Semantics of Portions and Partitive Nouns for NLP 
Salvador Climent 
Facultat de Filologia, Sccci6 Lingtifstica General 
Universitat de Barcelona 
Gran Via 585 
08007 Barcelona 
Spain 
climent@ goliat.upc.cs 
Abstract 
This paper describes a system of representation 
of nouns denoting portions, segments and 
relative quantities of entities, in order to 
account for this case of part-whole 
relationship. The semantics of both 
constructions denoting portions aad nouns 
used to build them arc discussed and eventually 
formalised in a unification-based formalism 
(LKB-IA~L) in terms of Pustciovsky's Theory 
of Qualia and Jackendoff's Conceptual 
Semantics. 
1. Introduction and Motivation 
Processes of inference of meaning concerning part- 
whole relations can be drawn from a lexicon bearing 
meronymic links between words (ef. \[WAI~881) e.g. 
component-whole links (hand-arm), member- 
collection (tree-forest) and so. The case of portions, 
segments and relalivc quantities of objects or 
substances (slices, lumps, buckets, spoon.rids, grains, 
tops or tips of things) is the exception, since this is a 
relation which is encoded in the language by means of 
constructions. Coutrm'y to that which some authors 
posit (\[CIIAS8\], \[WIN87\]), it doesn't seem to be a 
productive linguistic gencr~disation to set in a lexicon 
some part-of link between slice and cake. In any case, 
such relalion would exist between cake and slice of 
cake -namely, the part-of relalion shouhl stand 
between slice and any sliceable thing. 
Generally speaking, the relation portion may be 
charactcriscd, semantically, in Ihat lhe whole pre- 
exists the part and the part retains most of the 
properties of lhe whole (\[IRI88\]), and, syntactically, 
as surfacing in <X of NP> structures, being 
potentially <X> an apparently heterogeneous 
collection of words which, henceforlh, billowing 
\[CO1×)2\] We will refer to ~ts Partitive Nouns (l'Ns). 
On Ihc other hand, portions denoted by such 
constructions differ from their wholes in some 
aspects, basically iudividuation, quantity, process of 
bringing about, and shalx:. Such properties, since they 
are present in <X of NI~ but they were not in <N1)>, 
are assumed to be carried to the coustruclion by the 
noun (<X>). 
I'll try to show here Ihat it is plausible to give a 
glob~d account of such heterogeneous set of words, 
since they bear a range of common and distinctive 
linguistic features, and 1'11 try to provide a 
representation feasible for NLP which account both 
for PNs as a general class and for the homogeneous 
subclasses which wilhin them could be distinguished 
and defined 1. 
2. Framework 
We assume some general familiarity with the 
framework Wc work within: LKB-I,Pd~ (\[CO1×32\]) as 
a formalism of computational representation, The 
Geueralive Lexicon (\[P\[ 1S95 I) as a theoretical ground 
lbr the fonmdisatiou of lexical signs, and Conceptual 
Semantics (\[JAC91\]) for the conceptualisation of 
parts and Ixmndaries of entities. 
LKB-I~RL is an IIPSG-liko formalism based on 
typed feature structures (\[CAR92\]) developed within 
the Acquilex Project which makes use of unification 
and mechanisms of defaull inheritance. There are four 
basic levels of representation: ()RTII, CAT, SEM and 
RQS. CAT encodes syntax using a eategorial 
grammar approach, so there are simple (e.g. noun: N) 
and complex (e.g. adjective: N/N) categories. It is to 
be noticed that in complex categories the active 
element is not a category but a lexical sign, in a way 
that selective restrictions may be set at this level by 
specifying the semantic type or other features of the 
selected sign. SEM encodes logic,'d semantics, RQS 
is basically equivalent to Pustejovsky's Qualia 
SlruCltlre (henceforth QUAI,IA). 
The Theory of Qualia is embedded in that of the 
Generative Lexicon and has as a basic aim lo improve 
compositionalily by endowing lexical signs with a 
rich internal structure which accounls for different 
facets of human knowledge about lexical-semantic 
content, in a way that, iu many cases, it allows for 
avoiding listing separate entries to account for lexic~d 
polysemy. \[PUS95\] posits the lexical entry to be 
constituted by four stn~ctures: Fveut, Argument, 
Lcxical-lnheritauce and QUALIA. The latter consists 
of lout Quales: Agentivc (origin or 'bringing ~d×mt' of 
objects), Telic (purpose and function), Formal (Ihat 
which distinguishes it withiu a larger domain: 
magnitude, shape, dimcusionality) and Constitutive 
(relation between au object and its constituents or 
\[ \]'his work has been dcvelopped for Spanish. 
