SEMANTICS

Semantic Theories

1) Sense and Reference

In the philosophy of language, the distinction between sense and reference was an innovation of the
German philosopher and mathematician Gottlob Frege in 1892 (in his paper “On Sense and
Reference”), reflecting the two ways he believed a singular term may have meaning. For him, the
word ‘sense’ was Sinn and ‘reference’ was termed as Bedeutung by him. The reference of a proper
name is the object it indicates, its sense is what the name expresses or the thought that it expresses.

The sense of a word concerns its linguistic boundaries in a particular language. The reference of a
word concerns which concepts it refers to in the real world. Sense is the linguistic meaning and
reference is the real world concept. A referent is the concrete object or concept that is designated by a
word or expression. The objects in the real world are referents, the concept which we have of them in
our minds is the reference and the meaning of a lexical item is sense.

2) Intension and Extension

Intension and Extension describe two ways of indicating the meaning of a word or name.
Intension assumes the word has an intrinsic meaning by definition and thus ‘analytic’. Extension is
the set of objects in the world to which the word corresponds. Because extension involves things in
the world it is called ‘synthetic’. Our mental definition of a word is an intension, and the particular
things in the world that a word can refer to are the extensions of a word.

For instance, the intension of “ship” is “vehicle for conveyance on water,” whereas its extension
embraces such things as ‘cargo ships’, ‘passenger ships’, ‘battleships’, and ‘sailing ships’. The
intension of “dog” is a member of the genus Canis (canines), which is the most widely abundant
terrestrial carnivore. And the extension of the word “dog” is the set of all dogs in the world: the set
includes Bulldog, Labrador, Poodle, German shepherd, Fido, Rover, Lassie, Rex, and so on.

3) Connotation and Denotation

Connotation and Denotation are two principal methods of describing the meanings of
words. These terms were first introduced by the English philosopher John Stuart Mill in his article “A
System of Logic” (1843). Connotation is a word's emotional meaning; suggestions and associations
that are connected to a word whereas denotation is the precise, literal definition of a word.
Connotation represents the various social overtones, cultural implications, or emotional meanings
associated with a word. Denotation represents the explicit or the direct meaning of a word. For
example, the denotation of the word ‘rose’ is that it ‘is a flowering shrub of the genus Rosa’. The
connotation is that it is a symbol of passion and love—this is what the rose represents. The denotation
of the word ‘home’ is ‘a dwelling place’, while it connotes such things as warmth, comfort, and
affection. The words ‘mansion’ and ‘hut’ have the semantic meaning (denotation) of “structure in
which people dwell,” but ‘mansion’ connotes wealth and ‘hut’ connotes poverty. The denotation of
the word ‘childish’ is ‘of or relating to a child’. It has a negative connotation implying an adult
behaving immaturely.

Implication Relations

The native speakers of a language have certain intuitions about what sentences or utterances convey,
about the content of what is said, about what can be inferred on the basis of the sentence uttered, and
about what is suggested. We often say that a sentence or utterance implies something. What is implied
can be expressed by a sentence. Thus implication relations are inferential relations between sentences.
If A implies B, we often say that A suggests or conveys B or that B can be inferred from an utterance
of A. Implication relations can be classified into two types: Entailment and Presupposition.

Entailment and Presupposition

One sentence entails another when it includes the meaning of the other sentence. A entails B if
and only if:
a) Whenever A is true, B is true.
b) The information that B conveys is contained in the information that A conveys.
c) A and not B is contradictory.
Thus, the sentence “The earth moves around the sun” entails the sentence “The earth moves”. The
sentence “John ate chocolate ice cream” entails the sentence “John ate ice cream”. The sentence “Jane
ate oats for breakfast this morning” entails the sentence “Jane ate breakfast this morning”.
One sentence presupposes another when it implies an earlier meaning which is known. In
other words, presupposition is the previously known meaning which is implied in the sentence. For
example, the sentence “Shiva’s son is named Ganesh” presupposes that “Shiva has a son”. The
sentence “Joan regrets getting her Ph.D in Mathematics” presupposes that “Joan has a Ph.D”.
While entailment is a logical meaning inherent in the sentence, presupposition may depend on the
knowledge of the facts, shared by the speaker and the hearer.
Componential Analysis
Componential analysis is a method of semantic analysis which analyzes the components of a word’s
meaning. It is the analysis of words through sets of semantic features or semantic properties, which
are given as present or absent. The total meaning of a word is broken up into its basic distinct
components. Each component of meaning is expressed by a feature symbol with a + or – mark to
indicate the presence or absence of a certain feature. Thus componential analysis treats components in
terms of binary opposites, i.e. ‘+’and ‘-’ features. We can make a table of binary contrasts to
distinguish the meaning of one word from another, listing all the component parts. Thus the meanings
of some individual words can be expressed by the combination f these features:
Man: +Human +Adult +Male
Woman: +Human +Adult-Male
Boy: +Human-Adult +Male
Girl: +Human-Adult-Male
Child: +Human-Adult+/-Male

Prototypes
A prototype is the best example or cognitive representation of something within a certain category.
The prototype of any category is the member or set of members of a category that best represents the
category as a whole. Thus, a robin or a sparrow can be regarded as a prototype or a ‘good example’
of the category bird, whereas a penguin or an ostrich is a rather ‘bad example’ of this category.
Defining a prototype as the bundle of typical features of a category, we can thus imagine birds as
‘creatures that are covered with feathers, have two wings and two legs, and the majority of which can
fly’. Therefore, a penguin is a less ‘good’ bird, as it lacks some of the typical features, such as the
ability to fly.

