Báo cáo khoa học: "MODULAR LOGIC GRAMMARS" ppt

1980, it is possible to build logical forms approach... building of analysis structures .either logical forms or syntactic trees must be specified ex- modularity is then lost, because th

MODULAR LOGIC GRAMMARS

Michael C McCord IBM Thomas J Watson Research C e n t e r

P O Box 218

Y o r k t o w n H e i g h t s , N Y 10598

A B S T R A C T

This report d e s c r i b e s a logic g r a m m a r formalism,

Modular Logic Grammars, e x h i b i t i n g a high d e g r e e

of m o d u l a r i t y b e t w e e n syntax and semantics T h e r e

is a s y n t a x rule c o m p i l e r ( c o m p i l i n g into Prolog)

s t r u c t u r e s and the interface to a c l e a r l y s e p a r a t e d

s e m a n t i c i n t e r p r e t a t i o n c o m p o n e n t d e a l i n g w i t h

s c o p i n g and the c o n s t r u c t i o n of logical forms The

w h o l e system can w o r k in either a o n e - p a s s mode or

forms are built d i r e c t l y d u r i n g p a r s i n g through

i n t e r l e a v e d calls to semantics, added a u t o m a t i c a l l y

two devices w h i c h cause the a u t o m a t i c a l l y built

s y n t a c t i c s t r u c t u r e s to differ from d e r i v a t i o n trees

d e a l i n g w i t h l e f t - e m b e d d i n g c o n s t r u c t i o n s such as

E n g l i s h p o s s e s s i v e noun phrases w h i l e u s i n g right-

r e z u r s i v e rules (which are a p p r o p r i a t e for Prolog

parsing) (2) T h e r e is a d i s t i n c t i o n in the syn-

tactic f o r m a l i s m between s t r o n g n o n - t e r m i n a l s and

w e a k n o n - t e r m i n a l s , w h i c h is important for distin-

g u i s h i n g m a j o r levels of grammar

I INTRODUCTION

a logic p r o g r a m m i n g system ( i m p l e m e n t e d n o r m a l l y

in P£olog), w h i c h associates s e m a n t i c represent-

ations Cnormally in some v e r s i o n of p r e a i c a t e logic)

v a r y i n g degrees on m o d u l a r i t y in their t r e a t m e n t s

an isolatable s y n t a c t i c component

In w r i t i n g metamorpilosis g r a m m a r s (Colmerauer,

cial case of m e t a m o r p h o s i s g r a m m a r s , P e r e i r a and

Warren 1980), it is possible to build logical forms

approach T h e r e is c e r t a i n l y an appeal in b e i n g

dicect, but there are some d i s a d v a n t a g e s in this

seems d i f f i c u l Z to get an adequate t r e a t m e n t of the

s c o p i n g of q u a n t i f i e r s (and m o r e g e n e r a l l y

focalizers, McCord, 1981) w h e n the b u i l d i n g of log- ical forms is too c l o s e l y b o n d e d to syntax A n o t h e r

d i s a d v a n t a g e is just a general result of lack of

m o d u l a r i t y : it can be harder to d e v e l o p and un-

d e r s t a n d s y n t a x rules w h e n too m u c h is g o i n g on in them

The logic g r a m m a r s d e s c r i b e d in M c C o r d (1982, 1981) w e r e t h r e e - p a s s systems, w h e r e one of the m a i n points of the m o d u l a r i t y was a good t r e a t m e n t of scoping T h e first pass was the s y n t a c t i c compo- nent, w r i t t e n as a d e f i n i t e clause grammar, w h e r e

s y n t a c t i c s t r u c t u r e s were e x p l i c i t l y built up in the a r g u m e n t s of the n o n - t e r m i n a l s W o r d s e n s e

s e l e c t i o n and s l o t - f i l l i n g were done in this first pass, so that the o u t p u t analysis trees w e r e actu- ally p a r t i a l l y semantic The s e c o n d pass was a

p r e l i m i n a r y stage of s e m a n t i c i n t e r p r e t a t i o n in

w h i c h the s y n t a c t i c analysis tree was r e s h a p e d to reflect p r o p e r s c o p i n g of modifiers The third pass took the r e s h a p e d tree and p r o d u c e d logical forms

in a s t r a i g h t f o r w a r d w a y by c a r r y i n g out modification

of nodes by their d a u g h t e r s u s i n g a m o d u l a r s y s t e m

of rules that m a n i p u l a t e semantic items c o n s i s t -

ing of logical forms together w i t h terms that de- termine how they can combine

pass is a p u r e l y s y n t a c t i c c o m p o n e n t u s i n g an

extrapositJon g r a m m a r (Pereira, 1981) and p r o d u c i n g

s y n t a c t i c analyses in r i g h ~ o s t n o r m a l form The

s e c o n d pass handles w o r d sense s e l e c t i o n and slot-

p h e n o m e n a and the final s e m a n t i c interpretation One gets a great deal of m o d u l a r i t y b e t w e e n s y n t a x and s e m a n t i c s in that the first c o m p o n e n t has no elements of s e m a n t i c i n t e r p r e t a t i o n at all

In M c C o c d (1984) a o n e - p a s s s e m a n t i c inter-

p r e t a t i o n component, SEM, for the EPISTLE s y s t e m {Miller, H e i d o r n and Jensen, 1981) was d e s c r i b e d

g r a m m a r (Heidorn, 1972, J e n s e n and Heidorn, 1983),

as w e l l as to a logic grammar, SYNT, w r i t t e n as a DCG by the author T h e s e grammars are p u r e l y syn-

tactic and use the E P I S T L E n o t i o n (op cir.) of

approximate parse, w h i c h is s i m i l a r to P e r e i r a ' s

n o t z o n of r i g h ~ s ~ n o r m a l form, but was d e v e l o p e d

w i t h a c l e a r m o d u l a r i t y b e t w e e n s y n t a x and s e m a n - tics

building of analysis structures (either logical

forms or syntactic trees) must be specified ex-

modularity is then lost, because the grammar writer

must be aware of manipulating these structures, and

the possibility of using the grammar in different

grammar formalism was described, modifier structure

g r a m m a r s (HSG's), in which structure-building (of

grammars, with the additional ingredient that se-

mantic items (of the type used in McCord (1981))

can be indicated on the left-hand sides of rules,

and contribute automatically to the construction

HcCord (1981) These MSG's were used interpretively

in parsing, and then (essentially) the two-pass

three passes in this system

grammar system, m o d u l a r logic g r a m m a r s (MLG's),

with the following features:

There is a syntax rule compiler which takes care

of the building of analysis structures and the

interface to semantic interpretation

There is a clearly separated semantic inter-

the construction of logical forms

The whole system (syntax and semantics) can work

optionally in either a one-pass mode or a two-

pass mode

In the one-pass mode, no syntactic structures

are built, but logical forms are built directly

during parsing through interleaved calls to the

semantic interpretation component, added auto-

matically by the rule compiler

in the two-pass mode, the calls to the semantic

interpretation component are not interleaved,

but are made in a second pass, operating on

ically) in the first pass

left-embedding constructions such as English

possessive noun phrases ("my wife's brother's

friend's car") and Japanese relative clauses

~ne shift operator instructs the rule compiler

to build the structures appropriate for left-

trees, because the syntax rules are right-re-

cursive, because of the top-down parsing asso-

formalism between strong non-terminals and w e a k

non-terminals, which is important for distin-

guishing major levels of grammar and which

simplifies the working of semantic interpreta-

much more readable and natural linguistically

In the absence of shift constructions, these trees are like derivation trees, but only with nodes corresponding to strong non-terminals [n an experimental MLG, the semantic component handles all the scoping phenomena handled by that in McCord (1981) and more than the semantic

language is improved over that in the previous systems

The MLG formalism allows for a great deal of modu- larity in natural language grammars, because the

awareness of semantics or the building of analysis structures, and the very same syntactic component can be used in either the one-pass or the two-pass mode described above

Three other logic grammar systems designed with modularity in mind are Hirschman and Puder (1982), Abramson (1984) and Porto and Filgueiras (198&) These will be compared with MLG's in Section 6

2 THE MLG S Y N T A C T I C F O R M A L I S M The syntactic component for an MLG consists

[aration of strong non-terminals is of the form strongnonterminals(NTI.NT2 NTn.nil) where the NTi are the desired strong non-terminals

distinction will be explained below

MLG s y n t a x rules are of the form

A ~ -> B where A is a n o n - t e r m i n a l and B i s a r u l e b o d y A

r u l e b o d y i s any c o m b i n a t i o n o f surlCace t e r m i n a l s ,

logical terminals, goals, s h i f t e d n o n - t e r m i n a l s , non-tprminals, the symbol 'nil', and the cut symbol '/', using the sequencing operator ':' and the 'or'

with a colon instead of a comma, as is often done

Prolog terms (normally with arguments), and they are distinguished formally as follows

spond to ordinary terminals in DCG's (they match elements of the surface word string), and the notation is often [A] in DCG's

A l o g i c a l t e r m i n a l i s o f t h e form 0 p - L ~ , where

Op i s a m o d i f i c a t i o n o p e r a t o r and LF i s a l o g i c a l

s e m a n t i c i t e m s , the significance of which will

T h e r e can be any n u m b e r of them in a rule body

A goal is of the form $A, w h e r e A is a term re-

p r o v i s i o n for Prolog p r o c e d u r e calls, w h i c h are

often i n d i c a t e d by e n c l o s u r e in braces in

DCG's.)

A s h i f t e d non-terminal is either of the f o r m % A ,

or of the form F%A, w h e r e A i s a w e a k non-

the introduction, the shift o p e r a t o r '~' is used

to handle l e f t - e m b e d d i n g c o n s t r u c t i o n s in a

r i g h t - r e c u r s i v e ~ule system

forms and not 'nil' or the cut symbol is taken

to be a non-terminal

A terminal is either a surface terminal or a

amalysis structures

A syntax rule is c a l l e d s t r o n g or w e a k , .,u-

is s t r o n g or weak

It can be seen that on a purely formal level,

the only d i f f e r e n c e s b e t w e e n HLG syntax rules and

in rule bodies of MLG's, (2) the use of ~he shift

operator, and (3) the d i s t i n c t i o n b e t w e e n s t r o n g

guistic coverage, the s y n t a c t i c c o m p o n e n t of an MLG

will n o r m a l l y be more compact than the c o r r e s p o n d i n g

DCG because s t r u c t u r e - b u i l d i n g must be ,~xplicit in

DCG's In this report, the arrow ' >' (as o p p o s e d

to ' : > ' ) will be used for for DCG rules, and the

same n o t a t i o n for sequencing, terminals, etc will

be used for DCG's as for MLG's

What is the s i g n i f i c a n c e of the s t r o n g / w e a k

d i s t i n c t i o n for n o n - t e r m i n a l s and rules? Roughly,

a strong rule should be thought of as i n t r o d u c i n g

a new l®vel of grammar, w h e [ e a s a w e a k rule d e f i n e s

analysis w i t h i n a level M a j o r c a t e g o r i e s like

s e n t e n c e and n o u n p h r a s e are e x p a n d e d by s t r o n g

rules, but a u x i l i a r y rules like the reoursive rules

that find the p o s t m o d i f i e r s of a verb are w e a k

strong n o n - t e c m i n a l s are like the start c a t e g o r i e s

of s u b n e t w o r k s (with s t r u c t u r e - b u i l d i n g POP arcs

for termination), w h e r e a s w e a k n o n - t e r m i n a l s are

llke internal nodes

makes the f o l l o w i n g d i s t i n c t i o n for s t r o n g and w e a k

rules In the Horn clause ~ r a n s l a t i D n of a s t r o n g

~11e, a call to the s e m a n t i c i n t e r p r e t a t i o n compo-

nent is c o m p i l e d in at the end of the clause The

n o n - t e r m i n a l s a p p e a r i n g in rules (both s t r o n g and

weak) are given extra a r g u m e n t s w h i c h m a n i p u ! a K e

semantic s t r u c t u r e s used in the call to s e m a n t i c

p i l e d in for weak rules W e a k rules o n l y g a t h e r

g e n e r a t e s a call to s e m a n t i c s )

In the two-pass mode, w h e r e s y n t a c t i c a n a l y s i s

c o m p i l e r builds in the c o n s t r u c t i o n of a tree node

c o r r e s p o n d i n g t o e v e r y s t r o n g rule T h e node is labeled e s s e n t i a l l y by the n o n - t e r m i n a l a p p e a r i n g

also g e n e r a t e s the c o n s t r u c t i o n of a tree node.) Details of rule c o m p i l a t i o n will be g i v e n in the next section