Notwithstanding, for case of exposition, 1'11 exemplify 
the discussion by means of examples of English -when 
possible. In any case, for what concerns us here, Spanish 
and English are, hoth semantically and structurally, 
strongly comparable -the kernel <PN of NP> comes out 
in Spanish as a literal translation, <I)N de NP>. 
243 
proper parts). 
\[JAC91\] posits that speakers tmderstand and 
schematise a range of phenomcua such as mass-cotHlt 
distinction, plurality, parlilive conslruclions and 
boundary words in terms of clementmy conceptual 
features such as dimension~dity, idealised boundm'ies 
and internal structure, lie introduces features \[_B\] 
(botmdaries being or not in view or of concern) and 
\[+I\] (entailment or not about internal structure) for 
lx)th objects and events as expressing lhe generality of 
phenomena of boundedness and plurality -the notion 
of +I is present in one or another way in \[TAL78\] (cf. 
\[JAC91\]), \[KR1871 (of. \[COt×)2\]) and \[LAK87\]; that 
of boundedness in \[LAN91\]. This feature system 
comes out as: 
+B -I: individu~ds (a pig)/closcd events (,lohn ran to 
the store) 
+B+I: groups (a committee)/boundcd ilerativc events 
(the lightJlashed until down) 
-B-I: substances (water)/ unbounded homogeneous 
processes (,lohn shept) 
-B+I: aggregates (buses, cattle)/unbounded iterativc 
processes (the light flashed continually) 
Moreover, he posils that boundaries of entities are 
conceptualised as minimal elaborations (notated e) of 
their ideal topological boundm'ies (i.e.the tip of the 
tongue is tile portion which conesponds to a minimal 
elaboration of tile 0-dimensional point which would 
ideally be the tongue's tip). 
3. Portions and Partitive Nouns 
A portion designs a bounded region within a domain 
(\[I.AN91\]), hence tile pollion is an individuated entity 
(even in tile case tile whole be a substance or m,'t,;s). 
The syntactic effect is that, as pointed out in 
\[VOS94\], the construction which dcnolcs the portion 
is syntactically countable. 
A portion, an individuated (bounded), object has a 
shape different from thai of the whole. This 
information is contribuled to tile conslruclion by tile 
PN. There are PNs which clearly specify shape 
(ROI)AJA, lunzp) while others underspecify il 
(fragment). Ill many cases, PNs, as acljectives do, 
predicale properties of the portion, specially shape 
(tile translation of Spanish RODAJA must be lhe 
paraphrase round slice; a lath of anything is saliently 
elongated) or size, but also thickness, consislency or 
others (as in the c;me of MI);NDRUGO, equivalent to 
portion (of bread) except for lhe fact that entails that 
Ihe bread is not fi'esh bul stale). 
A portion always conveys a measure wilh relation 
to tile total magnitude of tile whole. Therefore, nouns 
such as bucket, ,slice, lump or grain are relalivc 
quantifiers in tile sense of II~AN91\]: 
a relative quanttfier is so-called because it 
specifies a quantity in relation to a reJ?.rence 
mass; in the de~mlt-case inteJpretation, this 
reference mass consists of the maximal 
instantiation of the pertinent categoJy (i.e. its 
ftdl extension in all conceivable worlds). 
A portion has been oblained by a diflbrent process 
lhan the whole: a cake has been obtained by baking it, 
but a slice o1' cake by cutting it off tile cake. The 
meaning of portions is many times tightly related to 
such agenlive process -if one has obtained 'slices' it 
necessarily has been by culling somelhing; there even 
exists the verb to slice. As pointed out in \[PUS95\], 
knowledge of 'coming into being' is a property of 
nominals which has remarkable linguistic 
consequences since it can account for a reduction of 
lexical polysemy. I:or instance, tile Spanish phrase 
IIACER PAN \[to-make bread\] means baking bread, 
whilst IIACER RI~,BANADAS (DE PAN) \[to-make slices 
(ofbread)\] means slicing (bread). This way, the very 
same verb IIACER shows two radically different 
meanings, which in principle should be listed 
scpm-alely in the lexicon. Nevertheless, both can be 
accounted for in a single entry which selects the 
Agentive Role of the complement. 
