A semantics theory of word classes.pdf

179
Croatian Journal of Philosophy
Vol. XIV, No. 41, 2014
A Semantic Theory of Word Classes
PETER GÄRDENFORS
Cognitive Science, Lund University
Sydney Technical University
Within linguistics a word class is deﬁned in grammatical terms as a set
of words that exhibit the same syntactic properties. In this paper the aim
is to argue that the meanings of different word classes can be given a
cognitive grounding. It is shown that with the aid of conceptual spaces,
a geometric analysis can be provided for the major word classes. A uni-
versal single-domain thesis is proposed, saying that words in all content
word classes, except for nouns, refer to a single domain.
Keywords: Conceptual spaces, cognitive semantics, word class-
es, single domain, convexity, noun, adjective, verb, preposition,
adverb.
1. Cognitively grounded semantics1
What is it that you know when you know a language? Certainly you
know many words of the language—its lexicon; and you know how to
put the words together in an appropriate way—its syntax. More impor-
tantly, you know the meaning of the words and what they mean when
put together into sentences. In other words, you know the semantics of
the language. If you do not master the meaning of the words you are
using, there is no point in knowing the syntax. Therefore, as regards
communication, semantic knowledge is more fundamental than syn-
tactic. (I am not saying the syntax does not contribute to the meaning
of a sentence, only that without knowledge of the meanings of the basic
words there is no need for syntax.)
In Gärdenfors (2014), I connect the semantics of various forms of
communication to other cognitive processes, in particular concept for-
mation, perception, attention, and memory. As Jackendoff (1983: 3)
puts it: “[T]o study semantics of natural language is to study cognitive
1
This article is, to a large extent, a summary of material in Part 2 of Gärdenfors
(2014).

180 P. Gärdenfors, A Semantic Theory of Word Classes
psychology”. My theoretical starting point is that our minds organize
the information that is involved in these processes in a format that
can be modelled in geometric or topological terms—namely in concep-
tual spaces. The theory of conceptual space was presented in an earlier
book (Gärdenfors 2000). My general semantic program is to show that
by using conceptual spaces, a unified theory of word meanings can be
developed.2
Most researchers within semantics look at the meaning of words
from a linguistic perspective. From this perspective it is difficult to free
oneself of syntactic concepts. For example, the “arguments” of verbs
show up in most semantic analyses (for example, Levin and Rappaport
Hovav 2005). The notion of argument derives, however, from syntax.
Among other things, this leads to the distinction between transitive
and intransitive verbs. However, this distinction does not correspond
to any clear-cut semantic distinction. Similarly, it is said that verbs
and adjectives are used in a “predicative” manner. The notion of pred-
icative derives from theories in philosophy and linguistics that aim at
grounding semantics in predicate logic. In my opinion, this is an artifi-
cial construction that does not have a cognitive grounding. In contrast,
my ambition is to develop semantic models that are constructed from
general cognitive mechanisms. The semantic theory of this article is
supposed to be syntax-free. In other words, the semantic notions should
not depend on any grammatical categories. This does not mean that I
deny that syntax contributes to meaning (Langacker 2008: 3–4). I only
claim that semantics of word roots can be treated independently from
syntax.
2. The semantics of word classes
One of the most fundamental concepts of linguistics is that of word
classes. In all languages, words can be grouped in distinct classes with
different semantic and syntactic functions.3
In English the words have
traditionally been classified into eight classes: nouns, pronouns, ad-
jectives, verbs, adverbs, prepositions, conjunctions, and interjections.4
When word classes are taught at an introductory level in school, se-
mantic criteria are used, for example that nouns stand for things and
verbs describe actions, but these criteria are seldom presented in a sys-
tematic and rigorous way.
In contrast, within linguistics a word class is defined in grammat-
ical terms as a set of words that exhibit the same syntactic proper-
2
In linguistics, the appropriate word for “word” is “part of speech”. When
I use “word”, I normally mean “word stem”, since I will not be concerned with
morphology.
3
There are other opinions: Gil’s (1994) work on Riau Indonesian suggests that it
has no distinctions between different kinds of words.
