TWO THEORIES FOR COMPUTING THE LOGICAL FORM OF MASS EXPRESSIONS 
Francis Jeffry Pelletier 
Lenhart K. Schubert 
Dept. Computing Science 
University of Alberta 
Edmonton, Alberta T6G 2El 
Canada 
ABSTRACT Applying the rules of translation is even simpler. In 
essence, all that is needed is a mechanism for arranging 
There are various difficulties in accomodating the traditional logical expressions into larger expressions in conformity with 
mass/count distinction into a grammar for English which the semantic rules. (For examples of parsers see Thompson 
has a goal the production of "logical form" semantic 
translations of the initial English sentences, The present 
paper surveys some of these difficulties. One puzzle is 
whether the distinction is a syntactic one or a semantic 
one, i.e., whether it is a well-formedness constraint or 
whether it is a description of the semantic translations 
produced. Another puzzle is whether it should be applied 
to simple words (as they occur in the lexicon) or whether 
it should apply only to longer units (such as entire NPs). 
Of the wide variety of possible theories, only two seem to 
produce the required results (having to do with plausible 
inferences and intuitively satisfying semantic representations). 
These two theories are developed and compared. 
According to Montague (Thomason 1974), Gazdar 
(Gazdar et al 1984) and a rapidly growing number of 
linguists, philosophers, and AI researchers, the logical form 
underlying sentences of a natural language are 
systematically--and simply--determined by the syntactic form 
of those sentences. This view is in contrast with a tacit 
assumption often made in AI, that computation of logical 
translations requires throngs of more or less arbitrary rules 
operating upon syntactic forms.* 
The following are a few grammar rules in 
approximately the style of Gazdar's Generalized Phrase 
Structure Grammar (GPSG). They differ from Gazdar's 
primarily in that they are designed to produce more or 
less "conventional" logical translations, rather than the 
intensional ones of Montague and Gazdar (for details see 
Schubert & Pelletier 1982). Each rule consists of a rule 
number, a phrase structure rule, and a semantic (logical 
translation) rule. 
1. S., NP VP, VP'(NP') 
2. VP., \[V +be\] PRED, PRED' 
3. PILED .* N, N' N,={water,wine,food,furniture,...} 
Parsing and translating in accordance with such rules is a 
fairly straightforward matter. Since the syntactic rules are 
context free, standard context-free parsing methods can be 
employed, except that allowance must be made for the 
propagation of features, with due regard for concord. 
'The work reported herein was partially supported by 
NSERC grants A5525 (FJP) and A8818 (LKS). We also 
wish to thank Matthew Dryer, David Justice, Bernard 
Linsky, and other members of the Univ. Alberta Logical 
Grammar Study Group for discussions on these topics. 
1981, Schubert & Pelletier 1982, Gawron et al 1982, 
Rosenschein & Shieber 1982). 
The topic of mass terms and predicates has a 
substantial literature within both linguistics and philosophical 
logic, with much of the recent research deriving inspiration 
from Montague Grammar (e.g., see Pellefier 1979, ter 
Meulen 1980, Bunt 1981, Chierchia 1982). There are three 
views on the mass/count distinction, namely that the 
distinction is (a) syntactic, (b) semantic,, and (c) 
pragmatic, Orthogonal to these views we have the further 
possibilities (i) that the mass/count distinction is lexical. 
and (ii) that it is determined by the context in which the 
expression occurs. We shall present arguments in the full 
paper to eliminate position (c), leaving us with four 
possible kinds of theories. (i) a syntactic expression 
(lexical) approach, (2) a syntactic occurrence approach. (3) 
a semantic expression approach, and (4) a semantic 
occurrence approach. This raises the question of what is 
the difference between syntactic approaches generally and 
semantic approaches generally. A syntactic approach treats 
+mass and +count as syntactic classifications or features, 
that is as features to be used by the syntactic rules in 
determining whether some longer stretch of words is 
well-formed. Central to the semantic approach is the claim 
that +count and +mass are not syntactic features or 
categories, but rather are a description of the semantic 
representation of the expression. In this approach, no 
syntactic rules refer to +count or +mass (since these are 
not syntactic objects). Rather, in sentences like Mary put 
apple in the salad vs. Mary put an apple in the. salad, 
the semantic approaches allow us to say that it was a 
mass or count semantic representation of apple only after 
inspecting the kind of thing that apple is true of in the 
sentences. 