More specifically talking about the lexical signs 
wc call PNs, \[IXO77\] shows that lhey correspond to 
the classifiers in languages as Tzeltal, Mandarin 
Chinese or Viemamese. In languages wilh classifiers, 
these words, semantically strongly similar to 
deterinincrs and quantifiers, have functions of 
individuation and enumeration, making surface 
notions such as sorl of entity, shape or measure. E.g. 
the Chinese phrase SAN BEN SIIU is translatable by 
three plane-entity book; three whiskies wotfld be 
conslructed with a mensural classifier, being the 
translation paraphrasablc by three unit/doses whisky. 
\[IXO77\] makes notice lhal words such as head (of 
cattle), sheet (of paper) or lump (of sugar) slaIId for 
exactly tile same function as classifiers in those 
languages. Specifically, ltt mp operates 
simultaneously as both a mensural (meaning 
conventional dose) and classal (denoting a cerlain type 
of aggrcgale) classifier. 
Some have assumed Ihat PNs select mass nouns 
(slice of cake, glass of wine), being mass nouns the 
way in which substances tipically surface in tile 
language. Instead, we posit that PNs select both kinds 
of nouns (count or mass) denoting both kinds of 
things (individuals or subslances), but in any case, 
crucially, surl'acing as expressing cumulative 
l'eli3rence. 
Let's consider t~OI)A.IA I)E I.IMON \[round-slice 
of lemon\]. To assume that \].IMON here is mass 
entails assuming that it has undergone a dcrivation~d 
'grinding' rule which converts countable individuals in 
masses. Nevertheless, a round-slice of lemon is 
always a slice of some individual lemon, not a special 
measure of substance which some time in the past 
was 'lemon'. In any case, if a 'lemon' weren't an 
individuated and bounded thing, it couldn't be sliced 
and tile shape of tile portion wouldn't depend on that 
of the whole. The confusing point is that I,IMON in 
tile example, RODAJA DI: LIMON, surfaces 
grammatically as substances usually do -namely, zero- 
delermined. Bul zero-detcrlninalion is not exclusively 
a ressource to refer to substances, it is the way of 
expressing cumulative rclcrence. Both individuals and 
substances may be refered to cumulatively, that is, bc 
construed as an indiffercntiated ~unassment. This 
surfaces in the language as a zero-determiner plus tile 
244 
noun in singular in the case of substances (a glass of 
wine), and either in singular or plural in the case of 
individuals (a slice of lemon, a basket of lemons). 
St), in our poinl of view PNs lipically select the 
nOllll of the whole as it surfaces when conSll'uing 
cumulative reference -bul this doesn't compulsorily 
enlails neither lhe referent is a substance nor it is 
refcred to by lliOallS of a lll}lSS llOHll, ht lhe case of 
individuals, referenls still are bounded things, hence 
both they can be sliced and the shape of lheir portions 
still can depend on that of the original whole. We 
can't go further with Ihe issue here but, at last, what 
the discussion above stands for is that human 
conceptualisation is c(mside,'ed as Ihe cause, and the 
mass-count distinction, as tb.e surface effect. 
PNs are not straightforwardly referential, as they 
predicate wilh reference Io another entity. This may Ix: 
noticed considering sentences such as '??.h;hn rite a 
slice or ??I dt-attgllt three CUl)S. They arc semantically 
tmcomplele as they don't allow the hearer to relricve 
fl'om Ihem the information the speaker wanls Io 
convey, l:urlher information as in ,lohn ate a slice of 
cake or It was an excellent cq\[lee. I draught three cups 
is needed to do the task. When appearing in the 
discourse, PNs need of further specificalion of the 
referent, either via of-compleinenlalion or via ellipsis 
or anaphora. Consequetltly, they can not bc tnnary bul 
relational predicates in Ihe sense of \[I,AN91 l, thai is, 
terms which are predicates cmly with reference to 
some other entity. 
A basic linguistic t'ealllre of PNs is lhal they, as 
relational predicates, bear seleclional restrictions. 
Namely, each kind at: PN Call combine with cerlain 
relercatial llOtlllS but Call 11o1 combine wilh others, 
depending on ccrlain fcaltlrcs of tile refcrelllial tlOUXl. 