4
There exist, however, other identifiable word classes, for example, numerals
and articles.

P. Gärdenfors, A Semantic Theory of Word Classes 181
ties, especially concerning inflections and distribution in sentences. I
do not believe in a universal definition of word classes (cf. Croft 2001,
ch. 3). Syntactic structure, including the division into word classes, is
language-specific. However, one can identify prototypical structures
among words that can be used in classifications. Croft (2001: 63) writes:
“Noun, verb, and adjective are not categories of particular languages
… [b]ut noun, verb, and adjective are language universal—that is,
there are typological prototypes … which should be called noun, verb,
and adjective.” In contrast, my position is that the syntactic markers
have evolved as effects of the divisions of words into categories, not as
causes.
The fact that major words classes such as verbs, nouns, and ad-
jectives can be identified in almost all languages suggests that there
are universal patterns in human cognition that make the division into
these classes particularly useful for communication (Dixon 2004). The
structure of communication is subject to the same cognitive constraints
as thinking and problem solving in general. Therefore it is reasonable
that the structure of language, at least to some extent, is determined
by such general cognitive principles. In particular, I assume that the
structure of language is governed by the same principles of processing
efficiency of representations as are other cognitive processes.
I do not claim that there is any simple mapping between word class-
es and structures in conceptual spaces. As an illustration, Dixon (2004:
2) writes: “[A] lexical root cannot be assigned to a word class on the
basis of its meaning. If this were so, then ‘hunger/(be) hungry’, ‘(be)
mother (of)’, ‘(be) two’, and ‘beauty/(be) beautiful’ would relate to the
same class in every language, which they do not.” Dixon also points out
that the concept of ‘needing to eat’ is expressed as nouns, adjectives, or
verbs in different languages and that mother and father are verbs in
some American Indian languages. Nor do words (word roots) necessari-
ly belong to particular word classes. An example from English is round,
which can be used as adjective, noun, verb, adverb, and preposition.
In this paper the focus will be on showing how the meanings of dif-
ferent word classes can be given a cognitive grounding. I will expand
on the analysis of nouns and adjectives that I outlined in Gärdenfors
(2000). Before embarking on that project, however, I will briefly pres-
ent conceptual spaces.
3. Conceptual spaces as a semantic framework
A conceptual space consists of a number of quality dimensions. Exam-
ples of quality dimensions are temperature, weight, brightness, pitch,
and force, as well as the three ordinary spatial dimensions of height,
width, and depth. Some quality dimensions are of an abstract non-
sensory character. In Gärdenfors (2014), I argue that force dimensions
are essential for the analysis of actions and events and thereby for the
semantics of verbs.

Quality dimensions correspond to the different ways stimuli can be
judged similar or different. For simplicity, I assume that the dimen-
sions have some metric, so that one can talk about distances in the con-
ceptual space. Such distances indicate degrees of similarity between
the objects represented in the space.
It is further assumed that each of the quality dimensions can be de-
scribed in terms of certain geometrical structures. A psychologically in-
teresting example is colour. Our cognitive representation of colour can
be described along three dimensions. The first is hue, represented by
the familiar colour circle going from red to yellow to green to blue, then
back to red again. The topology of this dimension is thus different from
the quality dimensions representing time or weight, which are isomor-
phic to the real number line. The second dimension is saturation, which
ranges from grey at the one extreme, to increasingly greater intensities
of colour at the other. This dimension is isomorphic to an interval of the
real number line. The third dimension is brightness, which varies from
white to black, and thus is also isomorphic to a bounded interval of
the real number line. Together, these three dimensions—one circular,
two linear—constitute the colour domain as a subspace of our percep-
tual conceptual space. It is typically illustrated by the so-called colour
spindle.
