Sentence relations and truth
Jong-Bok Kim [email protected]
Kyung Hee U.
April 8, 2013
JB Kim
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semantic relations
What is semantics? It is the study of meaning, focusing on the
relation between words, phrases, and sentences.
between words: synonymous, antonymous relations
between sentences: to know the meaning of a sentence is to know
under what condition that sentence would be ‘true’ or ’false’
JB Kim
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Paraphrase:
Two sentences that can have the same meaning.
(1) a.
b.
JB Kim
The police chased the burglar & The burglar was chased
by the police.
Paul bought a car from Sue & Sue sold a car to Paul
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Entailment:
a relation in which the truth of one sentence necessarily implies the
truth of another. Examples of asymmetrical entailment.
(2) a.
b.
JB Kim
The park wardens killed the tiger. & The tiger is dead.
Robin is a man & Robin is human
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Contradiction:
When two sentences cannot both be true.
(3) a.
Charles is a bachelor.
b.
Charles is married
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More:
Presupposition: an implicit assumption about the world/background
belief relating to an auuterance whose truth is taken for granted in
discourse.
(4) a.
b.
The Mayor of Seoul is a woman.
There is a mayor of Seoul.
(5) a.
b.
I regret stepping on your sandwich.
I stepped on your sandwich.
Tautologies: self-reinforcing statements that cannot be disproved;
automatically true
(6) a.
b.
JB Kim
Seoul is Seoul.
Hungry people are hungry.
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Logic and truth
Montague (1974): the tools of logic can help us to represent sentence
meaning
Why logic: search for the principles of valid argument and inference
(7)
b.
c.
modus ponens (MP: way to affirm):
If P, then Q. (If A is not in the bar, then he is in the
lounge)
P (A is not in the bar)
Therefore Q. (A is thus in the lounge.)
a.
b.
c.
modues tollens:
If P, then Q (If A is in the bar, then he is drunk).
not Q (A is not drunk)
Therefore not P. (A is not in the bar)
a.
(8)
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truth value
The truth value is empirical (contingent) since we have to have some
access to the facts of the words to know whether the statement is
true or not.
(9) a.
b.
My father was the first man to visit USA.
My father was the first man to visit Mars.
The truth conditions: the facts that would have to obtain in reality to
make a sentence true or false. one easy to check the effect of truth
conditions is to use negation
(10) a.
b.
JB Kim
You car has been stolen.
Your car has not been stolen.
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logical form/connectives
logical form
(11) a.
b.
p (The house is on fire.)
¬p (The house is not on fire.)
truth table
p ¬p
T F
F T
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propositional logic: conjunctive
conjunctive: the house is on fire and the fire brigade are on the way.
p q p∧q
T T T
T F F
F T F
F F F
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propositional logic: conjunctive
inclusive
p q
T T
T F
F T
F F
JB Kim
disjunctive: I will see you today or tomorrow
p∨q
T
T
T
F
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exclusive disjunction
is only true if just one of its disjuncts is true
You
p
T
T
F
F
will
q
T
F
T
F
JB Kim
pay the fine or you will go to jail
p ∨e q
F
T
T
F
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marterial implication
p → q is only false when p (antecednet) is true and q (the
consequent) is false
if it
p
T
T
F
F
rains, then I will go to the movies
q p→q
T T
F F
T T
F F
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biconditional
both have the same value
We
p
T
T
F
F
will leave if and only if were are forced to.
q p↔q
T T
F F
T F
F T
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predicate logic
the study of truth values with quantifiers: all, every, each, some,
one....
(12)
All birds that fly are birds.
logical words
(13)
JB Kim
If Korea beat Japan then Japan lose to Korea.
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entailment
redefining the sentence relations with truth relations
entailment defined by truth: A sentence P entails a sentence Q when
the P’s truth value guarantees the Q’s truth, and the P’s falsity
guarantees the Q’s falsity.
p
q
T
→ T
F
→ T or F
F
← F
T or F ← T
JB Kim
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presupposition
some examples
(14) a.
b.
Her husband is a fool.
She has a husband.
(15) a.
b.
I do regret leaving London.
I left London.
partly semantics and partly pragmatics
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two approaches to presupposition
first: Semantics consists of relating a sentence-object to other
sentence-objects
second: sentence as the utterances of individuals engaged in a
communication act (pragmatics)
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truth conditional approach to presupposition
examples
(16) a.
b.
p
T
F
T or F
JB Kim
John’s brother has just got back from Seoul.
John has a brother.
q
→ T
→ T
← T
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negating the entailment vs. presupposition
entailment
(17) a.
b.
I saw my father today.
I saw someone today.
no entailment with negation
(18) a.
b.
JB Kim
I didn’t see my father today.
I saw someone today
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negating presupposition
examples
(19) a.
b.
The mayor of Seoul is in town.
There is a mayor of Seoul
negation
(20) a.
b.
The mayor of Seoul isn’t in town.
There is a mayor of Seoul.
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pragmatic view of presupposition
views presupposition as one aspect of a speaker’s strategy organizing
information for maximum clarity for the listener
Two assertions
(21) a.
b.
JB Kim
Assertion 1: John has a brother X.
Assertion 2: X has come back from Seoul.
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presupposition failure
using a name or a definite description presupposes the existence of
the named or describe entity
(22) a.
b.
John is a vegetarian.
John exists.
(23) a.
b.
The King of France is bald.
There is a King of France.
there is no referent for the NP ’king’; the truth value can be either
true or false
pragmatic approach: a speaker’s use of definite NPs is governed by
conventions about the accessibility of the referents to the listener
JB Kim
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presupposition trigger
it-cleft
(24)
It was his behavior with frogs that disgusted me.
What disgusted me was his behavior with frogs.
Something disgusted me.
lexical triggers: factive verbs
(25) a.
b.
c.
Sam realized that Mary had dandruff. (factive)
Sam thought that Mary had dandruff.
Mary had dandruff.
(26) a.
b.
John started smoking cigars.
John used not to smoke cigars.
JB Kim
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defeasibility: the canceling of presuppositions
presupposition
(27) a.
She cried before she finished her thesis.
b.
She finished her thesis.
presupposition cancelled with a different verb
(28) a.
b.
JB Kim
She died before she finished her thesis.
She finished her thesis.
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