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1
INTRO LOGIC
DAY 09
2
UNIT 2
DERIVATIONS IN
SENTENTIAL LOGIC
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Basic Idea
We start with a few argument forms,
which we
presume
are valid,
and we use these
to demonstrate that other argument forms are valid.
We demonstrate that
a given argument form is valid by
deriving
(
deducing
) its conclusion
from its premises
using a few
fundamental modes of reasoning
.
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Example 1 – Modus Ponens (MP)
→
––––––
we can employ
modus ponens
(MP)
to
derive
the conclusion from
the premises.
if
then
––––––––––
P
P
Q
Q
R
R
S
––––––
S
a
derivative
argument form
3
5
Example 1 (continued)
/ S
; R
S
; Q
R
; P
Q
P
MP
Q
R
S
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Example 2 – Modus Tollens (MT)
we can employ
modus tollens
(MT)
to
derive
the conclusion from
the premises.
a
derivative
argument form
if
then
not
––––––––––
not
S
R
S
Q
R
P
Q
––––––
P
→
––––––
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Example 2 (continued)
/
P
; P
Q
; Q
R
; R
S
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This note was uploaded on 02/04/2012 for the course PHIL 110 taught by Professor Bohn during the Fall '08 term at UMass (Amherst).
 Fall '08
 BOHN

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