There are reasons for rejecting options (2) and (3). 
thus leaving us with only a syntactic expression approach 
and a semantic occurrence approach. (The reasons are 
given in Pelletier & Schubert 1985). These are the two 
theories of mass expressions that are to be discussed in 
the paper. They seem to us to be the most plausible 
candidates for an adequate theory of the logical form of 
sentences involving mass expressions. The fragment of 
English that the two theories of mass expressions are 
concerned with is roughly those sentences with a copular 
verb and either a mass or count expression as predicate, 
and whose subjects are either bare noun phrases or 
quantified noun phrases. A sentence is a noun phrase and 
a verb phrase. A verb phrase is a copula followed by a 
108 
PP. E Do 
hich in turn is either a bare noun (as in Claret is wine 
or This puddle is ma.......~n - -the latter said after an 
application of the universal grinder) 2 or an a followed by 
a noun (as in John is a man or Claret is aq wine) or is 
an entire noun phrase (as in John is the man most likely 
to succeed or Claret is ~ favourite red wine). A noun 
phrase is either a bare noun (as in Claret is a dry red 
wine or Dogs are barking outside) or else is a quantified 
term (as in All men are mortal or Sm red wine is tasty 
--we include as determiners this, all, some, sin, much, little, 
each, every, and the numeral quantifiers). Nouns may 
themselves be either an adjective-phrase noun combination, 
or just a noun. We consider here two cases of adjective 
modification: intersective and non-intersective. For the 
former we have in mind such adjectives as red, while for 
the latter we think of such adjectives as fake. 
The rules which give alternatives, such as 3p vs. 
3s, are those rules which are different for the two theories 
of mass terms. The p-rules are for the semantic 
occurrence approach while the s-rules are for the syntactic 
expression approach. The ontological underpinnings of these 
theories are that "reality" contains two sorts of items: (1) 
"ordinary objects" such as rings, sofas, puddles (and 
including here what many theorists have called "quantities 
of matter"). (2) "kinds", that is, "varieties", "substances", 
etc. We have in mind here such items as wine, claret, red 
wine, and the like, and also servings of such items. We 
wish to make no special metaphysical claims about the 
relationships that might hold between "ordinary objects" 
and "kinds"--instead we content ourselves with describing 
how such an ontology leads to a simple and natural 
description of various of the facts concerning mass (and 
possibly plural ) expressions. Linguistically, that is 
semantically, we take there to be three distinct types of 
predicates: (a) those which apply only to "kinds', e.g., is 
a substance, is scarce, is a kind of wine, is abundant, (b) 
those which apply only to "objects', e,g., is a quantity of 
goM, is a puddle, and (c) those which can apply to both 
"kinds" and "objects". In this last group we have in mind 
mass predicates such as is wine. is furniture, is food, and 
is computer software. 
Both of these theories take it that is wine is true 
of the (abstract) kind claret in addition to an individual 
quantity such as the contents of this glass. Moreover, they 
take is wine to be true of an object such as a drop or 
puddle of wine, occupying the same region as some 
quantity of wine. (This ring is goM or This hamburger is 
food are clearer examples of the application of mass 
predicates to objects.) Generally speaking, the theories view 
the kinds of M as forming an upper semilattice of kinds 
with M at the top. This is a "formal" semilattiee in that 
the union of any two elements of it is a member of the 
semilattice, and we view is wine as being true of any of 
these formal kinds. So a sentence like Cheap wine is wine 
will be true, since cheap wine names an element of the 
semilattice. Predicates like is a wine are true of 
conventionally recognized kinds (Claret is a wine is true) 
but not of every "formal" kind since, e.g., Cheap wine is 
2 The universal grinder (Pelletier 1975) takes objects 
corresponding to any count noun, grinds them up and 
spews the result from the other end. Put a table into it 
and after a few minutes there is sm table on the floor. 