The primary function of the dimensions is to represent various
qualities of objects in different domains. Since the notion of a domain
is central to the analysis, I should give it a more precise meaning. To
do this, I will rely on the notions of separable and integral dimensions,
which I take from cognitive psychology (Garner 1974, Maddox 1992,
Melara 1992). Certain quality dimensions are integral: one cannot as-
sign an object a value on one dimension without giving it a value on
the other(s). For example, an object cannot be given a hue without also
giving it a brightness (and a saturation). Likewise the pitch of a sound
always goes with a particular loudness. Dimensions that are not inte-
gral are separable: for example, the size and hue dimensions. Using
this distinction, a domain can now be defined as a set of integral dimen-
sions that are separable from all other dimensions.
A conceptual space can then be defined as a collection of quality
dimensions divided into domains. However, the dimensions of a con-
ceptual space should not be seen as fully independent entities. Rather,
they are correlated in various ways, since the properties of those ob-
jects modelled in the space co-vary. For example, in the fruit domain,
the ripeness and colour dimensions co-vary.
It is impossible to provide any complete listing of the quality dimen-
sions involved in the conceptual spaces of humans. Learning new con-
cepts often means expanding one’s conceptual space with new quality
dimensions (Smith 1989).

4. Properties and concepts
Conceptual spaces theory will next be used to define a property. The
following criterion was proposed in Gärdenfors (1990, 2000), where the
geometrical characteristics of the quality dimensions are used to intro-
duce a spatial structure to properties:
Criterion P: A property is a convex region in some domain.
The motivation for criterion P is that, if some objects located at x
and y in relation to some quality dimension(s) are both examples of a
concept, then any object that is located between x and y with respect to
the same quality dimension(s) will also be an example of the concept.
This is the definition of convexity.
Properties, as defined by criterion P, form a special case of concepts.
I define this distinction in Gärdenfors (2000) by saying that a property
is based on a single domain, while a concept is based on one or more
domains. This distinction has been obliterated in both symbolic and
connectionist accounts, which have dominated the discussions in cogni-
tive science. For example, both properties and concepts are represented
by predicates in first-order logic. However, the predicates of first-order
logic correspond to several different word classes in natural language,
most importantly those of adjectives, nouns, and verbs.
A paradigm example of a concept that is represented in several do-
mains is “apple” (compare Smith et al. 1988). One of the first problems
when representing a concept is to decide which are the relevant do-
mains. When we encounter apples as children, the first domains we
learn about are, presumably, those of colour, shape, texture, and taste.
Later, we learn about apples as fruits (biology), about apples as things
with nutritional value, etc.
The next problem is to determine the geometric structure of the do-
mains: i.e., which are the relevant quality dimensions. Taste space can
be represented by the four dimensions of sweet, sour, salty, and bitter;
the colour domain by hue, saturation, and brightness. Other domains
are trickier. For example, it is difficult to say much about the topologi-
cal structure of “fruit space”, in part because fruits (such as apples) can
be described relative to several domains. Some ideas about how such
“shape spaces” should be modelled have been discussed in e.g. Marr and
Nishihara (1978), Edelman (1999), and Gärdenfors (2000). Instead of
offering a detailed account of the structures of the different domains, let
me represent the “apple” regions in the domains verbally, as follows:
Domain Region
colour red-yellow-orange
shape roundish
texture smooth
taste regions of the sweet and sour dimensions
nutrition values of sugar content, fibre content, vitamins, etc.
fruit specification of seed structure, fleshiness, peel type, etc.

Concepts are not just bundles of properties. They are also correlations
between regions from different domains that are associated with the
concept. The “apple” concept has a strong positive correlation between
sweetness in the taste domain and sugar content in the nutrition do-
main, and a weaker positive correlation between redness and sweet-
ness. Such considerations motivate the following definition for con-
cepts.5
Criterion C: A concept is represented as a set of convex regions in a
number of domains, together with information about how the regions
in different domains are correlated.
Elements from theories in psychology and linguistics contribute to
the analysis of concepts I present here. The kind of representation in-
tended by Criterion C is, on the surface, similar to frames, with slots for
different features. Frames have been very popular within cognitive sci-
ence as well as in linguistics and computer science. However, Criterion
C is richer than frames, since it allows representing concepts as more
or less similar to each other and objects (instances) as more or less
representative of a concept. Conceptual spaces theory can be seen as
combining frame theory with prototype theory, although the geometry
of the domains makes possible inferences that cannot be made in either
of those theories (Gärdenfors 1990, 2000).
