Sense Relations
In this lecture we shall be looking
at some relations between words
that are of a semi-logical kind, i.e.
‘sense’ relations.
Some simple logic
We will use some simple way of formalizing
these relations between words using a
simplified form of predicate calculus.
John is a man
We have a predication in which it is said of the
individual John that he has the property of
being a man. Thus,
M(a)
Where M stands for the predicate ‘is a man’ and
(a) refers to the individual ‘John’.
We can extend this symbolism to deal with relations
where more than one individual is concerned.
John loves Mary
L(a,b)
The difference between this and the previous
formula is that we have two arguments, which are
ordered
Other predicates may take more arguments:
John gave Mary a book
G(a,b,c)
The purpose of this symbolization is to show
relations that hold between sentences (or
propositions).
If John is a bachelor, he is unmarried
B(a)→U(a)
The symbol
→ indicates entailment
John is a bachelor entails John is unmarried
We shall use the following:
 The letters
individual.
x, y, z as individual variables to refer to any
 The Universal quantifier ∀ (‘for all’)
 the sign ∼ for negation. Thus,
∀x (B(x)→ ∼ M(x))
if B(x) is the predicate "x is a bachelor",
Given any person x who is a bachelor, that person is not
married
Predicates with two or more arguments express relations
between the arguments. The relations can be:
 Symmetric: Holds for the arguments in both directions,
∀x ∀y (R (x, y)→R (y, x)), e.g.
Every person (every person x) has a relation with someone
(has a relation with y).
Be married to and cousin
∀x (Cat(x) ⇒ Mammal(x) )
∀x (Mammal (x) ⇒ Cat (x) )
 A relation R is asymmetric iff, if x is related by R to y, then y
is not related by R to x. For example, being the father of is
an asymmetric relation: if John is the father of Bill, then it is
a logical consequence that Bill is not the father of John.
 A relation R is non-symmetric iff it is neither symmetric nor
asymmetric. For example, loves is a non-symmetric
relation: if John loves Mary, then, alas, there is no logical
consequence concerning Mary loving John.
 Transitive: Holds both for x and y and for y and
z, also
holds for x and z,
∀x ∀y ∀z (R(x,y) & R(y,z)) → R(x,z), e.g.
being taller than is a transitive relation: if John is taller than
Bill, and Bill is taller than Fred, then it is a logical
consequence that John is taller than Fred.
Spatial terms (in front of, behind, above, below)
 A relation R is intransitive iff, if x is related by R to y, and y
is related by R to z, then x is not related by R to z. For
example, being next in line to is an intransitive relation: if
John is next in line to Bill, and Bill is next in line to Fred,
then it is a logical consequence that John is not next in line
to Fred.
 A relation R is non-transitive iff it is neither transitive nor
intransitive. For example, likes is a non-transitive relation:
if John likes Bill, and Bill likes Fred, there is no logical
consequence concerning John liking Fred.
 Hyponymy involves us in the notion of inclusion, e.g.
 Tulip and rose are included in flower
 Lion and elephant are included in mammal
 Scarlet is included in red
Inclusion is thus a matter of class membership.
 The ‘upper’ term is Superordinate
 The ‘lower’ term the Hyponym.
Notice: What we examined in the previous lecture are
co-hyponyms.
there is not always superordinate term, e.g. there is
no superordinate term for all colors including
white and black in English.
The mind sees the world in three levels of
abstraction going from the most general to the
most specific, with the basic level coming in the
middle as the most useful everyday term.
Regarding colours, the abstract superordinate level
is the word colour itself, which relates to the more
concrete basic level terms blue, red and so on,
which in turn relate to the subordinate terms skyblue, pillar-box red, and so on.
 The superordinate category vehicles in a sense
consists of basic terms cars and lorries etc, which
consist of subordinate terms sports-cars, fourwheel drives, etc.
 superordinate level
colour
basic level
red, blue, green, etc
subordinate level
pillar-box red, sky-blue,
 Levels of meanings in English
 Superordinate level fruit
tools
 Basic level
apple
hammer
 Subordinate level
russet claw hammer
 Hyponymy relations vary from language to
language.
The same term may appear in several places in the
hierarchy when it is polysemic, i.e. has several
meanings and in one of its meanings it may be
superordinate to itself in another meaning.