As indicated above, logical terminals, and m o r e

g e n e r a l l y s e m a n t i c items, are of the form

O p e r a t o r - L o g i c a l F o r m The O p e r a t o r is a term w h i c h d e t e r m i n e s how the semantic item can combine with o t h e r s e m a n t i c items

d u r i n g semantic interpretation (In this c o m b i n a - tion, new s e m a n t i c items are formed w h i c h ;ire no

most typically a s s o c i a t e d w i t h lexical items, al-

l e x i c a l i n g r e d i e n t s in l o g i c a l form a n a l y s i s An example for the lexical item "each" might be Q/P - e a c h ( P , Q )

Here the o p e r a t o r Q/P is such that w h e n the "each"

man(X), P gets u n i f i e d w i t h man(X), and the re-

s u l t i n g semantic item is

@ Q - each(~.an(X),Q)

w h e r e @q is an operator which causes Q t o get uni- fied w i ~ h the logical form of a further m o d i f i c a n d Details ,Jr the dse of s e m a n t i c items will be g i v e n

Now let us look at the s y n t a c t i c c o m p o n e n t of

a sample HLG w h i c h covers the same g r o u n d a s a

m a n i p u l a t i n g partial logical forms in a r g u m e n t s of the grammar symbols

s e n t f P ) > np(X,PI,P): vp(X,Pl)

np(X,P~,P) ~ d e t f P 2 , P I , P ) : noun(X,P3):

r e l c l a u s e ( X , P 3 , P 2 )

n p ( X , P , P ) - - > n a m e ( X )

v p ( X , P ) - - > t r a n s v e r b f X , Y , P l ) : n p ( Y , P l , P )

v p f X , P ~ - - > i n t r a n s v e r b ( X , P )

r e l c b t u s e ( X , P l , P l & P 2 ) - - > + t h a t : v p ( X , P 2 )

r e l c ~ a u s e ( * , P , P ) - - > n i l

d e t ( P I , P 2 , P ) - - > +D: $ d t ~ D , P I , P 2 , P ) nounfX,P) > +N: SnfN,X,P)

name(X) - - > +X: $ n m ( X )

t r a n s v e r b ( X , Y , P ) - - > +V: $ t v ( V , X , Y , P )

i n t r a n s v e r b ( X , P ) - - > +V: $ i v ( V , X , P ) / ~ L e x i c o n * /

n(maa,X,man(X) ) n(woman, X,woman ( X ) )

~ ( j o h n ) nm(mary)

d t ( e v e r y , P 1 , P 2 , a l l ( P 1 , P 2 ) )

d t ( a , P I , P 2 , e x ( P l , P 2 ) )

t v ( l o v e s , X , Y , l o v e ( X , Y ) )

i v ( l i v e s , X , l i v e ( X ) )

T h e s y n t a c t i c c o m p o n e n t of an analogous H L G is as

g r a m m a r will be c a l l e d MLGRAH

s t r o n g n o n t e r m i n a l s ( s e n t n p r e l c l a u s e d e t n i l )

sent ~ > np(X): vp(X)

np(X) = > dec: noun(X): relclause(X)

np(X) ~ > name(X)

relclause(X) ~ > +that: vp(X)

relclause(*) ~ > nil

d e t ~ > +O: S d t ( D , P 1 , P 2 , P ) : P Z / P I - P

n o u n ( X ) > +N: S n ( N , X , P ) : I - P

name(X) ~ > +X: Snm(X)

i n t r a n s v e r b ( X ) = > +V: $iv(V,X,P): l-P

This small grammar illustrates all the ingredients

and 'np' are s t r o n g c a t e g o r i e s but 'vp' is weak

A result is that there will be no call to s e m a n t i c s

at the end of the 'vp' rule Instead, the s e m a n t i c

s t r u c t u r e s a s s o c i a t e d w i t h the verb and object are

p a s s e d up to the 'sent' level, s o that the subject

and object are "thrown into the same pot" for se-

is not forgotten.)

T h e r e are o n l y two types of m o d i f i c a t i o n op-

erators a p p e a r i n g in the semantic items of this MLG:

m o d i f i c a n d (although its use in this small grammar

lustrated above

The semantic c o m p o n e n t will be given below in

sentence "Every m a n that lives loves a w o m a n " is

a l l ( m a n ( X l ) & l i v e ( X l ) , e x ( w o m a n ( X 2 ) , l o v e ( X l , X 2 ) ) )

show a sample parse in the next section

A fragment of an M L G illustrating the use of

phrases is as follows:

np ~ -> deC: n p l

n p l = > p r e m o d s : n o u n : np2

vp2 ~ > p o s t m o d s

np2 ~ > p o s s : % n p l

np, one reads an o r d i n a r y d e t e r m i n e r (deC), then

reading p o s t m o d i f i e r s (postmods), O R one m a y read

an a p o s t r o p h e - s (poss) and then S H I F T back to npl

I l l u s t r a t i o n for the n o u n phrase, "the old man's

d u s t y hat":

np det npl premods noun np2 poss %npl

premods noun np2 postmods

s t r u c t u r e s (in the two-pass mode) are m a n i p u l a t e d (in the c o m p i l e d rules) so that the initial np ("the old man") becomes a left-embedded s u b - s t r u c t u r e of

a p o s t r o p h e - s is encountered, then the s t r u c t u r e for

"the old man" remains on the top level

3 C O M P I L A T I O N O F M L G S Y N T A X R U L E S

In d e s c r i b i n g rule compilation, we will first look at the two-pass mode, where s y n t a c t i c struc- tures are built in the first pass, because the re- lationship of the analysis s t r u c t u r e s to the syntax rules is more direct in this case

c o m p i l e d rules are represented as s y n t a c t i c i t e m s ,

w h i c h a r e t e r m s o f t h e f o r m

syn(Features,Oaughters)

where Features is a feature list (to be defined), and

D a u g h t e r s is a list c o n s i s t i n g of s y n t a c t i c items

p l a y i n g procedures for s y n t a c t i c structures can

o p t i o n a l l y filter out one or the other of the two types A f e a t u r e l i s t is of the form nt:Argl, where

nt is the principal fun=tot of a s t r o n g n o n - t e r m i n a l

large grammars, to use this first argument Argl to hold a list (based on the o p e r a t o r ':') of gram-

n o n - t e r m i n a l (like n u m b e r and p e r s o n for noun phrases)

each non-terminal gets two extra arguments treated

as a d i f f e r e n c e list r e p r e s e n t i n g the w o r d string

a n a l y z e d by the non-terminal In c o m p i l i n g MLG rules, exactly the same thing is done to handle w o r d strings For h a n d l i n g s y n t a c t i c structures, the MLG rule compiler adds a d d i t i o n a l arguments w h i c h

tional arguments and the w a y they are used d e p e n d

on w h e t h e r :he non-terminal is s t r o n g or weak If the original n o n - t e r m i n a l is s t r o n g and has the form nt(Xl , Xn)

then in the compiled version we will have

nt(Xl Xn, Syn, Strl,Str2)

