- and (PUT-LAST)-arcs is not r e l e v a n t here)
Trang 3PRON-ATTR
Fig 1.4 A control g r a p h expressing
a t t r i b u t e c o n f i g u r a t i o n s of
syntactico-semantic w o r d category
NOUN-HUHAN
D e f i n i t i o n 1.6 ( C o n t r o l l e d graph language)
A c o n t r o l l e d g r a p h language (CGL)
corresponding to a c o n t r o l l e d r-graph
grammar CRG = (CG, RGG) is the set of
r-graphs derived by the CG using the s t a r t
graphs START and the productions of the
grammar RGG
2 A GRAPH GRAIItIAR PARSING SCHEME
2.1 Function and s t r u c t u r e
Figure 2.1 depicts a RGG-based parsing
scheme that we have applied to natural
language parsing Roughly s p o k e n , the
i n p u t of the parser, i e the set START
of a CRG, i s the morphological
representation(s) of a sentence The
output i s a set of corresponding semantic
deep c a s e representations Parsing is
~een as a multidimensional transformation
between the morphological and semantic
l e v e l s of a language T h e s e l e v e l s are
seen as g r a p h languages The parser
e s s e n t i a l l y defines a "meaning preserving"
mapping from the morphological
representations of a sentence i n t o i t s
semantic representations The
transformation is specified by a
c o n t r o l l e d r-graph grammar The control
graph is not predefined but i s constructed
dynamically according to the i n d i v i d u a l
words of the c u r r e n t sentence During
parsing morphological and semantic
representations are generated in p a r a l l e l
as words are read from l e f t to r i g h t
2.2 S p e c i f i c a t i o n of the morphological
and semantic graph languages
Morphological l e v e l The morphological
representation of a sentence consists of
s t a r - l i k e morphological representations of
the w o r d s ( f i g 1.1) t h a t are glued
togetiler by sequential >- and < - r e l a t i o n s
( f i g 1 3 )
Semantic l e v e l The semantic
representatien of a sentence consists of a
semantic deop case s t r u c t u r e corresponding
tc Lhe main verb Deep case c o n s t i t u e n t s
have t h e i r own semantic c a s e s t r u c t u r e s
corresponding to t h e i r main words
SOURCE GRAPH LANGUAG£
MORPHOLOGY
C o n t r o l l e d r - n r a p h c-~M
INTERPRE~R
g ramma r (CRG', /
i
GOAL GRAPH LANGUAGE
/ 3
SEtIANTI CS
\ PRODUCTIONS j
Fig 2.1 A parsing scheme for transforming
graph languages
Example: Figure 2.2 i l l u s t r a t e s the semantic representation of question " Kuka
l u e n n o i t s i j a on luennoinut jonkun
t i e t o j e n k ~ s i t t e l y t e o r i a s t a syksyll~ 1981" ("Which l e c t u r e r has l e c t u r e d some seminar-type course on computer science in the autumn 1981")
MAZN
Fig 2 2 Semantic graph representation of
a Finnish question Node properties are not shown
2.3 S p e c i f i c a t i o n of the graph language transformation
The transformation i s s p e c i f i e d by an agenda of p r i o r i t i z e d c-graphs
I n i t i a l l y , the agenda consists of a set of sentence independent " t r a n s f o r m a t i o n a l " c-graphs ( t h a t , f o r example, transform passive clauses i n t o a c t i v e o n e s ) and
Trang 4sentence dependent c-graphs corresponding
to the syntactico-semantic categories of
the i n d i v i d u a l words in the sentence For
example, the c-graph of f i g 1.4
corresponds to nouns belonging to category
NOUN-HUMAN I t t r i e s to i d e n t i f y semantic
case c o n s t i t u e n t s by the productions
corresponding to the arcs Fig 1.2
i l l u s t r a t e s the production ADJ-ATTR
( a d j e c t i v e a t t r i b u t e ) used i n the c-graph
of f i g 1.4 The i n t e r p r e t a t i o n of the
production i s : I f there is an a d j e c t i v e
preceeding a noun in the same c a s e and
number the w o r d s are in semantic KIND
r e l a t i o n w i t h each other As a whole, the