The distinction between properties and concepts is useful for
analysing the cognitive role of different word classes. In brief, I propose
that he main semantic difference between adjectives and nouns is that
adjectives like red, tall, and heavy typically refer to a single domain
and thus represent properties, while nouns like dog, apple and car con-
tain information about several domains and thus represent object cat-
egories. Next, I will look closer at these proposals.
5. Nouns
In informal definitions of nouns, it is said that they refer to things:
objects, persons, places, events, substances, etc. However, linguists are
in general not satisfied with this kind of description, since it is diffi-
cult to specify a complete list of categories. Furthermore, the definition
uses abstract nouns to define the very notion of a noun, which makes
it slightly circular.
There also exist abstract nouns that have no physical referents, for
example law, retirement, inflation, and mind. Lyons (1977: 442–445)
distinguishes three fundamental “orders”: (1) physical objects; (2)
events, processes, states-of-affairs; and (3) propositions, schemas, etc.
that “are outside space and time”.6
One of the main communicative
uses of the abstract nouns in Lyons’s second and third orders is as “hid-
den variables” in causal explanations. For example, the sentence “the
5
For a more precise definition, see Chapter 4 in Gärdenfors 2000.
6
See Paradis (2005) and Ravid (2006) for finer classifications of nouns.

economy is stagnating because the government cannot control infla-
tion” expresses a causal relation between three abstract nouns.
Names can be seen as special cases of nouns. The difference is that
names typically pick out a unique referent. If the basic communicative
function of a noun is to express a referent and names identify a unique
referent, why then does not everything have a name? It would seem
that if every object had a name, this would eliminate many ambiguities.
The reason why nouns are needed is one of cognitive economy (see for
example, Kemp and Regier 2012). Our memory is severely constrained
and it would be impossible to learn and remember a name for all ob-
jects one wants to communicate about. Nouns referring to basic-level
categories group objects in categories that are suitably large for com-
munication so that ambiguities become sufficiently rare. The cognitive
solution is a balance between the precision of the noun and the number
of words that have to be remembered.
6. Adjectives
My account of the semantics of adjectives will be based on my notion
of properties. The key idea is that adjectives express properties. This
generates the following thesis:
Single-domain thesis for adjectives: The meaning of an adjective can
be represented as a convex region in a single domain.
For many adjectives, the single-domain thesis seems to be valid, in
particular for adjectives that relate to domains that are acquired early
in language learning. In particular, I conjectured (Gärdenfors 2000)
that all colour terms in natural languages express convex regions with
respect to the colour dimensions of hue, saturation, and brightness.
This means, for example, that there should be no language that has a
single word for the colours denoted by green and orange in English (and
which includes no other colours), since such a word would represent
two disjoint areas in the colour space. Strong support for this conjec-
ture has been obtained by Jäger (2010).
Adjectives are also used for comparing things: Many languages
have comparatives such as taller and smarter that can be used both
as specifications (“the taller woman”) and predicatively (“Victoria is
smarter than Oscar”). Many languages also have superlatives, for ex-
ample, tallest and smartest, which again can be used as specifications
and predicatively.
Nouns seldom allow comparisons (Schwarzschild 2008: 319): Expres-
sions like *dogger, *more dog are hardly used. Why do nouns not allow
comparatives, when adjectives do? A comparison requires a well-defined
dimension along which the comparison is made. Since many adjectives
are based on one-dimensional domains, a comparative (and a superla-
tive) then simply involves a comparison of the values along this dimen-
sion: For example, “Oscar is taller than Victoria” means that Oscar’s
coordinate on the length dimension is greater than that for Victoria.

If the adjective is based on a multidimensional domain, the situa-
tion becomes more complex. In general the comparative means “closer
to the prototype for the adjective”: Greener means closer to the green
prototype in colour space, healthier means lower value on some of the
dimensions involved in illness.
