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1) Νόμοι Κατηγορηματικής Λογικής 1.1) Νόμοι Κατηγορηματικής Λογικής 1.2) Ταυτολογία - Αντίφαση 1.3) Μετονομασία Μεταβλητών Ποσοδεικτών 2) Κανονικές Μορφές 2.1) Κανονική Διαζευκτική Μορφή 2.2) Κανονική Συζευκτική Μορφή 2.3) Clausal Form 3) Κανονικές Μορφές 3.1) Μεγάλη Άσκηση Σ.Κ.Μ. 3.2) Γρήγορη Σ.Κ.Μ.
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31 2:
2.2: .. ..
.
.
1. 1.
2. -
3.
2 , 31, 2.2: wff
2.
1.
2.
3. Clausal Form
3.
1. ...
2. ...
.
.
wff
(-)
3 , 31, 2.2: wff
(-)
.
1. :
4 , 31, 2.2: wff
1
2 OR
3 De Morgan OR AND
~~)(~~~)(~
)(~~ ~
4
5
6
7
8
~~)(~
)()()()()()(
)()()()(
~~ B
~~
~~
xx
xx
xxx
xxx
}{}{
.
1. 1.-
5 , 31, 2.2: wff
.
.
1. 2.
,
.
:
6 , 31, 2.2: wff
)]](~),([()([~ yyxyxx pipi :
:
)]](~),([()([~ yyxyxx pipi
)]](~),([()([~ yyzyzz pipi
)]](~),([()([~ wwzwzz pipi
.
2.
3 :
clausal form
7 , 31, 2.2: wff
wff
8 , 31, 2.2: wff
: (), :
i :
Bj (literal)
n ...21
m ...21
.
2. 1.
:
.. :
...
)),(~)(()),()(( bobpamparentbobmanpamtomparenttomman
))()(~)(())(~)()(( dQdTdTdTcTaQ
.
2. 2.
9 , 31, 2.2: wff
: (), :
i :
B (literal)
n ...21
m ...21 Bj (literal)
:
.. :
...
)),(~)(()),()(( bobpamparentbobmanpamtomparenttomman
))(~)(~)(())()(~)(())(~)()(( dRcQaRdQdTdTdTcTaQ
.
2. 3. Clausal Form
10 , 31, 2.2: wff
nm ...... 2121
m...21
n ...21
212121212121 ~~)(~ =
.
1. wff
wff 7 :1. 2. 3. 4.
11 , 31, 2.2: wff
4. 5. 6. 7. AND
.
1. wff 1.
12 , 31, 2.2: wff
1 :
1 OR: ~
:: :
: OR:
)])],(~)([~)],(),([~)](~),([()([
yxyyxyyxyyyxyxx
pipipipi
)])],(~)([)],(),([~
)](~),([()([~
yxyyxyyxy
yyxyxx
pipi
pipi
.
1. wff 2.
13 , 31, 2.2: wff
2 : 2 .
De Morgan:
()
~~
~~
xx
xx
~~)(~~~)(~
()
:
De Morgan:
)])],(~)([)],(),([~
)](~),([()([~
yxyyxyyxy
yyxyxx
pipi
pipi
)])],(~)([)],(),([~
)](~),([()([~
yxyyxyyxy
yyxyxx
pipi
pipi
)])],(~)([)],(~),([~
)](~),([()([~
yxyyxyyxy
yyxyxx
pipi
pipi
.
1. wff 3. ()
14 , 31, 2.2: wff
3 : ()
,
..: )()]([ AQxQx
,
..:
)()]([ AQxQx
),()],([ AyyQxyQyx ),()],([ BAQyxQyx
)]),(([)],([ xxfQxxyQyx )]),,(([)],([ xzxfQzxxyQyzx
)],,(),,(([)],([ wyxgyxfQwyxkzQkwzyx
)]),(([)],([ xxparentxxyparentyx
.
1. wff 3. ()
15 , 31, 2.2: wff
()
:
)])],(~)([)],(~),([~
)](~),([()([~
yxyyxyyxy
yyxyxx
pipi
pipi
:
)])],(~)([)],(~),([~
))]((~))(,(([)([~
yxyyxyyxy
xxxxx
pipi
pipi
.
1. wff 4.
16 , 31, 2.2: wff
4 : 4 ,
! !
()
:
)])],(~)([)],(~),([~
))]((~))(,(([)([~
yxyyxyyxy
xxxxx
pipi
pipi
)])],(~)([)],(~),([~
))]((~))(,(([)([~
zxzz
xyyxyxxxxx
pipi
pipi
.
1. wff 5.
17 , 31, 2.2: wff
5 : 5
, ..
. .
()
)])],(~)([)],(~),([~
))]((~))(,(([)([~
zxzz
xyyxyxxxxx
pipi
pipi
)])],(~)([)],(~),([~
))]((~))(,(([)([~
zxz
xyyxxxxxzyx
pipi
pipi
.
1. wff 6.
18 , 31, 2.2: wff
6 :
:
:
()
)()()( )()()()(
()
:
:
)])],(~)([)],(~),([~
))]((~))(,(([)([~
zxz
xyyxxxxxzyx
pipi
pipi
)]]],(~)([)([~)]],(~),([~)([~
))]((~))(,(([)([[~
zxzx
xyyxxxxxxzyx
pipi
pipi
)]],(~)()([~)],(~),(~)([~
))]((~)([~))](,()([[~
zxzx
xyyxxxx
xxxzyx
pipi
pipi
.
1. wff 7. AND
19 , 31, 2.2: wff
7 : AND 7 AND
2 ( ( ).()
AND. :
)]],(~)()([~)],(~),(~)([~
))]((~)([~))](,()([[~
zxzx
xyyxxxx
xxxzyx
pipi
pipi
),(~)()(~),(~),(~)(~))((~)(~
))(,()(~
zvzv
uyyuuww
xxx
pipi
pipi
20 , 31, 2.2: wff
.
2. 1. ..
:
21 , 31, 2.2: wff
.
2. 1. ..
22 , 31, 2.2: wff
.
2. 2. ..
. ,
... :
. 1
23 , 31, 2.2: wff
:
(Q T) R, (Q P) R, S (T P), Q, S, T
.
. 2
24 , 31, 2.2: wff
... :( ) ( ) ( ) ( )( )( )( )wuRwvRwvtRvutRut ,,,,
25 , 31, 2.2: wff
:1: 2: 3: 4: 5: 6: () . : /1,__/2, /1 /2
. 3
: /1,__/2, /1 /2
26 , 31, 2.2: wff
()
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