Formal Semantics

SEMIOTICS
 (Charles Morris, 1938)the general science of
signs.
THREE BRANCHES OF INQUIRY
 SYNTAX—the study of “formal relation of signs
to one another.”
 SEMANTICS—the study of “the formal relation
of signs to the objects to which the signs are
applicable.”
 PRAGMATICS—the study of “the relation of
signs to the interpreter.”

Syntax concerns properties of
expressions, such a as about well-
formedness; Semantics concerns relations
between expressions and what they are
“about”, such as reference and truth-
conditions; and Pragmatics concerns
relations between expressions, their
meanings, and their uses in context, such as
complicature.

 The OBJECTIVES of FORMAL SEMANTICS:
1. Sense Relations
2.Truth Conditions
3. Inference
SEMANTICS is the scientific study of the
meaning of signs. But what is “meaning”?

 Giving you these flowers means that I love
you.
 Those mountains ahead mean trouble.
 He said that he would join us, be he didn’t
mean it.
 When I say X, I meanY.
 Gatte means spouse.

If your native language is not English, how would
you translate these examples?Which ones are
about semantics?
a. Smoke means fire.
b. Feuer means fire.
LINGUISTIC MEANING
o relates linguistic signs to non-linguistics
entities.
o is conventionalized.
o Is arbitrary.

 is about the meaning of syntactically complex
expressions.
 Literally means “using formal methods for
the study of meaning.”
[Nowadays there is also formal lexical
semantics and discourse semantics, but the
identification “formal semantics = formal
sentence semantics.”]

 DIACHRONIC SEMANTICS:
Examples:
1. Why do English sober and German sauber
different things even though they are
apparently related?
2. Why are so many synonyms in English (like
deep and profound)?
 STYLISTICS:
Example:
1. What is the difference in meaning between
policeman, cop, and bobby?

LEXICAL SEMANTICS:
Examples:
1. What is the relation between the words good
and bad, high and low etc, and what is the
system behind it?
2. Is there a common meaning of in in the
examples in this room and in good mood?

 How do these claims go together?
1. Sense Relations
• Synonymy
• Entailment
• Contradiction
• Inconsistency
• Consistency
• Tautology
2. Truth Conditions

The question is not what meanings are, but how
they behave. Formal Semantics studies
systematic semantic relations between linguistic
expressions, such as:
1. SYNONYMY
• Intuitively: A and B are synonymous if the y
have the same meaning.
• Vague, sometimes difficult to decide
• Formal Approach: A and B are synonymous if
for each sentence(S), S is true if and only if
S[B/A] is true.
Ex. Bachelor and unmarried male adult.

2. ENTAILMENT
 Intuitively: A entails B if we can infer from A
and B.
 Formal Definition: A entails B if under all
conceivable circumstances under whichA is
true, B must be true as well.
Ex. John owns a bike entails John owns
something.

3. CONTRADICTION
 Intuitively: A and B are contradictory if they
exclude each other.
 Formally: A and B are contradictory if there
are no conceivable circumstances where they
could be true at the same time.
Ex. Mary knows every book in the library and
There is a book in the library that Mary does
not know are contradictory.

4. INCONSISTENCY
 A is inconsistent if it is contradictory with
itself.
Ex.This square is round.
5. CONSISTENCY—the opposite of
inconsistency.
Ex.Tomorrow is Saturday.

6. TAUTOLOGY
 Intuitively:True but countless.
 Formally: Always true.
Ex. Every red apple is an apple.
There is no largest prime number.

 “Truth of a sentence” is central notion in
definition of sense relations.
 Basic Methodological Principles of formal
semantics:
1. If A and b are sentences, and A is true and B
false, then A and B do not have the same
meaning. (Cressewell’s “Most Certain
Principle”)
2. If a person knows the meaning of a sentence,
then he or she also know the necessary and
sufficient conditions for the truth and falsity of
this sentence.

3. Suppose a person knows the necessary and
sufficient conditions for the truth and falsity
of a sentence.Then this person knows the
meaning of this sentence.