A prototype is a cognitive reference point, i.e the proto-image of all representatives of the meaning of
a word or of a category. Accordingly, the members of a category can be graded according to their
typicality. A ‘good’ example is only rated as such by virtue of its features.

Truth conditional Semantics

Truth conditional semantics explains the logical meaning of sentences, treating a sentence as a logical
proposition or basic statement which can be either true or false. For example, “Mary lives in
Cambridge” is true if and only if Mary actually lives in Cambridge. According to truth conditional
semantics, to know the meaning of a sentence is to know the conditions under which it is true. A
native speaker of a language can infer the truth of propositions in that language from the truth of other
propositions. The speaker knows the conditions in which a particular sentence is true. A sentence is
true if all the necessary conditions of truth are satisfied. These conditions are conditional within the
language, i.e. within the entailment relations that prevail between the propositions. Thus the sentence
‘Rover is a hungry dog’ is true if ‘Rover is a dog’ and ‘Rover is hungry’ are both true. The first
sentence entails the other two propositions.

Propositions

The term proposition refers to the core meaning of sentences which expresses the factuality of a
given state of affairs. Thus, a proposition is the semantic kernel of a sentence that determines its truth
conditions. A proposition is that part of the meaning of a clause or sentence that is constant, despite
changes in such things as the voice or word order.
Example: “The tall, stately building fell” is said to express propositions corresponding to the
following:

“The building is tall”

“The building is stately”
“The building fell”

Another sentence, “A pretty girl with curly hair entered the class” expresses three propositions:
“The girl is pretty”
“The girl has curly hair”
“The girl entered the class”

Truth Values

The semantic status of a sentence is represented in terms of its truth value. Truth value refers to the
truth or falsity of a given statement. There are two truth values-True and False. We often talk of
statements having the properties of Truth and Falsity, where a statement has the property Truth if and
only if its truth value is True and a statement has the property of Falsity if and only if its truth value is
False. For instance, the truth value of “Mount Everest is a city” is False. The truth value of “Arjun is
a smart girl” is False.

Determining the Semantic Value of a Proposition

In any language all the sentences, which express different propositions possess semantic values.
Both lexical items and syntactic structure contribute to the meaning of the sentence – both contribute a
semantic value to the proposition. The semantic value of a proposition is its constituents.
Thus the sentence ‘James sits’ will express a structured proposition which contains the semantic
values of ‘Socrates’ and ‘sits’ as constituents. These semantic values might be the man James himself
and the property of sitting (respectively), or they might be representations of these entities.

Compositional Procedure

Compositionality is defined as the property that the meaning of a whole is a function of the meaning
of its parts. Compositional semantics deals with how the lexical meanings combine to form more
complex phrasal meanings. The overall meaning of a sentence must have something to do with the
meanings of those words contained within the phrase. “I don’t eat” and “I don’t drink”, for example,
express different ideas because of the difference in lexical meaning between “eat” and “drink.”
However, syntax, or the way in which the sentence is constructed, plays a role as well. Look at these
sentences:

1. I like you.
2. You like me.

Both sentences express totally different propositions, however, they have the same words and each
word has a clearly understood meaning. How is it that the meaning has changed? In sentence 1, “I” =
subject, “you” = object, while in the second sentence these are reversed. This means that overall
meaning relies not only on the meaning of each part but additionally on syntactic composition. This
premise is known as the principle of compositionality. All languages contain an infinite number of
word combinations, so memorization of each separate phrasal meaning is impossible. This means that
in order to understand the meanings of new phrases, one must rely on individual word meanings
combined with the specific syntactic structure.

Terms and Predicates

Predicate is the part of a sentence or clause containing a verb and stating something about the subject
(e.g. ‘went to Delhi’ in ‘John went to Delhi’). The subject and object of a sentence, which are nouns
or noun phrases, are known as terms/ arguments/variables. For example, in the sentence ‘The child
threw the ball’, ‘the child’ and ‘the ball’ are terms, because both are noun phrases.
Predicate Logic

Predicate Logic derives the meaning of the proposition from the meaning of its constituent predicates,
and variables. Basically, the semantics of Predicate Logic does two things. It assigns a meaning to the
individuals, predicates, and variables in the syntax. It also systematically determines the meaning of a
proposition from the meaning of its constituent parts and the order in which those parts combine.
In predicate logic, a predicate is often represented in capitals followed by its argument(s) in
parentheses. For example, the predicate logic of the sentence ‘Fred writes’ is represented as WRITES
(Fred). When a predicate takes two arguments (denotes a relation rather than a property), the
arguments are usually separated by commas. For e.g. LIKE (Fred, Mary) for ‘Fred likes Mary.
Thus predicate logic allows us to decompose simple sentences into smaller parts: predicates and
individuals.

(1) John is tall.

TALL (John)
(2) I ate an apple
ATE (I, apple)
(3) Arjun is happy
HAPPY (Arjun)
(4) I have a bike
HAVE (I, bike)
(5) Meenu is hungry
HUNGRY (Meenu)
(6) Anand and Vipin are sleeping
SLEEPING (Anand, Vipin)

Possible Worlds Semantics

Possible worlds semantics is a general approach to theories of meaning, on which meanings (or, more
precisely, semantic values) are assigned to sentences in terms of the truth-values they take across all
possible worlds. The intuition is that the meaning of a sentence specifies how the world would have to
be for that sentence to be true (or false). This is typically made precise by identifying the semantic
value of a sentence with its possible-worlds intension, a function from possible worlds to truth-values.
When those values are just true and false (and are mutually exclusive), possible worlds intensions are
equivalent to sets of possible worlds (the worlds at which the sentence is question is true). The
approach can be generalised by treating semantic values for sub-sentential items (such as nouns and
verbs) as functions from possible worlds to other entities (such as particulars, properties and
relations).