Here there is a single s y n t a c t i c s t r u c t u r e argument,

Syn, r e p r e s e n t i n g the s y n t a c t i c s t r u c t u r e of the

p h r a s e a s s o c i a t e d by nt w i t h the w o r d s t r i n g g i v e n

by the d i f f e r e n c e list (Strl, Sir2)

On the o t h e r hand, w h e n the n o n - t e r m i n a l nt

is weak, four s y n t a c t i c s t r u c t u r e a r g u m e n t s are

added, p r o d u c i n g a c o m p i l e d p r e d i c a t i o n of the form

nt(Xl, Xn, SynO,Syn, H o d s l , H o d s 2 , Strl,Str2)

Here t h e pair (Hodsl, Hods2) holds a d i f f e r e n c e list

for the sequence of s t r u c t u r e s a n a l y z e d by the w e a k

n o n - t e r m i n a l nt T h e s e s t r u c t u r e s could be 'syn'

s t r u c t u r e s or terminals, and they will be d a u g h t e r s

(modifiers) for a 'syn' s t r u c t u r e a s s o c i a t e d w i t h

the closest higher call to a s t r o n g n o n - t e r m i n a l

l e t us call this h i g h e r 'syn s t r u c t u r e the ma-

t r i x ' s y n ' s t r u c t u r e The o t h e r p a i r (SynO, Syn)

r e p r e s e n t s the changing view o f what the m a t r i x

' s y n ' s t r u c t u r e a c t u a l l y should be, a view t h a t may

change because a s h i f t is encountered w h i l e s a t i s -

f y i n g n t SynO r e p r e s e n t s the v e r s i o n b e f o r e s a t -

i s f y i n g n t , and Syn r e p r e s e n t s the v e r s i o n a f t e r

s a t i s f y i n g nt If no shift is e n c o u n t e r e d w h i l e

s a t i s f y i n g nt, then Syn w i l l just equal SynO But

if a shift is encountered, the old v e r s i o n SynO will

become a d a u g h t e r node in the new v e r s i o n Syn

In c o m p i l i n g a rule with several n o n - t e r m i n a l s

in the rule body, linked by the s e q u e n c i n g o p e r a t o r

Hods2) for w e a k n o n - t e r m i n a l s are linked, respec-

tively, across adjacent n o n - t e r m i n a l s in a m a n n e r

similar to the linking of the d i f f e r e n c e lists for

terminals a s s o c i a t e 'syn' s t r u c t u r e elements w i t h

the m o d i f i e r lists, just as surface terminals are

a s s o c i a t e d w i t h elements of the w o r d - s t r i n g lists

Let us look now at the c o m p i l a t i o n of a set

fragment i l l u s t r a t i n g the shift and shown above in

S e c t i o n 2, and repeated for c o n v e n i e n c e here, to-

g e t h e r w i t h d e c l a r a t i o n s of s t r o n g non-terminals

s t r o n g n o n ~ e r m i n a l s ( n p d e t n o u n p o s s n i l )

np = > det: npl

npl = > premods: noun: np2

np2 ~-> postmods

rip2 = > poss: %npl

The c o m p i l e d rules are as follows:

np[Syn, Strl,Str3) <-

det(Hod, Strl,Str2) &

n p l ( s y n ( n p : n i l , H o d : H o d s ) , S y n ,

Hods,nil, Str2,Str3)

npl(Synl,Syn3, H o d s l , H o d s 3 , Strl,Str4) <-

p r e m o d s ( S y n l , S y n 2 , H o d s l , H o d : H o d s 2 ,

Strl,Str2) &

noun(Hod, Str2,Str3) &

np2(Syn2,Syn3, H o d s 2 , H o d s 3 , Str3,Str4)

np2(Synl,Syn2, H o d s l , H o d s 2 , Strl,Str2) < -

n p 2 ( s y n ( F e a s , H o d s O ) , S y n , H o d : H o d s l , H o d s l , Strl,Str3) <-

p o s s ( M o d , Strl,Str2) &

n p l ( s y n ( F e a s , s y n ( F e a s , H o d s O ) : H o d s 2 ) , S y n , Hods2,nil, Str2,Str3)

In the first c o m p i l e d rule, the s t r u c t u r e Syn

to be a s s o c i a t e d w i t h the call to 'np' appears a g a i n

in the s e c o n d m a t r i x s t r u c t u r e argument of 'npl'

T h e first m a t r i x s t r u c t u r e a r g u m e n t of 'npl' is

s y n ( n p : n i l , M o d : H o d s )

s t r u c t u r e a s s o c i a t e d w i t h the d e t e r m i n e r 'det', and Hods is the list of m o d i f i e r s d e t e r m i n e d further

from the leading n o n - t e r m i n a l 'np' of this s t r o n g

(first) a r g u m e n t Argl.)

m a t r i x s t r u c t u r e pairs (first two arguments) and the m o d i f i e r d i f f e r e n c e list pairs are linked in a

s t r a i g h t f o r w a r d w a y to reflect sequencing

]'be fourth rule shows the effect of the shift Here s y n ( F e a s , H o d s O ) , the previous " c o n j e c t u r e " for the m a t r i x structure, is now m a d e simply the first

m o d i f i e r in the larger s t r u c t u r e

s y n ( F e a s , s y n ( F e a s , H o d s O ) : H o d s 2 )

w h i c h becomes the new " c o n j e c t u r e " by b e i n g p l a c e d

in the first argument of the further call to 'npl'