1. The meaning of a sentence are its truth
conditions.
2. The meaning of an expression is its
contribution to the truth conditions of the
sentences it occurs in.

SemioticTrichotomy:
SYNTAX—study of the structure of signs.
SEMANTICS—study of the meaning of signs.
 PRAGMATICS—study of the use of signs.
o It builds upon semantics, but cannot be
reduced to it.
o “Meaning = truth conditions” suggests that
primary purpose of language is descriptive.
o Blatantly false.

1. I hereby christen you Mary-Jane.
2. I promise you to be there at three.
3. I now pronounce you man and wife.
o Under appropriate conditions, these
sentences are true by virtue of their being
uttered.
o Technical term: Performative utterances

o Same effects can be achieved in a less explicit
way.
Examples:
a. Your name be Mary-Jane.
b. I’ll be there at three.
c. You are now man and wife.

1. LOCUTION—uttering a certain sentence of
a given langunage with a given grammatical
structure and a given meaning.
2. ILLOCUTION—performing a certain action
type (declaring, asking, promising,
baptizing, …)
3. PERLOCUTION—achieving a certain effect
by a causal connection between the speech
act and a change in the state of the world.

o All speech acts are explicit performative.
o Usually the performative verb is not
pronounced.
Examples:
a. Are you cold?
b. I hereby ask you whether you are cold.
[(a) means the same, in a technical sense, as
(b)]

o Problematic, because the locution of a
performative speech act is always true.
o Would render all sentences into
tautologies=>unintuitive.
o We have to live the tension between locution
(semantics) on the one hand and
illocution/perlocution (pragmatics) on the
other hand.

1. Propositional Logic
o Principle of Compositionality (“Frege’s
Principle”) –the meaning of a complex
expression is determined by the meaning of
its parts and the way they are combined.
o Meaning of a clause:Truth
Conditions=determinesTruthValue
 Bivalent Interpretation: Every sentence is
either true or false (“Tertium Non Datur”),
but not both.

o Meaning of a Clause:
 TruthValues: “True” and “False” (“T” and “F”,
“1” and “0”)
o For certain syntactic combinations:
Compositionality ofTruthValues
Examples:
a. The power is on and the outside
temperature is below freezing point.

b.The power is on.
c.The outside temperature is below freezing
point
[Example (a) is true if both (b) and (c) are true,
otherwise false.]

Examples:
a. The grapes are too high or you are too short.
b. The grapes are too high.
c. You are too short.
[Example (a) is true if at least one of (b) and (c)
are true, otherwise false.]

Examples:
a. I do not have the ace of hearts.
b. I have the ace of hearts.
[example (a) is true if (b) is false, and vice versa]
Examples:
a. If x is a prime number larger than 2, it is an odd
number.
b. X is a prime number.
c. X is an odd number.
[example (a) is false if (b) is true and (c) false,
otherwise it is true.]

Examples:
a. The light is on if and only if the switch is up.
b. The light is on.
c. The switch is up.
[Example (a) if both (b) and (c) are true or both
(b) and (c) are false, otherwise it is false.]

o Simple formal language
o Disregards internal structure of simple
clauses
o Conjunction, disjunction, negation,
implication and equilvalence are only
syntactic operations
o Compositionality of truth values.

1. PRINCIPLE OF COMPOSITIONALITY—the
meaning of an expression is uniquely
determined by the meanings of its parts and
their mode of combination. [Frege’s
Principle]
2. SUBSTITUTION PRINCIPLE—synonymous
parts may be substituted for each other
without changing the meaning of the
complex expression in which they occur.

 Compositionality:
a. WheneverToms sees a lollipop he wants to
eat it.
b. Tom sees a lollipop.
c. Tom sees a lollipop he wants to eat.

a. Tom is asleep.
b. Everyone who is identical withTom is
asleep.
 [the synonymy of the noun phrases Tom and
everyone who is identical withTom we may,
conclude that (a) and (b) must have the same
meaning]

a. Allan erroneously believes thatTom is
asleep.
b. Allan erroneously believes that everyone
who is identical withTom is asleep.
 [since (a) is an immediate part of thatTom is
asleep and (b) is an immediate part of that
everyone who is identical withTom is asleep,
the two that-clauses must be synonymous]

a. My brother, who live in Athens, is an oculist.
b. My brother, who dwells in Aix-la-Chappelle, is
an eye-doctor.
 [the way the words are combined in these two
sentences is obviously the same, the Principle of
Compositionality immediately implies that (a)
and (b) must have the same meaning. Clearly,
this is a non-trivial claim.]

