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Lecture 3: Translating
from spoken language
to formal notation
1. Translating five statement operators
2. Translating compound statements
3. Translating arguments
Five Statement
Operators: Negation
Negation is expressed in a
number of ways in English
The cat is on the mat.
The cat is
not
on the mat.
The cat is
n’t
on the mat.
It is false that
the cat is on the
mat.
Five Statement
Operators: Negation
The cat is on the mat. = C
The cat is
not
on the mat.
The cat is
n’t
on the mat.
It is false that
the cat is on the
mat.
~
C
Five Statement
Operators: Conjunction
Roses are red. = R
Violets are blue. = V
Roses are red and violets are blue.
Roses are red but violets are blue.
Both roses are red and violets are
blue.
R
!
V
Five Statement
Operators: Conjunction
Roses are red. = R
Apples are red. = A
Roses are red and apples are red.
Roses and apples are red.
Both roses and apples are red.
R
!
A
Five Statement
Operators: Conjunction
Apples are sweet. = S
Apples are red. = A
Apples are sweet and apples are
red.
Apples are sweet and red.
Apples are both sweet and red.
S
!
A
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View Full Document Five Statement
Operators: Conjunction
Components of a conjunction are
conjuncts
.
S
!
A
Five Statement
Operators: Disjunction
Dallas will win the Superbowl.
Buffalo will win the Superbowl.
Dallas will win the Superbowl or
Buffalo will win the Superbowl.
Either Dallas will win the
Superbowl or Buffalo will win the
Superbowl.
Five Statement
Operators: Disjunction
Either Dallas will win the
Superbowl or Buffalo will win the
Superbowl.
Either Dallas or Buffalo will win the
Superbowl.
Dallas will win the Superbowl
unless
Buffalo wins the Superbowl.
Five Statement
Operators: Disjunction
Dallas will win the Superbowl. = D
Buffalo will win the Superbowl. = B
Dallas will win the Superbowl or
Buffalo will win the Superbowl.
D v B
Five Statement
Operators: Disjunction
Components of a disjunction are
called
disjuncts
.
D v B
Five Statement
Operators: Conditional
You earn exactly 900 points. = N
You get a some form of A. = A
If
you earn exactly 900 points,
then
you will get some form of A.
N
㱭
A
Statement following ‘if’ is
antecedent, statement following
‘then’ is consequent. (Does not
apply to ‘
only
if’.)
Five Statement
Operators: Conditional
If
you earn exactly 900 points, you
will get some form of A.
N
㱭
A
Statement following ‘if’ is
antecedent, statement following
where the ‘then’
would be
is
consequent.
Five Statement
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This note was uploaded on 09/07/2011 for the course PHIL 10 taught by Professor Churchland during the Spring '08 term at UCSD.
 Spring '08
 churchland

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