If the shift o p e r a t o r had been used in its b i n a r y form FO%npl, then the new c o n j e c t u r e w o u l d be

syn(NT:F,syn(NT:FO,Mods0):Hods2)

w h e r e the o l d c o n j e c t u r e was s y n ( N T : F , H o d s O ) [n

p l e t e l y c o r r e c t feature list N T : F O for the left-

e m b e d d e d modifier

from the grammar H L G R A M in S e c t i o n 2 The c o m p i l e d rule is

d e t ( s y n ( d e t : n i l , + D : P 2 / P I - P : n i l ) , D.Str,Str) <-

d t ( D , P I , P 2 , P )

logical terminal P2/PI-P are e n t e r e d as m o d i f i e r s

of the 'det' node T h e s e m a n t i c i n t e r p r e t a t i o n

c o m p o n e n t looks only at the logical terminals, but

in c e r t a i n a p p l i c a t i o n s it is useful to be able to

tures As m e n t i o n e d above, the d i s p l a y p r o c e d u r e s for s y n t a c = i ¢ s t r u c t u r e s can o p t i o n a l l y show o n l y

o n e t y p e o f t e r m i n a l

s e n t e n c e "Every m a n loves a w o m a n " p r o d u c e d by

M L G R A M is as follows

s e n t e n c e : n i l

np:Xl

det:nil

X 2 / X 3 - a l I ( X 3 , X 2 )

l-man(Xl)

l-love(Xl,XA)

n p : X A

det:nil

X S / X 6 - e x ( X 6 , X S )

l-woman(X&)

Note that no 'vp' node is shown in the parse tree;

p r o d u c e d for this tree by the semantic c o m p o n e n t

given in the next section is

all(man(Xl), e x ( w o m a n ( X 2 ) , l o v e ( X I , X 2 ) ) )

Now let us look at the c o m p i l a t i o n of syntax

adds extra arguments to n o n - t e r m i n a l s for manipu-

the top-level semantic i n t e r p r e t a t i o n procedure,

'semant'

The p r o c e d u r e 'semant' builds c o m p l e x semantic

structures out of simpler ones, w h e r e the original

b u i l d i n g blocks are the logical terminals a p p e a r i n g

struction, it w o u l d be p o s s i b l e to w o r k with se-

m a n t i c items (and in fact a s u b s y s t e m of the rules

do w o r k d i r e c t l y w i t h semantic items), but it ap-

pears to be more e f f i c i e n t to w o r k with s l i g h t l y

more elaborate s t r u c t u r e s w h i c h we call a u g m e n t e d

sem(Feas,Op,LP),

w h e r e Op and [2 are such that O p - L F is an o r d i n a r y

for the initial a u g m e n t e d s e m a n t i c items a s s o c i a t e d

w i t h logical terminals

As in the two-pass mode, the number of analysis

s t r u c t u r e arguments added to a n o n - t e r m i n a l by the

compiler depends on w h e t h e r the n o n - t e r m i n a l is

s t r o n g and has the form

nt(Xl, , Xn)

then in the compiled version w e will have

nt(Xl, ., Xn, Semsl,Sems2, Strl,Str2)

Here (Semsl, Sems2) is a d i f f e r e n c e list of aug-

m e n t e d semantic items r e p r e s e n t i n g the list of se-

m a n t i c s~ruotures for the p h r a s e a s s o c i a t e d by n ~

w i t h the w o r d s~ring given by the d i f f e r e n c e list

o n l y one argument (for a 'syn') is n e e d e d here, but

r a i s i n g p h e n o m e n o n n e c e s s a r y for p r o p e r scoping,

w h i c h w e w i l l discuss in S e c t i o n s A and 5

W h e n the n o n - t e r m i n a l nt is weak, five e x t r a

a r g u m e n t s are added, p r o d u c i n g a c o m p i l e d predi-

c a t i o n of the form nt(Xl, ., Xn, Fees, SemsO,Sems, S e m s l , S e m s 2 ,

Strl,Str2) Here Fees is the feature list for the m a t r i x s t r o n g

n o n - t e r m i n a l The pair (SemsO, Sems) r e p r e s e n t s the c h a n g i n g " c o n j e c t u r e " for the c o m p l e t e list of

d a u g h t e r (augmented) semantic items for the m a t r i x node, and is analogous to first extra argument pair

a d i f f e r e n c e list for the sequence of s e m a n t i c items

a n a l y z e d by the weak n o n - t e r m i n a l nt Semsl will

course be a final sub|ist of Semsl

added at the end of the c o m p i l e d form of the rule The form of the call is

semant(Feas, Sems, Semsl,Sems2)

Here teas is the feature list for the n o n - t e r m i n a l

v e r s i o n of the list of d a u g h t e r s e m a n t i c items

r e s u l t i n g from the s e m a n t i c i n t e r p r e t a t i o n for this

n o n - t e r m i n a l on the left-hand side of the s t r o n g rule A call to 'semant' is also g e n e r a t e d w h e n a

actual w o r k i n g of 'semant' is the topic of the next section

the c o m p i l e d rules are as follows

d e t ( S e m s l , S e m s 2 , Strl,Str2) &

npl(np:nil, Semsl,Sems3, Sems2,nil, Str2,Scr3) a

s e m a n t ( n p : n i l , Sems3, Sems,SemsO)

npl(Feas, Semsl,Sems3, Semsa,Sems7, Strl,St[~) <- premods(Feas, Semsl,Sems2, SemsA,Sems5,

Strl,Str2) &

n o u n ( S e m s 5 , S e m s 6 , Str2,Str3) &

np2(Feas, Sems2,Sems3, Sems6,SemsT, Str3,StrA) np2(Feas, Semsl,Sems2, Sems3,Semsd, Strl,Str2) <-

p o s t m o d s ( F e a s , Semsl,Sems2, Sems3,SemsA,

Strl,Str2)

npE(Feas, Semsl.SemsA, SemsS,Sems6, Strl,Str3) <-

p o s s ( S e m s S , S e m s 6 , Strl,Str2) &

semant(Feas, Semsl, S e m s 2 , S e m s 3 ) &

npl(Feas, Sems2,Sems~, Sems3,nil, Str2,Str3)

In the first compiled rule (a s t r o n g rule), the pair (Seres, SemsO) is a d i f f e r e n c e list of the s e m a n t i c

can be more w h e n m o d i f i e r s of the noun phrases

c o n t a i n q u a n t i f i e r s that cause the m o d i f i e r s to get

p r o m o t e d s e m a n t i c a l l y to be s i s t e r s of the n o u n

p h r a s e ) T h i s d i f f e r e n c e l i s t i s t h e o u t p u t o f t h e

c a l l t o ' s e m a n t ' c o m p i l e d i n a t t h e e n d o f t h e f i r s t