 Moreover, the complex verb erroneously
believes is clearly synonymous with itself
and, once more, combining it with either that
Tom is asleep or the synonymous that
everyone who is identical withTom is asleep
must result in two synonymous verb phrases.

 also known as SEMANTIC
SHIFT or SEMANTIC
PROGRESSION describes the evolution
of word usage — usually to the point that the
modern meaning is radically different from
the original usage.
 (Diachronic/Historical Linguistics) is a change
in one of the meanings of a word.

Every word has a variety of senses
and connotations which can be added,
removed, or altered over time, often to the
extent that cognates across space and time
have very different meanings. The study of
semantic change can be seen as part
of etymology, onomasiology, semasiology,
and semantics.

There are different types of change
which will be discussed presently. The most
neutral way of referring to change is simply to
speak of semantic shift which is to talk of
change without stating what type it is. To
begin with a series of shifts are presented to
familiarize by the students with what is
possible in the realm of semantic change.

 Awful - Originally meant "inspiring wonder (or
fear)". It is a portmanteau of the words "awe"
and "full", used originally as a shortening for "full
of awe". In contemporary usage the word usually
has negative meaning.
 Demagogue - Originally meant "a popular
leader". It is from the Greek demagogos (leader
of the people), from demos (people)
+ agogos (leader). Now the word has strong
connotations of a politicianwho panders to
emotions and prejudice.

 English fæger ‘fit, suitable’, Modern
English fair came to mean ‘pleasant,
enjoyable’ then ‘beautiful’ and ‘pleasant in
conduct’, from which the second modern
meaning ‘just, impartial’ derives.The first
meaning continued to develop in the sense of
‘of light complexion’ and a third one arose
from ‘pleasant’ in a somewhat pejorative
sense, meaning ‘average, mediocre’, Ex. He
only got a fair result in his exam.

 Gentle was borrowed in Middle English
in the sense of ‘born of a good-family,
with a higher social standing’. Later the
sense ‘courteous’ and then ‘kind, mild in
manners’ developed because these
qualities were regarded as qualities of
the upper classes.

 Lewd (Old English læwede)
originally meant ‘non-ecclesiastical,
lay’, then came to mean
‘uneducated, unlearned’ from which
it developed into ‘vulgar, lower-
class’ and then through ‘bad-
mannered, ignorant’, to ‘sexually
insinuating’.

 Sophisticated meant ‘unnatural,
contaminated’ but now has the
sense of ‘urbane, discriminating’.
The word sophistry (from Old
French sophistrie) still has its original
meaning of ‘specious, fallacious
reasoning’.

 Artificial originally meant ‘man-
made, artful, skillfully constructed’,
compare artifice ‘man-made
construction’. But by comparison
with ‘natural’ the word came to
acquire a negative meaning because
everything which is natural is
regarded positively.

 Nice (Latin nescius ‘not knowing') is
recorded from the 13th century in
the sense of ‘foolish’, then it shifted
to ‘coy, shy’ and by the 16th century
had the meaning ‘fastidious, dainty,
subtle’ from which by the 18th
century the sense ‘agreeable,
delightful’ developed.

 Silly (Old English sēlig ‘happy, fortuitous') had
by the 15th century the sense of ‘deserving of
pity’ and then developed to ‘ignorant, feeble-
minded’ and later ‘foolish’.
 Fast (OE fæste ‘firm') later developed the
meaning ‘quick’.The original sense is still
seen in steadfast ‘firm in position’.