Nouns refer to things and verbs say something about what happens
to things. So why are there adjectives in language?7
Firstly, an adjec-
tive can be used as a specification of a noun (or noun phrase) that helps
in identifying a referent. For example, if you want somebody to fetch
you a particular book and there are several books present in the con-
text, you specify it further by saying “the green book” or “the big book.”
In addition to this kind of “element identification”, Frännhag (2010)
also considers “kind identification”. For example, you may request “a
thick book” when you want something to put on a chair for a child to sit
on, but it does not matter which book is delivered.8
Here, the goal is not
a particular object, but something that has a desired property.
Secondly, a typical function of an adjective is predicative. You can
utter “The stove is hot” as a warning. Linguistically, the adjective is
then a complement to a copula (“is”) or an intransitive verb (“the meal
tastes wonderful”). The specification function and the predicative func-
tion may very well be cognitively separated. Therefore, it is not obvious
that these functions should be expressed by only one word class. Dixon
(2004: 30) notes that some languages indeed have two different word
classes, one fulfilling the first function and another fulfilling the sec-
ond. Actually, some words classified as adjectives in English only have
one of the functions: Afraid and alive can only be used predicatively
and absolute and main can only be used as specifications (attributive-
ly) (Paradis 2005). The specification function can also be fulfilled by a
noun. For example “The silk scarf” can be used to distinguish among
several scarves.
7. Verbs
In linguistics, the semantic role of verbs has been described as predi-
cation (for example, Croft 2001). However, the notion of predication is
rather abstract—it derives from the Fregean view of language—and it
does not capture the communicative role of verbs. Also within philoso-
phy, there is recent criticism of the general use of predication (see e.g.
7
There has been discussion as to whether there are languages without adjectives.
For example it has been claimed that in Mandarin all adjectives are verbs. Dixon
(2004) reviews the evidence and he concludes that something that has the role of
modifiers can be found in all languages. He writes: “In some languages, adjectives
have similar grammatical properties to nouns, in some to verbs, in some to both
nouns and verbs, and in some to neither. I suggest that there are always some
grammatical criteria—sometimes rather subtle—for distinguishing the adjective
class from other classes” (Dixon 2004: 1).
8
Note that, in contrast to element identification, an indefinite determiner is used
for kind identification.

Ben-Yami (2004) and McKay (2006)). Ben-Yami (2004: 142–143) points
out that the common semantic content of what is called predication is
minimal. He writes the following about Frege’s notion of predication:
Ironically, Frege was mislead into a mistaken view of concepts, […]
by what he time and again warned against: mistaking mere grammati-
cal uniformity for a logical and semantic one. The semantic diversity
of predication, acknowledged by logicians from Aristotle’s Categories
on, disappeared under Frege’s pseudo-homogenous semantic relation
of falling under a concept. (Ben-Yami 2004: 143)
Furthermore, adjectives are used predicatively too, so the notion
does not characterize the use of verbs.
Verbs are necessary components in linguistic descriptions of events.
Gärdenfors and Warglien (2012) and Warglien et al. (2012) describe
events as complex structures built up from an agent, an action, a pa-
tient, and a result. Agents and patients are objects with different prop-
erties.9
It is assumed that the agent is able to act, which in the proposed
framework amounts to exerting a force (Gärdenfors 2007, Gärdenfors
and Warglien 2012).10
An action is modelled as a force vector (or a se-
quence of force vectors as in walking). The result of an event is mod-
elled as a change vector representing the change of properties before
and after the event. When the result vector is just a point, that is, when
the result is no change, then the event is a state.
Elsewhere, I have proposed that when we describe an event at
least one of the force and result vectors and at least one of the pa-
tient and the agent are part of the description (Warglien et al. (2012),
Gärdenfors 2014). When describing an event, agents and patients are
typically expressed by noun phrases and actions and results by verb
phrases.11
Given this suggestion for event expressions, the model thus
explains the linguistically basic distinction between nouns phrases and
verb phrases. In contrast to mainstream linguistics, this distinction is
made on a semantic basis derived from the cognitive representation of
events.