, !

d e t e r m i n e r (if there is one), and the list is con-

tinued in the list Sems2 of m o d i f i e r s d e t e r m i n e d

the initial list Semsl is g i v e n in the s e c o n d ar-

final list of m o d i f i e r s of the noun phrase Sems3,

being in the next argument of 'npl', is the "final

version" of the np m o d i f i e r list, and this is the

list given as input to 'semant' [f the p r o c e s s i n g

of 'npl' e n c o u n t e r s no shifts, then Sems3 will just

equal 5ems I

" v e r s i o n s " of the total list of m o d i f i e r s are [inked

in a chain

(Semsl, 5ems2, Sems3)

in the s e c o n d and third a r g u m e n t s of the w e a k non-

terminals The actual m o d i f i e r s p r o d u c e d by this

rule are linked in a chain

(SemsA, Sems51 Sems6, SemsT)

in the fourth and fifth a r g u m e n t s of the w e a k non-

terminals and the first and s e c o n d arguments of the

s t r o n g non-terminals A s i m i l a r s i t u a t i o n holds

for the first of the 'np2' rules

[n the second 'npZ' rule, a shift is encount-

n e c e s s a r y b e c a u s e of the shift of levels; the mod-

ifiers p r o d u c e d so far r e p r e s e n t all the m o d i f i e r s

in an np, and these must be c o m b i n e d by 'semant'

call to 'semant', we take the list Semsl, w h i c h is

the current v e r s i o n of the m o d i f i e r s of the m a t r i x

np T h e output is the d i f f e r e n c e list (Sems2,

'npl' as the new current v e r s i o n of the m a t r i x

m o d i f i e r list The tail Sems3 of the d i f f e r e n c e

is the f~.nal uersion of the m a t r i x m o d i f i e r list,

d e t e r m i n e d by 'npi I , and this i n f o r m a t i o n is also

put in the third a,'gument of 'np2' The d i f f e r e n c e

p r o d u c e d by 'poss', and this list tails off the list

Semsl

W h e n a s e m a n t i c item O p - L F occurs in a rule

m a n t i c item s e m ( t e r m i n a l : n i l , O p , L F ) As an example,

the w e a k rule

t r a n s v e r b ( X , Y ) ~ > +V: $tv(V,X,Y,P): I-P

compiles into the c l a u s e

t r a n s v e r b ( X , Y , Feas, S e m s l , S e m s l ,

s e m ( t e r m i n a l : n i l , l , P ) : S e m s 2 , S e m s 2 ,

V S t r , S t r ) <- tv(V,X,Y,P)

The strong rule

compiles into the c l a u s e

d e t ( S e m s l , S e m s 2 , D S e m s A , S e m s & ) < -

d t ( D , P 1 , P 2 , P ) &

s e m a n t ( d e t : n i l ,

s e m ( t e r m i n a l : n i l , P 2 / P I , P ) : n i l , Semsl,Sems2)

4 S E M A N T I C I N T E R P R E T A T I O N FOR MLG'S

T h e s e m a n t i c i n t e r p r e t a t i o n schemes for both

m a n t i c items are c o m b i n e d with one another, forming

is c o n s t r u c t e d w h i c h represents the s t r u c t u r e of

two c o m p o n e n t s are discarded We will d e s c r i b e the top levels for both modes, then d e s c r i b e the c o m m o n core

T h e top level f o r the one-pass mode is simpler, because s e m a n t i c i n t e r p r e t a t i o n works in tandem w i t h the parser, and does not itself have to go t h r o u g h the parse tree The p r o c e d u r e 'semant', w h i c h has

i n t e r l e a v e d calls in the c o m p i l e d s y n t a x rules,

is some m i n o r c l e a n i n g up that has to be done If

for the o n e - p a s s mode can be

a n a l y z e C S e n t ) <-

s e n t e n c e ( S e m s , n i l , S e n t , n i l ) &

semant(top:nil,Sems,sem(*,e,iF):nil,nil) &

o u t l o g f o r m ( L F ) Normally, the first argument, Sems, of 'sentence' will be a list c o n t a i n i n g a s i n g l e a u g m e n t e d se-

m a n t i c item, and its logical form c o m p o n e n t will

grammars, the ~dditional call to 'semant' is n e e d e d

to c o m p l e t e the m o d i f i c a t i o n process The p r o c e d u r e 'outlogform' simplifies the logical form and o u t p u t s

it

~ne d e f i n i t i o n of 'semant' itself is g i v e n in

a single clause:

s e m a n t ( F e a s , S e m s , S e m s 2 , S e m s 3 ) <-

r e o r d e r ( S e m s , S e m s l ) &

m o d l i s t ( S e m s l , s e m ( F e a s , i d , t ) ,

Sem,Sems2,Sem:Sems3)

H e r e , t h e p r o c e d u r e ' r e o r d e r ' t a k e s t h e l i s t Sems

of a u g m e n t e d semantic items to be c o m b i n e d and re-

likely) scoping This p r o c e d u r e belongs to the

c o m m o n core of the two m e t h o d s of s e m a n t i c inter-

The p r o c e d u r e 'modlist' does the following A call

m o d l i s t ( S e m s , S e m O , S e m , S e m s l , S e m s 2 )

takes a list Sems of (augmented) s e m a n t i c items and

combines them w i t h (lets them modify) the item SemO,

w i t h a d i f f e r e n c e list (Semsl, Sems2) of items w h i c h

m e m b e r of Sems acts as the o u t e r m o s t modifier

Thus, in the d e f i n i t i o n of 'semant', the result list

Sem:Sems3) where the result Sem is r i g h t - a p p e n d e d

common core, and will be d e f i n e d below

The top level for the two-pass system can be

d e f i n e d as follows

analyze2(Sent) <-

s e n t e n c e ( g y n , S e n t , n i l ) &

s y n s e m ( S y n , S e m s , n i l ) &

s e m a n t ( t o p : n i l , g e m s , s e m ( * , e , L F ) : n i t , n i I ) &

outlogform(LF)

The only d i f f e r e n c e b e t w e e n this and 'analyze' above

is that the call to ' s e n t e n c e ' produces a syntactic

s y n s e m ( S y n , S e m s I , S e m s 2 )

takes a syntactic item Syn and produces a d i f f e r e n c e

representing the s e m a n t i c s t r u c t u r e o f Syn (Typ-

i c a l l y , this list will just have one element, but

it can have more if m o d i f i e r s get promoted to sis-

ters of the node.)