 Egregious - Originally described something that
was remarkably good.The word is from
the Latin egregius (outstanding) which is from e-,
ex- (out of) + greg- or grex (flock). Now it means
something that is remarkably bad or flagrant.
 Gay - Originally meant feelings of being "carefree",
"happy", or "bright and showy"; it had also come to
acquire some connotations of "immorality" as early
as 1637.The term later began to be used in
reference to homosexuality, in particular, from the
early 20th century, a usage that may have dated
prior to the 19th century.

 Guy - Guido (Guy) Fawkes was the alleged leader of
a plot to blow up the English Houses of Parliament on 5
November 1605.The burning on 5 November of a
grotesque effigy of Fawkes, known as a "guy," led to the
use of the word "guy" as a term for any "person of
grotesque appearance" and then to a general reference
for a man, as in "some guy called for you." In the 20th
century, under the influence ofAmerican popular
culture, "guy" has been gradually replacing "fellow,"
"bloke," "chap" and other such words throughout
the English-speaking world, and, in the plural, can refer
to a mixture of genders (e.g., "Come on, you guys!"
could be directed to a group of men and women).

 The above cases are all cases of
shift, the original meaning is not
available anymore, or only in an
opaque compound (see last
example).The process whereby two
meanings arise from a single original
one is termed Semantic
Differentiation.

 In English there has been considerable
fluctuation in the preterite and past participle
ending after sonorants for weak verbs: either
a voiced /-d/ or a voiceless /-t/.This has
resulted in the exploitation of the two options
for semantic purposes.The situation for most
varieties of English today is that the ending -
ed stresses the process of the verb and the
ending -t emphasises the result as seen in the
following examples

A number of classification schemes have
been suggested for semantic change.The most widely
accepted scheme in the English-speaking Academic
World is from Bloomfield (1933):
1. NARROWING
2. METAPHOR
3. METONYMY
4. SYNECDOCHE
5. MEIOSIS
6. HYPERBOLE
7. DEGENERATION
8. ELEVATION

1. Narrowing—Change from superordinate
level to subordinate level. For
example, skyline used to refer to any
horizon, but now it has narrowed to a
horizon decorated by skyscrapers.
2. Widening—Change from subordinate level
to superordinate level.There are many
examples of specific brand names being
used for the general product, such as
with Kleenex.

3. Metaphor—Change based on similarity of
thing. For example, broadcast originally
meant "to cast seeds out"; with the advent of
radio and television, the word was extended
to indicate the transmission of audio and
video signals. Outside of agricultural circles,
very few people use broadcast in the earlier
sense.

5. Metonymy—Change based on nearness in
space or time, Ex. Jaw--> "cheek" →
"mandible".
6. Synecdoche—Change based on whole-part
relation.The convention of using capital cities
to represent countries or their governments
is an example of this.

7. Meiosis—Change from weaker to
stronger meaning, e.g., kill "torment" →
"slaughter“
8. Hyperbole—Change from stronger to
weaker meaning, e.g., astound "strike
with thunder" → "surprise strongly".

9. Degeneration—Ex. knave "boy" →
"servant" → "deceitful or despicable
man".
10. Elevation—Ex. knight "boy" →
"nobleman".

1. Metaphor: Change based on similarity
between concepts, e.g., mouse "rodent" →
"computer device".
2. Metonymy: Change based on contiguity
between concepts, e.g., horn "animal horn"
→ "musical instrument".
3. Synecdoche: Same as above.
4. Specialization of meaning: Downward shift
in a taxonomy, e.g., corn "grain" → "wheat"
(UK), → "maize" (US).

5. Generalization of Meaning: Upward shift in
a taxonomy, e.g., hoover "Hoover vacuum
cleaner" → "any type of vacuum cleaner".
6. CohyponymicTransfer: Horizontal shift in a
taxonomy, e.g., the confusion
of mouse and rat in some dialects.
7. Antiphrasis: Change based on a contrastive
aspect of the concepts, e.g., perfect lady in
the sense of "prostitute".

8. Auto-antonymy: Change of a word's sense
and concept to the complementary opposite,
e.g., bad in the slang sense of "good".
9. Auto-converse: Lexical expression of a
relationship by the two extremes of the
respective relationship, e.g., take in the
dialectal use as "give".