Verbs cannot mean just anything. Kiparsky (1997) proposed that a
verb can express inherently at most one semantic role, such as theme,
instrument, direction, manner, or path. Rappaport Hovav and Levin
(2010: 25) strengthened this by associating semantic roles with argu-
ment and modifier positions in an event schema, and proposed that ”a
root can only be associated with one primitive predicate in an event
schema, as either an argument or a modifier”. By using the cognitive
notion of a domain, I can refine and strengthen the constraints pro-
posed by Kiparsky and by Rappaport Hovav and Levin:
9
There exist events without agents such as event of falling, dying, and growing.
10
The force may also be ”mental” or ”social”. See Warglien et al. (2012).
11
Languages also have other means of describing results of actions, for example
by some generic verb such as “go” or “become” together with an adjective or a
prepositional phrase.

Single-domain thesis for verbs: The meaning of a verb (verb root) is
a convex region of vectors that depends only on a single domain.
For example, push refers to the force vector of an event (and thus
the force domain), move refers to changes in the spatial domain of the
result vector and heat refers to changes in the temperature domain.12
The single-domain thesis for verbs is analogous to the single domain
thesis for adjectives. The thesis entails that there are no verbs that
mean ‘walk and burn’ (multiple domains) and there are no verbs that
mean ‘crawl or run’ (not convex).
Since the model requires that an event always contains two vectors,
the constraint entails that a single verb cannot completely describe an
event, but only bring out an aspect of it. However, the two-vector model
has the testable consequence that a construal can always be expanded
to contain references to both the force and result vectors. More precise-
ly, for any utterance based on a construal involving only a force vector,
one can always meaningfully ask “What happened?”; and for any utter-
ance based on a construal involving only a result vector one can always
ask “How did it come about?”
According to the model, verbs have two main roles: (1) To describe
what has happened (or will happen); and (2) to describe how it hap-
pened (or will happen). This is reflected linguistically by the distinc-
tion between result verbs, for example, run, hit, and wipe, and manner
verbs, for example, fall, boil, and clean (Rappaport Hovav and Levin
2010; Warglien et. al 2012). A special case is when nothing happens,
that is, when the event is a state. Verbs describing states such as stay,
live and the most general is are all result verbs.
8. Prepositions
Adjectives modify a noun by specifying a property in a domain belong-
ing to the object category that is referred to. Most prepositions can be
grouped into two classes: locative, indicating where something is, and
directional, indicating where something is going. Locative prepositions
modify a noun (noun phrase) by specifying the location (a region) in the
(visuo-)spatial domain: “Give me the bottle behind the bread!” Another
function is fulfilled by directional prepositions. In a sentence such as
“Oscar went to the library,” the phrase “to the library” has the same
function as a result verb: it specifies the result vector of an event. Note
that in both functions, the preposition is combined with a noun (or a
noun phrase). My proposal is that locative prepositions are represented
by convex sets of points and directional prepositions by convex sets
of paths. In line with the analyses of the semantics of adjectives and
verbs, I therefore put forward the following thesis:
12
Possible exceptions to this general rule are verbs that describe changes in
ontology (see section 4.4) and verbs like give that describe intentional actions
involving recipients (see section 4.6). These are discussed in Gärdenfors (2014,
Section 10.3.2).

Single-domain thesis for prepositions: Prepositions represent con-
vex sets of points, paths or vectors in a single domain.
Locational and directional prepositions depend on the (visuo-)spatial
relations. In order to model the meaning of prepositions I need to make
some assumptions about how to model the spatial domain. Normally,
this domain is represented with the aid of the Cartesian coordinates x,
y, and z, representing ‘width’, ‘depth,’ and ‘height’ and where distances
are measured using a Euclidean metric. However, there is another way
of representing space, namely in terms of polar coordinates that rep-
resent points in space in terms of distance and angles. A new defini-
tion of ”between”, and thereby convexity, that differs from standard
Euclidean betweenness can be defined in terms of polar coordinates.