The d e f i n i t i o n of 'synsem' is as follows

s y n s e m ( s y n ( F e a s , M o d s ) , S e m s 2 , S e m s 3 ) <-

s y n s e m l i s t ( M o d s , S e m s ) &

reorder(Sems,Semsl) &

modlist(Semsl,sem(Feas,id,t),

Sem,Sems2,Sem:Sems3)

Note that this differs from the d e f i n i t i o n of

recursively process the d a u g h t e r s Mode of its input

esses the daughters is d e f i n e d as follows

s y n s e m l i s t ( s y n ( F e a s , M o d s 0 ) : M o d s , S e m s l ) <- /&

s y n s e m ( s y n ( F e a s , M o d s O ) , S e m s I , S e m s 2 ) &

s y n s e m l i s t ( M o d s , S e m s 2 )

s y n s e m l i s t ( ( O p - L F ) : M o d s ,

s e m ( t e r m i n a l : n i l , O p , L F ) : S e m s ) <- /&

synsemlist(Mods,Sems)

s y n s e m l i s t ( N o d : M o d s , S e m s ) <-

synsemlist(Mods,Sems)

synsemlist(nil,nil)

The first c l a u s e calls 'synsem' r e c u r s i v e l y w h e n the d a u g h t e r is a n o t h e r 'syn' structure T h e s e c o n d

c l a u s e replaces a logical terminal by an a u g m e n t e d

s e m a n t i c item w h o s e feature list is terminal:nil The next c l a u s e ignores any other type of d a u g h t e r (this w o u l d n o r m a l l y be a s u r f a c e terminal)

Now we can p r o c e e d to the common core of the two s e m a n t i c i n t e r p r e t a t i o n systems The p r o c e d u r e 'modlist' is d e f i n e d r e c u r s i v e l y in a s t r a i g h t f o r -

w a r d way:

m o d l i s t ( S e m : S e m s , Sem0, Sem2, Semsl,Sems3) <-

m o d l i s t ( S e m s , SemO, Seml, Sems2,Sems3) & modify(Sem, Seml, Sem2, Semsl,Sems2)

m o d l i s t ( n i l , Sem, gem, Sems,Sems)

Here 'modify' takes a single item Sem and lets it operate on Seml, g i v i n g Sem2 and a d i f f e r e n c e list (Semsl, Sems2) of sister items Its d e f i n l t i o n is modify(Sem, Seml, Seml, Sem2:Sems,Sems~ <-

r a i s e ( S e m , S e m l , S e m 2 ) &/

m o d i f y ( s e m ( * , O p , L F ) ,

s e m ( F e a s , O p l , L F I ) ,

s e m ( F e a s , O p 2 , L F 2 ) , Sems,Sems) <- mod(Op-LF, OpI-LFI, Op2-LF2)

item Seml so that it becomes a sister of the item

raising, although in most cases, gem2 equals geml

R a i s i n g occurs for a noun phrase like "a c h i c k e n

in every pot", w h e r e the q u a n t i f i e r "every" has higher scope than the q u a n t i f i e r "a" The s e m a n t i c item for "every pot" gets promoted to a left s i s t e r

of that for "a chicken" 'raise' is d e f i n e d bas- ically by a s y s t e m of unit clauses w h i c h look at

M L G R A M of S e c t i o n 2, no raising is necessary, and the d e f i n i t i o n of 'raise' can just be omitted

key ingredients of r e s h a p i n g (the m o v e m e n t of se-

m a n t i c items to handle scoping problems), w h i c h was

d i s c u s s e d e x t e n s i v e l y in McCord (1982, 1981) [n

of s e m a n t i c interpretation, but },ere, as in M c C o r d (198&), r e s h a p i n g is interleaved with the rest o f

reordering are b a s i c a l l y the same as in the previous

further discussion

T h e p r o c e d u r e 'mod', used in the s e c o n d c l a u s e for 'modify', is the heart of semantic interpreta- tion

mod(Sem, Seml, Sem2)

modifies (combines with) the item Semi to give the item Sem2 'mod' is d e f i n e d by a s y s t e m c o n s i s t i n g

b a s i c a l l y of unit clauses w h i c h key off the m o d - ification operators a p p e a r i n g in the s e m a n t i c items

In the e x p e r i m e n t a l MLG d e s c r i b e d in the next sec-

M L G R A M of S e c t i o n 2, the f o l l o w i n g set of clauses

suffices

m o d ( i d -~, Sem, Sem) <- /

mod(Sem, id -~, Sem) <- /

mod(l-P, Op-Q, Op-R) <- and(P,Q,R)

m o d ( P / Q - R , Op-Q, @P-R)

mod(@P-Q, Op-P, Op-Q)

'i' as a l e f t - c o n j o i n i n g o p e r a t o r (its c o r r e s p o n d i n g

logical form gets l e f t - c o n j o i n e d to that of the

m a n t i c item like P / Q - e a c h ( Q , P ) to o p e r a t e on an item

The final clause then allows this item to o p e r a t e

on I-live(X) to give l - e a c h ( m a n ( X ) , l i v e ( X ) )

The low-level p r o c e d u r e 'mod' is the same (in

purpose) as the p r o c e d u r e 'trans' in H c C o r d (1981),

(1982) and 'mod' in M c C o r d (198&), so we refer to

this previous w o r k for m o r e illustrations of this

approach to m o d i f i c a t i o n

i n t e r p r e t a t i o n r e m a i n i n g to be d e f i n e d is 'reorder'

We can d e f i n e it in a way that is s o m e w h a t more

but w h i c h employs a t e c h n i q u e useful for larger

grammars Each a u g m e n t e d s e m a n t i c item is a s s i g n e d

a p r e c e d e n c e number, and the r e o r d e r i n g (sorting)

is d o n e so that w h @ n item B has higher p r e c e d e n c e

number than item A, then B is o r d e r e d to the left

in a way suitable for MLGRAM

reorder(A:L,H) <-

reorder(L,Ll) & insert(A,Li,M)

reordef(nit,n£1)

prec(A,PA) & p r e c ( B , P B ) & gt(PB,PA) & / &

insert(A,L,Li)

insert(A,L,a:L~

p r e c ( s e m ( t e r m ~ n a l : * , e , ~ ) , 2 ) <- /

p r u c ( s e m ( r e l c ! a u s e : e , e , e ) , l ) <- /

prec(e,3)