(We regularly represent the unstressed some by sin.) 
a wine is not true. (Sauterne mixed with claret is a wine 
is also not true, showing that is a wine is not true of 
unions of elements of the semilattice). These predicates are 
not only true of the conventional kinds but also of 
conventional servings such as the bottle of wine on the 
table or the 250ml in this glass. Note that these can again 
be abstract entities: but rather than potentially being 
abstract conventional kinds of wine, they can be abstract 
conventional kinds of servings of wine. Finally such 
predicates are true of individual quantities--as when we say 
we have ordered four wines, all of the same kind and 
size. When a bare mass noun phrase (or indeed other bare 
noun phrases, although we shall not dwell on them here) 
is used as a subject (or object, but again we shall not 
consider that here), it is taken to name the kind. So in 
Cheap wine is wine, the subject cheap wine names a kind; 
and since the sentence is true it must name a "formal 
kind" so that is wine can be predicated of it. But since 
Cheap wine is a wine is not true, the formal kind cannot 
be a conventionally recognized kind (nor, for that matter, 
a conventional serving nor an individual quantity). Both 
theories hold that mass CN's should be translated into the 
semantics as predicates. Strictly this is not required: for, 
all we have given direct evidence for is that mass VP's be 
translated as predicates with a mixed object/kind extension. 
It could be the case that mass CN's are quite different, 
yet in the formation of a mass VP the entire VP gets 
assigned a mixed, predicate denotation. Still, it would be 
simple, and in keeping with much philosophical and 
linguistic analysis, to assume coincidence of CN and "is 
CN" denotations (at least when tense is ignored, as here). 
With just this much of the theory sketched, we 
can overcome various of the difficulties that plagued other 
theories. For example, it is most unclear that any other 
theory can adequately translate sentences like 
Tap water is water 
This puddle is water 
Consider also sentences like 
All wine is wine 
wherein the subject all wine seems to quantify over both 
kinds of wine and quantities of wine, entailing both White 
wine is wine and The litre of wine in this bottle is wine, 
for example. It seems to us that no other theory allows 
this comprehensiveness. An even clearer example of such 
comprehensive denotation is (a), from which both of (b) 
and (c) follow, given that rice is edible and this sandwich 
is edible. (Note also the comprehensive denotation of 
edible). No other theory we know of can account for the 
validity of these two arguments. 
a. Everything edible is food 
b. Rice is food 
c. This sandwich is food 
Both of these theories will want to be able, in the 
semantics, to form predicates which are true of kinds, or 
of servings, or of individuals, given a predicate which has 
comprehensive extension. So, for example, from the 
predicate water' which is assumed to be true of quantities, 
servings, and kinds, we shall want to be able to form (k 
water') which is true of conventional kinds of water, to 
form (p water') which is true of conventional portions 
(and kinds of portions) of water, and to form (q water') 
109 
which is true of quantities of water, Conversely, if we 
have a predicate which is true of individuals and kinds, 
we shall want to form a predicate true of all the entities 
that mass predicates are true of--qnantities of stuff, kinds 
of stuff, and objects coincident with quantities of stuff. 
For example, if man' is a predicate true of objects and 
kinds, then (s man') is the mass predicate formed 
therefrom. Also, we shall want to be able to form the 
name of a kind from a predicate: (# water') is the name 
of the kind water and (# (cheap'(wine')) is the name of 
the kind cheap wine. 
The rules for the relevant portion of our two 
theories are () is our symbol for lambda abstraction): 
1. S -) NP VP. VF(NF) 
2. VP -) \[V +be\] PRED. FRED' 
3p. FRED .) N. N' 
3s. FRED .) \[N +MASS\]. N' 
4p. FRED .) \[DET +a\] N. (tx)\[(k N')(x) v (p N')(x)\] 
4s. FRED .* \[DET +a\] \[N +COUNT\]. N' 
5. FRED ,, NP. ()x)(x=NF) 
6. FRED -) ADJP. ADJF 
7p. NP .) N. (# N') 
%. NP .) \[N +MASS\]. (~ N') 
8. NP .* DET N. DET(N') 
9. \[N + ADJ F \] .) \[ADJ P + INTERSECT\] N, 
()x)\[ADJP'(x) & N'(x)\] 
10. \[N +ADJP\] -) \[ADJP ",INTERSECT\] N. ADJF(N') 
The S-theory distinguishes in the lexicon mass from count 
nouns. And it has what might be called "lexical extension" 
rules to give us the "stretched" meaning of nouns that we 
have earlier talked about. For example, it has 
\[N +COUNT\] ~ sofa, man, substance .... 
\[N +MASS\] ~ wi.e.w.,er .... 