These fealures are nlostly linguistic (type, 
countabilily, singular or plural) bul also can depend 
on knowledge of the world (physical slale, etc.). We 
hypothesise that, in general, distinctions belween 
classes of PNs contcerning selectional restrictions 
must be due to linguistic reasons, while further 
specifications within each class would be due to 
properties of the referent, l:,.g., it could be asstlmed 
that containers (CUlrV, baskets) select \[-BN items 
(substances and plurals), and more specifically, cttps 
select liquids and baskets non-liquids. 
4. Sorts of PNs 
We are not committed here to represent individuation 
of groups (temn, committee) or aggregates (cattle, 
fimfiture), ha our background ontology, which is 
inlended to represent things in the world as 
conceplualised by humans (rigA), these conslilute a 
different class since, in this class of words, speakers' 
conceptualisalion focuses not on the elemenl entities 
but in their aggregation, l'lurals are considered as 
representing an aggregation (Iherefore a -B+t concept) 
of bounded things (therefore cithcr individuals or 
groups) by means of a derivative (lexical) rule applied 
on signs denoting those elements (fig.2) - e.g. cow 
--> cows, team --> teams; but gold,callle --> 
*golds/*callles). 
lNl'IYllkq (±1) COILECHONS(+I) 
INI)IVII)UAI.S(+B) SUBSTANCKS(-B)(IROUPS(+B) A(IGREGATFN(-g) 
Figure 1. Ontology 
Entity-portioning terms have been sorted as fl)llows: 
Contents (hellceforlh CENT) (a bucket of water, a 
basket of wheat, a basket of lemons). They are 
metonymies of containers expressing a 
conventionalised measure or quantity of a l-B\] entity. 
Shape is not relevant -a bathtub may contain a bucket 
o1: water without Ihere being any bucket in it 
(IIANgll) 
in: I 
+B \] -- 
TYPF: x 
SYNcount 
I -B +1 out: TYpl':aggregate A(;R: phuu'al ('ONST:liI:\['S: x 
Figure 2. l'luralizatiml (I,exical) Rule 
i,\]lements (\]:d\]l') tUN GAJ() l)li I,IMON \[an 'inncr-pre- 
existent-division-of-some-fiuits'of lemon\], a grain of 
rice). They are individuations of pre-existing parts of 
the whole. They select \[+II entities, either individuals 
or substances. They are not committed to an Agentive 
process as they may remain attached to the whole. 
Shape and measure, if considered relevant, are inherent 
to the portion itself. 
Boundaries (BOUND) (the tip of the tongue, the 
su(~we of the sea, the top of a box). They are 
idealisations of physical boundaries of the whole. 
Select \[+B\] entities. They are non-Agentive either. 
Their shape is tightly related to Ihat of the whole bt|t 
one of their dimensions is concepmalised as close to 
non-existence (\[JAC9 l\]). Analogously, they denote a 
minimal quantity of the whole. 
Bolh Detached (IY\['CII) (a slice of cake, a slice of 
lemon) and Modelled (MI)LI)) portions (a lump o.f 
sugar, a sheet ofpcq?er) have been drawn out of the 
whole and bear a shape straightforwardly determined 
by such Agenlive process. The meaning of the former 
focus on the Agentive, which is a process of cul or 
fragmentation el' a \[+B solid. The latter focus on 
shape, which is often conceptualised 
schematically(sheet: a plane; lump, ingot: brick- 
shaped). The Agenlivc is a process of inodelling of a 
\[-B \] substance. 
Sulnmarising abotlt seleclional restrictions of 
these sorts of PNs, they come out as follows: 
El,T: select \[+1\] entities (=individuated or substance) 
(a 'pre-existing-inner-division' of I.IMON, wheat, 
sugar) 
BOUNI): \[+B\] entities (=individuated) (a 'boundary'of 
245 
ORTt h slice 
IN FCAT: NP "77 CAT: / NP SIGN :/SAM: P(y) = \[2\] I I 
\[~outcr: true LQUALIA: WilLIe: 'dic =\[33J 
SEM: slice(x,y) & P(y) = \[1\] & \[2\] 
QUALIA: FORMAL: bounded \] 
I CONST: sXice(x,y) = t~q I TELIC: \[31 | 
k AGEN\]IVE: cu' \] 
" ORTtI: 'slice of cake' 
CAT: \[~OU1VI,: ,rue \] 
SEM: slice(x,y) & cake(y) 
\['FORMAL: bound¢'d \] 
QUALIA: \['rELIC: eat l LAGEbrrlV E: 
cul J 
Figure 3. 