For example the set of point of a semicircle convex points with respect
to polar convexity (see Zwarts and Gärdenfors (2014) and Gärdenfors
(2014, Ch. 11) concerning the technical details). Given this definition
of convexity, it can be shown that most locative prepositions, such as
inside, outside, near, far, in front of, and behind, can be represented by
convex set of points.
Similarly, a betweenness relation for paths is easy to define and
thereby convexity of sets of paths. On the basis of such a definition, it is
easy to show that the meaning of directional prepositions, for example,
to, from, into, out of, through, along, and across, correspond to convex
sets of paths.
In contrast to most analyses within linguistics, I argue that preposi-
tions do not only refer to the (visuo-)spatial domain. Some prepositions
refer to the time domain. In English, the most common ones are before
and after.13
In addition, most typical uses of the prepositions against,
over, on and in depend on the force domain (see Vandeloise (1986) and
Gärdenfors (2014, Ch. 11) for arguments).14
In parallel to the theses for adjectives and verbs, the single-domain
thesis for prepositions claims that each use of a preposition refers to a
single domain, but it is not required that all uses are based on the same
domain. What makes the thesis for prepositions a bit complicated is
that there are frequent metaphorical transformations of meanings that
bring prepositions that have the force domain as their basis into the
(visuo-)spatial domain. And spatial prepositions are often used meta-
phorically for other domains. For example, in “Oscar came out of his
depression”, the directional out of is used to refer to a path going from a
state of depression to a non-depressed on in the emotional domain. As
a matter of fact, metaphorical uses of prepositions are ubiquitous. Nev-
ertheless, I submit that for each preposition there is a central meaning
that depends on a primary domain.
13
Historically, however, before and after referrred to the spatial domain
14
There are also “epistemic” prepositions such as despite, except, and regarding.

9. Adverbs
It is a challenge to describe the class of adverbs in semantic terms.
There are very many kinds of adverbs, for example adverbs of man-
ner, adverbs of frequency, adverbs of time, adverbs of place, adverbs of
certainty. To some extent the adverbs form a leftover class: Adjectives
modify nouns—adverbs modify everything else.
To give but one example of how adverbs are classified, Parsons
(1990) divides them into speech-act modifiers, sentence modifiers, sub-
ject-oriented modifiers, verb phrase modifiers, and a remainder class. I
cannot provide an analysis of all kinds of adverbs. As a complement to
the semantics of verbs presented above, I will focus on adverbs modify-
ing verbs (verb phrases).
In the semantic model of verbs presented in section 7, verbs refer to
vectors. Vectors can vary in terms of dimension, orientation, and mag-
nitude. Therefore, adverbs that are modifiers of verbs should refer to
change in these features. For example, in “I speak slowly,” the adverb
selects one of the several dimensions from the sound domain of speak.
“I speak loudly” selects another.15
In “I walked backwards” the adverb
refers to the orientation of my motion. Finally, in “e pushed the door
softly,” the magnitude of the force vector representing push is dimin-
ished by the adverb. When an action involves a pattern of forces, ad-
verbs can modify the whole pattern by providing dynamic information,
for example “She walked limply”, “He smiled wryly”, or “She kicked
aggressively”. What is common to these examples is that the adverb
restricts the regions associated with the meanings of the manner verbs.
Similarly, in relation to a result verb describing a concatenation of
changes (as in a path), an adverb can provide information about the
form the path takes, for example, “She crossed the park crookedly.” In
brief, the function of adverbs modifying verbs is parallel to how adjec-
tives modify nouns.16
As long as adverbs function as multipliers (diminishers or magni-
fiers) within a particular domain, the convexity principle can be de-
fended. For example, if certain voice volumes v1
and v2
both count as
speaking loudly, then any volume between v1
and v2
, will also count as
loudly. And for adverbs expressing the form of a path, the principles
of path convexity that were mentioned in section 8 will apply. It is an
open question whether the convexity principle can also be applied to
other adverbs.