\[N +COUNT\]., \[N +MASS\]. (k N') 
\[N +C(mJNT\] - \[N +MASS\]. (p N') 
\[N +MASS\] .) \[N +COUNT\], (s N') 
Now. both of these theories can give the correct semantic 
representation to a wide range of sentences involving mass 
terms, given certain meaning postulates. (The two theories 
do it slightly differently, as might be expected since they 
have somewhat different semantic understandings of the 
lexical nouns. For example, the s-theory takes man to be 
true of individual men and of kinds of men, while the 
p-theory takes it also to be true of the stuff of which 
men are made. In the p-theory, when a sentence uses a 
--as in a man --then the semantic operators convert this 
"basic" meaning into one that is true of individual men 
and of kinds of men. The s-theory rather has a lexical. 
extension rule which will convert the lexical count noun 
man into one which is a mass noun and is true of the 
stuff of which men are made. They will also take a 
different tack on what quantified terms designate, although 
that has been hidden in rule $ above by assigning the 
same logical form to both theories. Nonetheless, the 
meaning postulates of the two theories will differ for 
these.) In addition to the sorts of examples stated above, 
both these theories can generate and give the correct 
logical form to such sentences as 
Wine is wine (two readings, both analytic) 
Wine is a wine (false) 
All wine is wine (analytic) 
Claret is a wine (true) 
Cheap wine is a wine (false) 
*All wine is a wine (semantically anomalous) 
Water is dripping from the faucet (entails: sm water 
is dripping from the faucet) 
Water is a liquid (entails: water is liquid) 
Both theories make the following six inferences valid 
i. Claret is a wine, wine is a liquid, so claret is a 
liquid 
2. Claret is a wine, wine is a liquid, so claret is liquid 
3. Claret is a wine, wine is liquid, so claret is a liquid 
4. Claret is a wine, wine is liquid, so claret is liquid 
5. Claret is wine, wine is a liquid, so claret is liquid 
6. Claret is wine, wine is liquid, so claret is liquid 
And they both make these two inferences invalid 
7. Claret is wine, wine is a liquid, so claret is a 
liquid 
8. Claret is wine, wine is liquid, so claret is a liquid 
We know of no other theories which can do all these 
things. Yet the two theories are radically different: one 
has a mass/count distinction in the syntax and the other 
doesn't, and they have different extensions assigned to the 
lexical items. So the question naturally arises- -which is 
better? What can be said against the two theories? There 
is not space in a paper of this size to go into this in 
detail, so we shall content ourselves with just hurling the 
main charge that each one directs against the other. 
Briefly, the p-theory charges the s-theory with 
pretending to use syntactic features +mass and +count but 
allowing them to do no syntactic work. For every, sentence 
which has a mass term in a given location, there is 
another sentence which has a count term in that position. 
No constructious are ruled out; the only use of the 
+mass/+count features is in directing the semantic 
translation process. And that suggests that the features 
should all along have been semantic. The s-theory charges 
the p-theory with being unable to give coherent meaning 
postulates because of its committment to a comprehensive 
extension to the lexical terms. For example, suppose one 
wanted to give as a meaning (or factual) postulate that A 
larab has fur. The s-theory can do this without difficulty: 
lamb' is true of individual lambs and the meaning postulate 
says of each of them that they have fur. But the 
p-theory cannot easily do this: lamb' is true of stuff, so 
the predicate must be converted to one which is true of 
individuals. But there is no provision in the p-theory for 
doing this- -the closest that it could come is with a 
predicate that is true of both conventional kinds and 
"conventional portions" (i.e., ordinary Iambs). 
Given the above rules (augmented with additional 
features such as number and person agreement features in 
rule i) we are able to extend the capabilities of our 
parsers (Schubert & PeIletier 1982) so that they deliver 
logical form translations of sentences involving mass 
expressions. These translations have the desired semantic 
properties and, with an extension of the inference 
mechanisms to allow for predicate modification and 
~-abstraction. allow the above valid arguments to be 
duplicated. So. which theory is to be preferred? That is a 
topic for further research. The time for studies of mass 
ii0 
expressions with only casual reference to the syntax and 
semantics of language is past. Only systematic attempts to 
account for large classes of mass expressions within formal 
syntactic-semantic-pragmatic frameworks can hope to resolve 
the remaining i~sues. 
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