a tongue, box, cake, LIMON) 
CONT: I-B\] things (=substances, plurals/aggregates) 
(a 'container' of wheat, sugar, water, paper, cakes, 
tongues, boxes) 
DTCHD: \[+B\] entities (=individuated) (a 'detached 
portion' of a lemon, cake) 
MDLD: \[-B\] entities (=substances) (a 'shaped mass' 
of sugar, wheat, paper) 
With respect to shape, it has to be noticed that 
while that of ELT and MDLD is inherent to the 
portion itself (in ELT because the porlion pre-existed 
as an individual; in MDLD because the whole was an 
mnorphous mass and it is tile process of portioning 
what has bounded the new thing), in BOUND and 
DTCIID shape is somehow relative to the whole. 
This way, a RODAJA is round because it is a cross-cut 
of either approximately-spherical (lemon)or 
cylindrical (sausage) objects; a slice of bread will be 
elliptic or square depending oil whether the 'bread' is 
the classical lo~ff or tile modem ixflyhedfic-shapcd one; 
top of a box will show identic~d behaviour. 
Something similar happens with relative 
quantification. While the measure conveyed by 
CONT, ELT and MI)LD is absolute, that of BOUND 
and DTCttl) is relative: a top of a box or a slice of 
bread will be bigger or smaller depending on tile 
magnitude of the box or the loaf of bread. 
Composition 
5. Representation 
To represent PNs in the LKB we have made some 
interpretations for FORMAL aud CONST Quales of 
the QUALIA. 
We assume that the minimal and most basic 
FORMAL distinction among entities (as 
conceptualised by speakers) is that of their 
bouudedness or not in terms of \[JAC91\]. Therefore, 
this Quale will be a~signed to one of both types (or a 
coherent subtype). Similarly, the miuimal 
constitutive distinction to be done is assumed to be 
that of entaihnent or not about internal structure of 
ORTI 1: 'cake' 
CAT: NP 
SEM: cake(y) 
QUALIA: 1" THLIC: eat \] L AGENTIVE: 
bake 
things. Therefl)re, the CONST role will be assigned 
to one of both \[_+I\] types (i str true/i str false). 
In this way, selectional restrictions of PNs will be 
basically defined as selection of signs hearing 
appropriate types lot their FORMAL mid CONST 
Quales. 
As defined ill \[PUS951, SltAPE ~md magnitude 
(MAGN) are features of the FORMAL Role. Their 
values cml be, as discussed above, either absolute or 
relative, depending on tile kind of portion. In the latter 
cases, SIIAPE and MAGN of portions will be a 
function of file corresponding values of file QUALIA 
of tile whole 2. This interpretation of the MAGN 
feature accounts for the nature of relative quantifiers of 
PNs. 
At their turn, \[+I\] CONSTs be~ the feature ELTS 
e.g. riee:QUALIA:CONST:ELTS:grain. (vid. 
\[\]ACgll, ,also \[CO1×)21). 
\[PUS95\] (assuming \[VIK94\] interpretation) 
attributes the CONST Role the function of 
representing the predicative relation Part-Of. 
Coherently, we assume CONST as encoding a 
relational predicate R(x,y), being R a type 
taxonomically daughter of Part-Of. In the default case, 
R will be 'Portion' and in more fine-grained cases, a 
daughter type of it -e.g. 'Slice'. 
The Logical Semantics of PNs (SEM) will 
account for their both pm'titive and relational nature 
by adopting as predicate-,'ugulnent structure that of 
their CONST Role. For the sake of unification, in the 
LKB, SEM will be the conjunction of this predicate 
and the SEM value of the sign deuoting the whole. 
qhis way (vid.fig.3), that of 'slice of cake' will result 
in SLICE(x,y) & CAKE(y) -thus accounting /'or the 
logics of John eats a slice of cake as EAT(e,John,x) 
& SLICE(x,y) & CAKE(y) versus that of John eats 
cake as EAT(e,John,x) & CAKE(x). 
2 \[JAC9I\] develops a method to formalise relative 
shapes including judgements about dimensionality. 