Next, I turn to the domain specificity of adverbs. The structure of
the domains underlying adjectives to some extent determines which
adverbs can be combined with the adjective. For example, for scalar do-
15
There are also interpretations of speak involving the communicative intentions
(the illocutionary act) that involve more than the sound domain: “He spoke
convincingly.”
16
Dixon (2004: 26) notes that in some languages adjectives also have adverbial
function. Such a double function makes sense from the single-domain perspective.

mains with endpoints, there are “totality adverbs” such as completely,
absolutely, and almost that mark nearness to an endpoint: completely
full, almost ripe (Paradis 2001: 50–51). The totality adverbs do not
combine with open-ended scalar domains: *completely long, *absolutely
warm. Similar arguments can be applied to adverbs modifying verbs.
In particular, force vectors have dimensions that are not shared by pa-
tient spaces representing results. The magnitude of force is peculiar to
the force domain only and therefore adverbs expressing such magni-
tude, for example strongly, should apply to manner verbs (push strong-
ly, hit strongly), but not to result verbs (*move strongly, *fall strongly,
*break strongly). This principle functions well for manner verbs that
are represented by a single force vector, for example contact verbs. For
manner verbs that are represented by patterns of forces, however, the
situation is less transparent (?walk strongly, ?swim strongly). While
force magnitude is peculiar to manner, direction clearly is not. Hence
modifiers expressing direction are generally shared by force and result
vectors, for example ahead and left (push ahead, move ahead). On the
other hand, some adverbs are tied to domains that are mainly associ-
ated with result verbs and thus they cannot be combined with manner
verbs. For example, darkly relates to the light or the colour domain,
but does not apply to the force domain (glimmer darkly, *push darkly,
*hit darkly).
These considerations give some support for a thesis that that I for-
mulate as a first approximation:
Thesis about adverbs: Verb-modifying adverbs refer to a single do-
main.
This thesis can be defended at least for adverbs functioning as mul-
tipliers. To what extent the thesis is more generally valid, also for other
types of adverbs, remains to be further evaluated. One limitation of the
more general thesis is that adverbs modifying adjectives (and other ad-
verbs) can be zero-dimensional, for example, very and completely, and
therefore cannot be associated with any domain.
10. Conclusion: The general single-domain thesis
In this article I have presented a semantic analysis of the major word
classes based on conceptual spaces as a modelling tool. The observant
reader has noticed that I have tried to argue for a general semantic
rule:
Universal single-domain thesis: Words in all content word classes,
except for nouns, refer to a single domain.
I am not certain how far I can push this thesis. To a large extent, its
validity is dependent on how abstract domains are described. There are
also word classes I have not considered, for example quantifiers and
connectives, where the general single-domain thesis may not be valid
or may not even apply. And I have noted that certain adverbs are zero-
dimensional and thus not dependent on any domain.

Nevertheless, I want to put forward the thesis as a strong heuristic
that language learners (implicitly) apply when learning the meaning
of a new word. The default rule that if a newly encountered word is
not a noun, then its meaning depends only on a single domain will
simplify the acquisition of the meaning for the learner (cf. Bloom 2000,
Chapter 8). In general, the syntactic markers of a word indicate its
semantic role. Thus the markers help identify the relevant domain for
the word. Lupyan and Dale (2010: 8) make “the paradoxical prediction
that morphological overspecification, while clearly difficult for adults,
facilitates infant language acquisition.” Mandler (2004: 281) argues
along the same lines:
Many of the grammatical aspects of language seem impossibly
abstract for the very young child to master. But when the concepts
that underlie them are analyzed in terms of notions that children
have already conceptualized, not only does the linguistic problem
facing the child seem more tractable but also the types of errors
that are made become more predictable. The invention of grammat-
ical forms to express conceptual notions that are salient in a young
child’s conceptualization of events seems especially informative.
Since the relevant domain is often determined by the communica-
tive context in which the word is uttered, applying the single-domain
thesis will make the identification of the new meaning much more effi-
cient. Thus I propose that a general single-domain bias provides one of
the fundamental reasons why humans can learn a language as quickly
as they do.17
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