10. Ellipsis: Semantic change based on the
contiguity of names, e.g., car "cart" →
"automobile", due to the invention of
the (motor) car.
11. Folk-etymology: Semantic change based
on the similarity of names, e.g.,
French contredanse, orig. English country
dance.

1. Widening/Extension
range of meanings of a word increases so that
the word can be used in more contexts than
were appropriate before the change
EXAMPLES:
 -dog =>specific powerful breed of dog => all
breeds or races of dog
 -cupboard =>table upon which cups or vessels
were placed, a piece of furniture to display
plates => closet or cabin with shelves for the
keeping cups and dishes =>AE: small storage
cabinet

2. Narrowing (Specialisation, Restriction)
=> range of meaning is decreased so that a word
can be used appropriately only in fewer contexts
than before the change
 meat => 'food' in general ;
 hound => OE hund 'dog in general' => species of
dog (long eared hunting dog) ;
 wife => OE 'woman' =>'woman of humble
rank or low employment' => 'married
woman, spouse'
 girl => ME 'child or young person of either sex'
=>'female child, young woman'

3. Metaphor
=>involves relationship of perceived similarity
 root (of plant) => > root of plant, root of
word, root in algebra, source
 stud => 'good-looking sexy man '(of slang
origin) derived from stud 'a male animal used
for breeding
 chill => "relax, calm down' of slang origin,
original 'to cool'

4. Metonymy
=>inclusion of additional senses which were
originally not present but which are closely
associated with word's original meaning
 tea => 'drink' => 'evening meal accompanied
by drinking tea’.
 cheek 'fleshy side of the face below the eye' <
OE: cēace ' jaw, jawbone‘.

5. Synecdoche
=>kind of metonymy, involves part-to-whole
relationship.
EXAMPLES:
 hand --'hired hand, employed worker';
 Tongue --'language'

6. Degeneration / Pejoration
=>sense of a word takes on a less positive, more
negative evaluation in the minds of the users
 knave 'a rogue' < OE: cnafa ' a youth, a child' >
'servant' ;
 spinster 'unmarried woman' < 'one who spins' ;
 silly 'foolish, stupid' < ME sely 'happy, innocent'
< OE sælig ''blessed, blissful'
 disease 'illness' < 'discomfort' (cf. dis+ease)

7. Elevation /Amelioration
=>shifts in the sense of a word in the direction
towards a more positive value in the minds of
the users
 Pretty-- OE: prættig 'crafty, sly‘
 Knight-- 'mounted warrior serving a king' 'lesser
nobility' < OE cniht 'boy, servant' >'servant' >
'military servant';
 Dude--'guy, person' < in 1883 a word of ridicule
for 'man who affects an exaggerated
fastidiousness in dress, speech and deportment',
a dandy'

8.Taboo Replacement and Avoidance of
Obscenity
 Ass-- 'long-eared animal related to a horse'
=> donkey;
 Cock-- 'adult male chicken' => rooster,
 bloody nose => blood nose/bleeding nose
 Toilet--bathroom, lavatory, restroom, loo, john

9. Hyperbole
=>shift in meaning due to exaggeration by
overstatement.
 terribly, horribly, awfully-- 'very'
10. Litotes
=>exaggeration by understatement.

Blank has tried to create a complete
list of motivations for semantic change.They
can be summarized as:
 Linguistic forces
 Psychological forces
 Socio-cultural forces
 Cultural/encyclopedic forces

This list has been revised and slightly
enlarged by Grzega (2004):
 Fuzziness (i.e., difficulties in classifying the
referent or attributing the right word to the
referent, thus mixing up designations)
 Dominance of the Prototype (i.e., fuzzy
difference between superordinate and
subordinate term due to the monopoly of the
prototypical member of a category in the real
world)
 Social Reasons (i.e., contact situation with
"undemarcation" effects)

 Institutional and non-institutional linguistic
pre- and proscriptivism (i.e., legal and peer-
group linguistic pre- and proscriptivism,
aiming at "demarcation")
 Flattery
 Insult
 Disguising Language (i.e., "mis-nomers")
 Taboo (i.e., taboo concepts)