agenda c o n s t i t u t e s a modular, sentence
dependent c-graph
Parsing i s performed by i n t e r p r e t i n g the
agenda D i f f e r e n t s t r a t e g i e s could be
applied here; the s t r u c t u r e of the
c-graphs depend on the choice In our
experimental system parsing i s performed
by i n t e r p r e t i n g the f i r s t c-graph i n the
agenda The c-graohs are defined in such
way t h a t they interpret each other and glue
morphological representations of words
i n t o the d e r i v a t i o n graph (arcs (READWORD)
and (PUTLAST) in f i g 1.4) u n t i l a
grammatical semantic representation (or in
ambiguous cases several ones) i s reached
2.4 L i n g u i s t i c and computational
motivations
Most i n f l u e n t i a l l i n g u i s t i c t h e o r i e s and
ideas behind our parser are dependence
grammar, semantic c a s e grammar, and the
notion of "word expert" parsing The idea
is t h a t the c-graphs of w o r d categories
a c t i v e l y t r y to f i n d the dependents of the
main words and i d e n t i f y i n what semantic
roles they are ( c f the
ADJ-ATTR-production of f i g 1 2 ) In
some cases i t i t useful to assign a c t i v e
role to dependents The c-graphs serve as
i l l u s t r a t i v e l i n g u i s t i c d e s c r i p t i o n s of
the syntactico-semantic features of word
categories and other fenomena
Computationally, our formalism and parsing
scheme gives high expressive power but i t s
time complexity i s not high Only
p o t e n t i a l l y r e l e v a n t productions are t r i e d
to use during parsing Graphs are
i l l u s t r a t i v e and can be used to express
both procedural and d e c l a r a t i v e knowledge
New w o r d category models can be added to
the parser r a t h e r independently f r o m the
other models
Our small experimental g r a p h grammar
parser f o r Finnish (Hyv6nen 1983) is s t i l l
l i g u i s t i c a l l y quite naive c o n t a i n i n g some
150 l e x i c a l e n t r i e s , 50 productions, and
50 c-graphs A l a r q e r subset of Finnish
needs to be modelled in order to evaluate
the approach p r o p e r l y We are c u r r e n t l y
developing the graph grammar approch
f u r t h e r by g e n e r a l i z i n g the formalism i n t o
h i e r a r c h i c graphs By t h i s w a y , f o r example, large graph s t r u c t u r e s could be manipulated more e a s i l y as s i n g l e e n t i t i e s and i d e n t i c a l s t r u c t u r e s could have
d i f f e r e n t i n t e r p r e t a t i o n s in d i f f e r e n t contexts Also, a m o r e elaborate coroutine b a s e d control s t r u c t u r e f o r
i n t e r p r e t i n g the c-graphs is under developement We feel t h a t the idea of seeing parsing as a multidimensional transformation of r e l a t i o n a l graphs in stead of as a d e l i n e a r i z a t i o n process of a
s t r i n g i n t o a parse tree i s worth
i n v e s t i c a t i n g f u r t h e r
3 ACKNOWLEDGEMENTS Thanks are due to Rauno Heinonen, Harri J~ppinen, Leo Ojala, J o u k o Sepp~nen and the personnel of D i g i t a l Systems Laboratory f o r f r u i t f u l discussions Finnish A c a d e m y , Finnish C u l t u r a l Foundation, S i e m e n s Foundation, and Technical Foundation of Finland have supported our work f i n a n c i a l l y
4 REFERENCES Bunke H (1982): A t t r i b u t e d g r a p h grammars and t h e i r a p p l i c a t i o n to schematic d i a g r a m i n t e r p r e t a t i o n IEEE Trans of pattern a n a l y s i s and machine
i n t e l l i g e n c e , No 6, pp 574-582
Hyv~nen E (1983): G r a p h grammar approach to natural language parsing and understanding Proceedings of IJCAI-83, Karlsruhe
Rajlich V (1975): Dynamics of d i s c r e t e
s t r u c t u r e s and pattern reproduction Journal of computer and s y s t e m sciences,
No 11, pp 186-202