246 
For ease of exposition, the syutax (CAT) of PNs 
is represented here as the colnplex category 
N/NP_sigu, where the NP_sign is app!'opriately 
lex-poriion-sign 
~.'A'I': NP 1 CAT: /NP SIGN= ISEM: P(y) = \[2\] 
E UALIA: TELIC: relic=\[3\] COUNT: true 
SEM: \[11 & \[2\] (= R(x,y) & P(y) 
IND: individual 
~TORMAL:I ...... dcd \] 
QUALLa: ICONST: R(x,y)=\[1} 1 
\[TELIC: \[3\] J 
Figure 4. General Portion Sign 
speeilied to account for selectional reslrictions and 
transitivity of properlies between the whole and the 
porlion via feature reeiitraucies. This way, the 
eoinlx)sition of slice (N/NP) alld cake (NP) will restlll 
iu au N (slice of cake). This accotulls fof the fact thai 
partitive constructions (e.g. slice qf cake) do bern" the 
combinatorial possibilities of nouns, while those of 
PNs are distinct and specific. The pleposiliou (oJ) is 
omitted here -not in the LKB implelneimltiou- since it 
is unrelewmt its it lacks senianlie COllteilt. We assume 
so \[CI IO81\] aualysis which cousiders of in lhis kiud 
of COllSlrtlclious a lnere surface case-marker. This 
view is confinned by data of Spauish (tIN VASe VINe 
=: UN VASe )\].~._VINO, \[IN "I'ROZO PAN : I 1N 'I'I{OZO 
PAN) \['a glass witie' = 'a glass o1__~ wine', 'a portioli 
bread' = 'a porlion of bread'\] in which the preposition 
is elidible -soinelhiug which is not possible in the 
case of couleutful prepositions (VENGO 1) I{ 
BARCELONA-> *VF, NGO BARCEI,ONA) \['l-come from 
Barcelolm'-> *'I-colne Barcelona'l. 
Moreover, CAT bears the feature COUNT 
slaildiug, as well for ease of exposition, for the range 
of (surface) gramlnalical belmviour of lexical signs 
usually refened to as couulability/uncounlability (see 
discussiou alxwe). 
lex-BOllND-porti0n-sign 
CAT: COUNT:true 
CAT:N / NP .SIGN : SEM: IND: individual 
~ounded G 
QUALIA: FORMAl.: I SilaPiZ:~l, ap< = {211 
tMA(IN: nlagi' = \[3~ 
QUALIA:FORMAL: "SIIAPE:tunclion oil2\] \] 
I MAGN: fundi0n_0f-\[3\] (=e) j/ -- 
Figure 5. Boundary Portions 
Provided all which has boon discussed up to here, 
the general lex-PORTION-sign is defined as in 
fig.4; that is, as selecting NPs and resultiug in 
FORMAL:\[+B\] entity-denoting signs (lherefore 
individuated and syntactically couutable) where the 
only QUALIA feature which percolale from the whole 
is the TELIC Role -the rest of Quales may be 
oveiTiddeu by that of the PN. 
Specific sub-types are shown in figs. 5 to 9. 
BOIINI) PNs (fig.5) select \[+B\] entities (Iherefore 
individuated and countable) (the tip of the tongue). 
Being \[+B\], such wholes bear definite shape and 
magnitude; therefore such values for the portiou will 
be fuiictious of those of the whole. MAGN, 
specifically, is assumed to be conceptualised as 
solnehow ininiln~d, therefore notated 'e' (\[JAC91\]). 
f • 
'x-l)TCl I- portion-sign 
"1 
SEM: INI): individual / 
CAT:N/NP SIGN = i \[hounded \]1 
\[ QUALIA: r<)RMAL: I sttAPl3: sh.~ : \[llll 
i I MAGN: magn = t:}ll -- 
..... <"'Jl AGI{NI'IVI{: detachment j 
Figure 6. Detached Portions 
Similmly, StlAPE and MAGN of 1)TCItD PNs 
(fig.6) arc fuactious of SIIAPE and MAGN of the 
wholes they select. The difforcuco with BOUND l'Ns 
is that Ihe MAGN value doesu't tend to be minilnal. 