LIVING
↓
↓
↓
vegetable
animal
↓
↓
↓
↓
bird fish
insect
↓
human
NON-LIVING
↓
animal
↓
↓
animal
 The word sheep is used for all creatures of a certain species; it is
the superordinate term of ewe, lamb, ram.
 The word horse is the superordinate for stallion, mare, colt.
 The word pig is the superordinate for sow, boar, piglet.
 But the superordinate term for dog is dog, though dog is also
the hyponym as distinct from bitch.
sheep
dog
↓
↓
↓
↓
↓
↓
ram
ewe
lamb
dog
↓
bitch
↓
puppy
Hyponymy involves entailment. To say This is a tulip
entails This is a flower:
∀x(T(x)→F(x))
Such a formula by itself will not bring out the
hierarchical classification involved in hyponymy, for
since a tulip and a flower are also plants, we can say:
∀x(T(x)→P(x)) and ∀x(F(x)→P(x))
 In the previous example, tulip and flower are not co-
hyponyms of plant. We need to specify that
 flower is an Immediate hyponym of plant
 tulip is an Immediate hyponym of flower.
SYNONYMY is used to mean ‘sameness of
meaning’. For the dictionary maker many sets of
words have the same meaning; they are
synonymous, or are synonyms of one another.
We can define synonymy as symmetric hyponymy.
Thus if mavis and thrushes are synonymous, we can say:
all mavises are thrushes and all thrushes are mavises.
∀x(M(x)→T(x)) and ∀x(T(x)→M(x))
It can, however, be maintained that there are no
real synonyms, that no two words have exactly the
same meaning.
Indeed it would seem unlikely that two words with
exactly the same meaning would both survive in a
language.
If we look at possible synonyms there are at least
five ways in which they can be seen to differ.
Belong to different dialects, e.g. fall and autumn.
Belong to different styles, e.g. pass away, die, pop off.
Same cognitive meaning but different emotive or
evaluative meanings, i.e. different connotations, e.g.
politician and statesman, hide and conceal,
liberty and freedom, each implying approval or
disapproval. The function of such words is to
influence attitudes.
Positive & Negative Connotations
Positive
Negative
 Generous
 Extravagant, immoderate
 Resolute
 Stubborn
 Thrifty
 Stingy, cheap
 Industrious
 Workaholic
 Shrewd
 Cunning, sly
 Tolerant, broad-minded
 Unprincipled
 Confident
 Bossy
 Extraordinary
 Bizarre
 Childlike
 Childish
More about connotation
People sometimes change names to avoid such
connotations, and there is a natural process of
change with taboo words. Because the word is
associated with a socially distasteful subject, it
becomes distasteful itself, and another word, a
‘euphemism’ takes its place.
(Homework: collect a list of taboo words in Arabic
and/or in English and their replacements).
 Some words are collocationally restricted, i.e. these are
true synonyms-differing only in that they occur in
different environments.
 Many words are close in meaning, i.e. their meanings
overlap. There is, in other words, a loose sense of
synonymy, which is exploited by the dictionary-maker,
e.g. possible synonyms for mature are adult, ripe,
perfect, and due. Possible synonyms for govern are
direct, control, determine. Possible synonyms for loose
are inexact, free, relaxed, vague, unbound. Each one in
the set would make a set further away from the meaning
of the original word.
Ways of testing synonymy
1.
Substitution. It has been suggested that true or total
synonyms are mutually interchangeable in all their
environments. But it is almost certainly the case that
there are no total synonyms in this sense. Some
words are interchangeable in certain environments
only, e.g. deep and profound sympathy but only deep
water.
2. Investigate
the opposites, e.g. superficial is
contrasted with both deep and profound, but
shallow is contrasted only with deep.
Two further phenomena handled under
synonymy
1. Context-dependent synonymy where two items appear
to be synonymous in a particular context, e.g. buy and
get. However, these seem to be more related in terms of
hyponymy, i.e. one term being more specific than the
other and the context supplies the specific information
that is lacking in one of them.
2. Synonymy found between bull and male adult bovine
animal, which are totally not interchangeable; it is
created by the linguist or lexicographer for the purpose
of definition and paraphrase. It relates more to
componential analysis than to synonymy.
Antonymy
Antonymy means oppositeness of
meaning. Words that are opposite
are ANTONYMS.
Kindes of antonyms
1.