~nus terminals are o r d e r e d to the end, e x c e p t not

and object of a s e n t e n c e are o r d e r e d b e f o r e the verb

s s r a i g h t f o r w a r d process of m o d i f i c a t i o n in :mod'

to scope the q u a n t i f i e r s of the subject and o b j e c t

d e f i n i t i o n of 'prec' to get finer d i s t i n c t i o n s in

1981)

no t r e a t m e n t of s c o p i n g phenomena, the total tom-

p r e t a t i o n c o m p o n e n t w e have g i v e n in this Section,

is c e r t a i n l y g r e a t e r than that of the c o m p a r a b l e

the m o d u l a r i t y is d e f i n i t e l y w o r t h w h i l e concep- tually, and p r o b a b l y in the total size of the sys- tem

5 AN E X P E R I M E N T A L MLG This s e c t i o n d e s c r i b e s b r i e f l y an e x p e r i m e n t a l MLG, c a l l e d HODL, w h i c h covers the same linguistic

g r o u n d as the g r a m m a r (called HOD) in H c C o r d (198l) The s y n t a c t i c c o m p o n e n t of HOD, a DCG, is essen-

feature of these s y n t a c t i c c o m p o n e n t s is a system- atic use of s l o t - f i l l i n g to treat c o m p l e m e n t s of verbs and nouns This m e t h o d increases m o d u l a r i t y

b e t w e e n syntax and lexicon, and is d e s c r i b e d in detail in McCord (1982)

One purpose of HOD, w h i c h is c a r r i e d over to MODL, is a good treatment of s c o p i n g of m o d i f i e r s

logical form language used by >IODL as the target

of semantic i n t e r p r e t a t i o n has been improved some-

of the c h a r a c t e r i s t i c s of the new logical form language, called LFL, and give sample LFL a n a l y s e s

o b t a i n e d by MODL, but we defer a more d e t a i l e d de-

s c r i p t i o n of LFL to a later report

The main p r e d i c a t e s of LFL are w o r d - s e n s e s for

example, b e l i e v e l ( X , Y ) in the sense "X believes that

Y holds" Q u a n t i f i e r s , like 'each', are special cases of w o r d - s e n s e s T h e r e are also a small number

for past tense, or s y n t a c t i c c o n s t r u c t i o n s , like 'yesno' for yes-no questions, or have s i g n i f i c a n c e

at d i s c o u r s e level, d e a l i n g for instance w i t h topic/comment The a r g u m e n t s for p r e d i c a t e s of LFL can be constants, variables, or other logical forms (expressions of LFL)

E x p r e s s i o n s of LFL are either p r e d i c a t i o n s (in

e x p r e s s i o n s using the c o n j u n c t i o n '&' and the in-

d e x i n g operator ':' S p e c i f i c a l l y , if P is a log-

indexed logical form P:E appears as part of a larger

as s t a n d i n g for P together w i t h its "context" Contexts include references to time and place w h i c h

W h e n P specifies an event, as in s e e ( j o h n , m a r y ) ,

w r i t i n g P:E and s u b s e q u e n t l y u s i n g E will g u a r a n t e e

form language used in M c C o r d (1981), event v a r i a b l e s

powerful because it can index c o m p l e x logical forms

as v e r i f y i n g P and b i n d i n g E to an i n s t a n t i a t i o n

forms without contexts, ':' can be defined by the

A specific purpose of the MOD system in McCord

(1981) was to point out the importance of a class

method for dealing with them in semantic interpre-

adverbs, and adjectives (or their word-senses), as

well as certain non-lexical predicates like 'yesno'

Focalizers take two logical form arguments called

focalizer(Base,Focus)

The Focus is often associated with sentence stress,

the SCOpe of the focalizer

The adverbs 'only' and 'even' are focalizers

which most clearly exhibit the connection with

different analyses depending on focus

John only buys books at Smith's

only(at(smith,buy(john,X1)), book(X1))

John only buys books at Smith's

only(book(Xl)&at(X2,buy(john,Xl)), X2=smith)

'seldom', studied by David Lewis (1975), are also

the sense that they quantify over all the free

ample, in

John always buys books at Smith's

always(book(Xl)&at(X2,buy(john,Xl)), X2=smith) •

paraphrase is "Always, if X1 is a book and John buys

X1 at X2, then X2 is Smith's".)

focalizers (and are unselective quantifiers); they

quantificational adverbs ('all' - 'always', 'many'

paraphrases:

Leopards often attack monkeys in trees

often(leopard(Xl)&tree(X2)&in(X2,attack(Xl,X3)),

monkey(X3))

Many leopard attacks in trees are (attacks)

on monkeys

many(leopard(Xl)&tree(X2)&in(X2,attack(Xi,X3)),

monkey(X3))

Adverbs and adjectives involving comparison

or degree along some scale of evaluation (a wide

base of comparison, and the focus singles out what

adverb "fastest":

John ran fastest yesterday

fastest(run(john):E, yesterday(E))

John ran fastest yesterday

fastest(yesterday(run(X)), X=john)

I n the first sentence, with focus on "yesterday", the meaning is that, among all the events of John's running (this is the base), John's running yesterday

on "John", the meaning is that among all the events

of running yesterday (there is an implicit location

As an example of a non-lexical focalizer, we have yesno(P,q), which presupposes that a case of

(P, Q) is like Topic/Comment for yes-no questions.) Example:

yesno(yesterday(see(john,X)), X=mary)

It is possible to give Prolog definitions for most of the focalizers discussed above which are suitable for extensional evaluation and which amount

be discussed in a later report on LFL

A point of the grammar HODL is to be able to produce LFL analyses of sentences using the modular

preceding section, and to arrive at the right (or most likely) scopes for focalizers and other modi-

heuristics involving precedences, on very reliable cues from the syntactic position, and even on the specification of loci by explicit underlining in

adverbial loci, it is important that the system can get the right logical form after having some spec-

specification might be obtained from prosody in spoken language, or might come from the use of

of the modularity of the system that it can use the same syntactic rules and parse path no matter where the adverbial focus happens to lie

Most of the specific linguistic information

clauses for the procedure 'mod', most of which are

cation operators, four of which were illustrated

in MODL is taken fairly directly from the corre- sponding procedure 'trans' in HOD (McCord, 1981), although there are some changes involved in handling the new version of the logical form language (LFL),