'lhe AGI{N'I'IVI: Role is here relevant -as it as well is 
in MI)I J) PNs. 
lex-MDl,D-portlon-sign 
\[ CA'I': COUNT: fldse 11 I SliM: IND:subslance 
('AT: N / NP SIGN = l \[~FORMAL: unbounded I I"°"sw:P'" <:"l 1 
L L F, o..AL: s<,,<,,,.q-1 
/ i><'N:'"<" J I 
/,,>NST: ptl q / 
iii o~\]elling / 
_ J 
li'igure 7. Modelled l)ortions 
What is more remarkable in MDLD PNs (fig.7) 
it that the CONST type of the whole (thelelore its 
value for CONST:I{LTS) is iuherited by the portion 
-e.g., if 'sugm + 'is \[+1\] and consists of grains, a lump 
of sugar so; if 'paper 'has no entailment about internal 
structure, a sheet of paper has not either. MAGN is 
absolute (i.e., not related to that of the whole, since 
that is l-B\]; e.g., in broad outline, ',all the sugm'/paper 
of the world'). SHAPE is assumed to be schematic 
(vid. §4). 
SIIAPE and MAGN of ELT portions (fig.8) me 
also nou-relative. These PNs select \[+I\] eutities, 
usually substances ('wheat', 'rice') but also possibly 
individuals ('lelnou', as conventioualised in Spanish 
as internally-structured in GAJOS). The value for 
CONST:ELTS of the whole will be the CONST 
247 
predicate of the portion, titus its SEM predicate -e.g. 
rice:QUALIA:CONST:ELTS:grain=> 
grain:QUALIA:CONST:grain(x,y) => 
grain-of-rice:SEM:grain(x,y) & rice(y). 
ex-ELT.portion.sign 
EM: P(y) = 131 
CAT:N/ NP SIGN \]Qt,ALIA: CONS'I':\[~ str true 71 
SEM: \[2\] & \[31 L LELTS: ~lt~ = \['lJ.J 
QUALIA: \]-FORMM,: \[~l IAI'\[{: sha peT" \] 
/ L~'AGN: magnJ \] 
ICONST: ~_str ral~ 71 
_ L j 
-N 
! 
Figure 8. Flenlent l'ortions 
Last, CONT PNs (fig,9) select \[-B\] items 
(therelbre substances but also plurals) 3. The portion 
retains the constitution o1' the whole. As discussed 
above, SIIAPE is not relevant, measure (MAGN) is. 
AGENT1VI{, if cousidercd relevant, will be a process 
of filling the container. 
lex-CONT-porlbn-sign 
2AT: N/ NP SIGN= 
QUAIJA: 
I A'\[': C()(JNT: false 
IX) NST: f~'LP~f~ ::|'s = \[ 2\]~ 
QUAI ,IA: ~ORMA\],: Ul|b~llded 
I I"OP, MAL: \[\] ....... dcd \]7 LMAGN: mag,J\] CONST: Jill \] / U ws:l \] / AGENTIVE: filling ..J 
Figure 9. Container Portions 
6. Concluding Remarks 
In lhis paper we presented a system of representation 
of relational nouns denoting per'lions, segments and 
relative quanlities of entities according Io the Theory 
of Qualia (\[PUS95\]), which has been parlially re- 
interpreted and adapted to the insights of Conceptmd 
Semantics (\[JAC91\]). This syslem accounts for a 
range of linguistic facts, being the most remm'kable 
the following: 
1. Portions m'e mainly encoded in the language by 
means of constructions inslead of by single lexical 
units 
2. Portions are both bounded entities aml relative 
measures of the wholes of reference 
3. Portions inherit li'om their wholes their purpose 
or function, but, on the contrary, they show 
distinctive shape, mafimlude and origin 
3 Possibly also \[-B\] collections (groups) (a wagon of 
cattle), but, as said before, we're not commited here to 
discuss individuation of collections. 
4. Partitive Nouns (PNs) select whole-denoting 
nouns according to the properties of the referent 
wholes ,'ks conceptualised by speakers 
PNs havc been classified according to the semantic 
regulmities they show, resulting in a system of five 
basic types, which have been represented in a 
unification formalism, LKB-LRL (\[COP92\]), 
allowing for composition of PNs (e.g. slice) and NPs 
(e.g. cake) (plus the semanlically void preposition 
'of; in Spanish, DE) into portion-denoting signs (e.g. 
slice of cake). 
Acknowledgements. I'd like to thank Drs. Toni 
Marti and Iloracio Rodriguez for their comments and 
support. This research is funded by the project PB-94- 
0830 of the DGICYT. 
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