Graded Adjectives, such as, wide/narrow, old/young,
wide/narrow, big/small, that may be seen in terms of
degrees of the quality involved, i.e. a road may be wide,
very wide, wider than another. We have, thus, gradation
of width, age, size, etc. The comparative forms of these
adjectives (those ending in –er or occurring with more)
are explicitly graded. They are placed on a graded scale
of comparison.
Gradable antonyms are characterized by the following:
they are graded against different norms. The norm
is set by the object being described, e.g. A wide
stripe on a dress as opposed to a wide stripe on a
road.
Gradable antonyms are characterized by the following:
The temperature of cold ice cream is not the same
temperature as a cold shower.
An old man is much older than an old dog.
 For most antonyms a set of relationships hold
between the comparative forms:
The road is wider than the lane.
The lane is narrower than the road.
The road is less narrow than the lane.
The lane is less wide than the road.
since these antonyms are gradable, there are often
intermediate terms, e.g. hot/warm/cool/cold, with
intermediate warm and cool forming a pair of
antonyms themselves.
In each pair one of the terms is the MARKED term
and the other UNMARKED, i.e., one is used to ask
about or describe the degree of the gradable quality,
e.g. How high is it? How wide is it? It is three feet high,
It is four yards wide, with no implication that it is high
or wide.
On the other hand, How low is it? How narrow is it?
Imply that the object in question actually is low or
narrow, thus it is the marked term. However, this
doesn’t seem universal, e.g. English talks of thickness
gauge, whereas Japanese talk of thinness gauge.
2. Binary Antonyms: Pairs of the type male/female,
married/single, alive/dead are treated in terms of
COMPLEMENTARITY, the items are complementary to
each other. Strictly these belong to the set of
incompatible terms, but with one specific
characteristic-that they are members of two-term sets
instead of multiple-term sets. With these pairs if we say
something is NOT the one is to say that it is the other.
On the other hand, with the gradable antonyms it is not the
case that to say something is not wide is to say that it is
narrow. The possibility of being neither wide nor narrow is
left open.
List of Binary Antonyms
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Man
push
dead
off
forget
day
right
absent
against
exit
sink
employ
married
question
true
attack
accidental
former
depart
exterior
solid
vacant
Inward
input
exhale
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
woman
Pull
alive
on
Remember
night
Wrong
present
for
Entrance
Float
dismiss
single
Answer
false
Defend
Intentional
latter
Arrive
interior
fluid
occupied
outward
output
inhale
Finally,
some gradable antonyms
characteristics of the dichotomous pairs:
A. There
have
some
are some pairs of adjectives, e.g.
honest/dishonest, obedient/disobedient, open/shut
that are gradable in terms of more and less, yet in
which the denial of one is usually taken to assert the
other.
B. Some pairs of antonyms are not ‘symmetrically
reversible’. Those to which the relationship of more
and less cannot be applied, e.g. brilliant and stupid.
Relational opposites
A quite different kind of opposite is found with pairs of
words which exhibit the reversal of a relationship between
items.
1. servant master
2. husband wife
3. doctor patient
4. buy sell
5. parent child
6. borrow lend
7. predator prey
8. instructor pupil
9. above below
10. give receive
11. teach learn
12. come go
13. toward away
14. employer employee
15. customer supplier
Some of their relational characteristics are:
There are several verbs that are pairs in this way,
e.g. buy/sell, lend/borrow, give/receive. There are
also nouns, e.g. husband/wife, parent/child,
teacher/pupil, terms referring to spatial position,
e.g. above/below, in front of/behind, north of/south
of.
 Terms involved in relational opposition may be
transitive, e.g.
above, below.
 They cannot be symmetric, for symmetric relations, e.g.
married to, beside, meet, are those in which the SAME
relation holds between the arguments in both
direction, so that one term, not two, is required.
Relational opposites involve two relations (R and Ŕ):
∀x ∀y(R(x,y)→ Ŕ(y,x))
Symmetric relations involve only one relation (R):
∀x ∀y(R(x,y)→ R(y,x))
 Kinship terms are especially interesting in a discussion
of relational opposites for two reasons:
A. Many of them indicate not only the relationship, but
the gender of the person concerned, e.g. father,
daughter, which blocks reversibility. A small number
of terms in English do not indicate gender, e.g. cousin,
parent, child, grandparent, grandchild. Further, there
are other terms that avoid gender reference and so are
symmetric, e.g. spouse, sibling.
B. Whether a term is symmetric or not is a matter of the
language, e.g. cousin in some languages both the
gender and the precise relationship of the parent are
indicated.