The document outlines key concepts in semantics, focusing on sentence relations, truth, and logic, as taught in an English 311 course. It discusses various types of sentence relations, including entailment, presupposition, and contradictions, as well as methods of argument such as modus ponens and modus tollens. Additionally, it addresses the nature of truth, including necessary and contingent truths, while highlighting the importance of understanding logical connectives and empirical truths.

1. 1
English 311: Semantics
Course Instructor: Tania Rahman (TRn)
SENTENCE RELATIONS,
TRUTH & LOGIC

2.  Recap
 Truth
Logic and Truth
Entailment
Presupposition
 TAM: Tense, Aspect and Modality
 Mood and Evidentiality
2
Overview

3. A and B are synonymous (B is the paraphrase of
A): A means the same as B
My brother is a bachelor
My brother has never married.
A entails B: if we know A then we know B
The child killed the cat.
The cat is dead.
A contradicts B: A is inconsistent with B
Fred has long hair.
Fred is bald.
3
Meanings can be related

4. A presupposes B: B is part of the assumed background of A
The King of Pop is dead.
There was a King of Pop
I regret eating your lunch.
I ate your lunch.
A is necessarily true — tautology: A is true but not informative
Smart people are smart.
A is necessarily false — contradiction: A is inconsistent
with itself
?It is entirely made of copper and it is not made of metal.
A is not A.
4

5.  Classical logic is an attempt to find valid principles
of argument and inference.
a If something is human then it is mortal premise
b Socrates is human premise
c Socrates is mortal conclusion
 Can we go from a and b to c? Yes
 Truth is empirical: The premises need to correspond
with the facts of the world
 Sentences have truth values (true, false or unknown)
 The state of the world that makes a sentence true or
false are its truth conditions
5
Logic

6. Þ and (p q)
∧
Þ or (p q: disjunction, inclusive or)
∨
Þ xor (p q: exclusive or, either or)
⊕
Þ if (p q: if then, material implication)
→
Þ iff (p q: if and only if) ((p q) (q p))
≡ → ∧ →
Þ not (¬p: contradiction)
An argument is a connected series of statements
attempting to establish a proposition.
6
Logical Connectives

7.  Modus Ponens
a If something is human then it is mortal
b Socrates is human
c Socrates is mortal
p q, p q
→ ⊢
 Modus tollens
a If something is human then it is mortal
b Zeus is not mortal
c Zeus is not human
p q, ¬q ¬p
→ ⊢
7
Methods of Argument

8. Modus
ponens
p → q if someoneishumanthentheyare
mortal
p
a. Allh
u
m
a
n
sa
re mortal
b. Socratesis h
uman
c. Therefore,Socratesis mortal q
p q p → q
T T T
T
F
F
F
T
F
F
T
T
Þ The waythat affirms byaffirming (Latin)
Þ p → q, p ⊢ q
Þ material implication (Not quite the same as
English if )

9. Modus tollens
¬
q
a If something is hu
man then it is mortal
p → q b Z
e
u
s
is not mortal
c Z
e
u
sis not h
uman
¬
p
p q p → q
T
T
F
T
F
T
T
F
T
F F T
Þ The w
a
ythat n
eg
a
t
e
sbynegating
(Latin)
Þ p → q, ¬q⊢¬p
Yes it is

10.  Hypothetical syllogism
a If something is human then it is mortal
b If something is mortal then it dies
c If something is human then it dies
p q, q r p r
→ → ⊢ →
 Disjunctive syllogism
(modus tollendo ponens: affirm by denying)
p Either a human is mortal or a human is immortal
q A human is not immortal
r A human is mortal
p q,¬p q
⊕ ⊢
10
Methods of Argument

11. 11
Empirical truths and connectives
➣ Words themselves often carry more implications
I did A and B often implies I did A first
➣ There are many ways of saying the operations

12. Þ Formal
Affirming the consequent: p q, q p
→ ⊢
professors talk too much, you talk too much you are a professor
⊢
Þ Informal
Equivocation: The sign said ”fine for parking here”, and since it was
fine, I parked there.
No True Scotsman: X doesn’t do Y; a is an X and does Y; a is not a
true X
Slippery Slope: We mustn’t allow text abbreviations or students will
not be able to write normal text.
False Dilemma: You are with us or against us
Guilt by Association: Hitler was a vegetarian vegetarianism is
⊢
bad
12
Bad Arguments

13.  ➣ Arguments from the speaker’s knowledge
➢ A priori truth is truth that is known without experience.
➢ A posteri truth is truth known from empirical testing.
 ➣ Arguments from the facts of the world
➢ Necessary truth is truth that cannot be denied without forcing a
contradiction.
➢ Contingent truth can be contradicted depending on the facts.
 ➣ Arguments from our model of the world
➢ Analytic truth Truth follows from meaning relations within the sentence.
 can include word meaning
➢ Synthetic truth Agrees with facts of the world.
13
Necessary Truth, A Priori Truth and
Analyticity

14. Þ Arguments from our model of the world
Analytic truth Truth follows from meaning relations within the
sentence.
need to know word meaning
Synthetic truth Agrees with facts of the world.
Þ Normally these give the same results, but not always. Why?
If we include our model of word meaning in our reasoning, then
an apple is a fruit is analytic. So it is important to have an explicit
model: these models are typically called ontologies.
Þ What about the apple of my eye?
Building an inference engine is actually very, very hard, … But
very useful for question answering
14

15. ➣ Entailment
a. The evil overlord assassinated the man in the red shirt.
b. The man in the red shirt died.
A sentence p entails a sentence q when the truth of the first
(p) guarantees the truth of the second (q), and the falsity of the second
(q) guarantees the falsity of the first (p).
➣ Sources of Entailment
➢ Hyponyms
(7) I rescued a dog today. vs I rescued an animal today.
➢ Paraphrases
(8) My mom baked a cake.vs A cake was baked by my mom.
15
Entailment

16. 16
Paraphrases:Mutual entailment
Þ
(11)
(12
)
My mom baked a cake.
A cake wasbaked by my mom.
p q
T
F
F
T
→
→
←
←
T
F
F
T
Þ This is synonymy
Þ What about contradiction?

17. 17
Presuppositions
➣ Many statements assume the truth of something
else
➣ Negating the presupposing sentence a doesn’t affect the
presupposition
b whereas negating an entailing sentence destroys the entailment.
➣ Sources of Presuppositions
➢Names presuppose that their referents exist
➢Clefts (it was X that Y ); Time adverbials; Comparatives
➢Factive verbs: realize; some judgement verbs: blame; …
➣ Presupposition is one aspect of a speaker’s strategy of
organizing in- formation for maximum clarity for the listener.
(9) a. Kim’s spouse bakes the best
pies.
b. Kim has a spouse.

18. Þ A sketch from episode 29 of Monty Python’s
Flying Circus
Þ An argument is a connected series of
statements intended to establish a proposition
18
The Argument Clinic