 Aesthetic-Formal Reasons (i.e., avoidance of
words that are phonetically similar or
identical to negatively associated words)
 Communicative-Formal Reasons (i.e.,
abolition of the ambiguity of forms in
context, keyword: "homonymic conflict and
polysemic conflict")
 Word Play/Punning
 Excessive Length of Words

 Morphological Misinterpretation (keyword:
"folk-etymology", creation of transparency
by changes within a word)
 Logical-Formal Reasons (keyword: "lexical
regularization", creation of consociation)
 Desire for Plasticity (creation of a salient
motivation of a name)
 Anthropological Salience of a Concept (i.e.,
anthropologically given emotionality of a
concept, "natural salience")

 Culture-Induced Salience of a Concept
("cultural importance")
 Changes in the Referents (i.e., changes in
the world)
 WorldView Change (i.e., changes in the
categorization of the world)
 Prestige/Fashion (based on the prestige of
another language or variety, of certain word-
formation patterns, or of certain
semasiological centers of expansion)

Changes in meaning are as
common as changes in form. Like the
latter they can be internally or externally
motivated. The equivalent to the
paradigm in morphology is, in
semantics, the word field in which words
and their meanings stand in a network
of relationships.

The alteration of meaning occurs
because words are constantly used and
what is intended by speakers is not
exactly the same each time. If a
different intention for a word is shared
by the speech community and becomes
established in usage then a semantic
change has occurred.

SOURCES:
1. www.wikipedia.org/semanticchange
2.Webster Encyclopedia, 2nd Edition
3. Lecture of B. H. Partee on Formal Semantics,
April 25, 2005 p.1-6
4. Handouts of Gerhard Jager: jaeger@ling.uni-
potsdam.de
Thank you for listening 

TEST I: Listen attentively and answer the
following questions. Write 1 if the statement
corresponds to Formal Semantics, and 0 if the
statement says otherwise.
1. I hereby affixed my signature on January 30,
2012.
2. You are now man and wife.
3. I will be there at 5:00 pm.
4. Your name is Maria Salve.
5. I promise to give her a birthday present.

TEST II: Supply the correct Semantic Change.
1. The Modern English of fair came to mean
_______________.
2. _______was borrowed in Middle English originally
means ‘born of a good-family with a higher social
standing’.
3. Lewd (Old English læwede) originally meant
___________then came to mean ‘uneducated,
unlearned’.
4. Fast (Old Eng fæste ‘firm') later developed the
meaning ________.
5. Silly come from Old English _____which means
happy and fortuitous.

6. ______comes from Latin nescius which means ‘not
knowing‘ and later became agreeable and
delightful.
7. Artificial originally meant ______________.
8. Sophisticated originally means ‘unnatural,
contaminated’ but now has the sense of _________.
9. The process whereby two meanings arise from a
single original one is termed_____________.
10.Semantic change, also known as
__________that describes the evolution
of word usage.

TEST III. ENUMERATION.
1-5 Give at least five words that undergone
SemanticChange.
6-10 Cite at least 5 types of Semantic Change
according to Bloomfield 1933.
TEST IV. ESSAY. Discuss briefly.
1. Formal Semantics
2. SemanticChange

 TEST I: 1 0 0 0 1
 TEST II:
1. Pleasant, enjoyable
2. Gentle
3. Non-ecclesiastical, lay
4. Quick
5. Sēlig
6. Nice
7. Man-made, artful, skillfully constructed
8. Urbane, discriminating
9. Semantic Differentiation
10. Semantic Shift or Semantic Progression

TEST III:
1-5 Awful, demagogue, egregious, guy, gay, fit, gentle,
lewd, sophisticated, artificial, Nice, Silly, Fast
6-10  Narrowing, Metaphor, Metonymy, Synecdoche,
Meiosis, Hyperbole, Degeneration, Elevation.
TEST IV:
1. is about the meaning of syntactically complex
expressions. Literally means “using formal methods for
the study of meaning.”
2.Semantic change, also known as semantic
shift or semantic progression) that describes the evolution
of word usage.

Formal Semantics

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