!"
#$%&'()
*
+""
%
,
'
"
,
-
"
+
.,
-
P3,1 → B2,1 ∧ B3,2 ∧ B4,1
You need to repeat a similar sentence for all possible locations of a pit.
It would be nice to write one sentence explaining that squares adjacent to
pits are breezy.
&,
&/
-0
-
-0
Hunt the Wumpus
Squares adjacent to pits are breezy
Squares adjacent to the wumpus are stinky
!
"#$
What can be known
What exists,
the model
Objects
1
'23
-4"4
5
Allows speaking about groups of objects
∀ -- for all
∃ -- there exists
-0
-
-0-
"
-0
#"%&
"
4"
-0(,
"
-0
,"
,
-0
-0(7
,%,"
-0
#234234A2&4?3
B
,--
'"
-0
,
?
8&"
?24C
3
"
2"%
-,-'?2D4C
3
-03
:
-02
,
3
:
"27
43
:27
44E3
E227
34E
27
33
27
3<#'
&F?
4
4?
67
44894
:
4;4<4
between objects
=4""4 Relations
attributes of objects
%4'44-4
Refer to objects
¬4⇒4∧4∨4⇔
∀4∃
Like in propositional logic
1
>-
?
@"
G-
"
-0
E27
3
?,
¬4⇒4∧4∨4⇔
,'%,'
∀∃
H
∀%¬52%413
¬∃%52%413
H
∀%52%4!,3
¬∃%¬52%4!,3
B
'
.-
="
B
?-="
∀%¬1≡¬∃%1
∀%1≡¬∃%¬1
¬∀%1≡∃%¬1
∃%1≡¬∀%¬1
'(
>-"
,
-0
:
"2%43⇒ #'2%3
@"
?-
"
-0
∀%2:
"2%43⇒ #'2%33
∃%2:
"2%43 ∧ #'2%33
G?-
-="
,5
?,
)*+$(
&I8J
?"
∀⇒
IG5
J
∀%62%3∧1
2%3
∀%62%3⇒1
2%3
&I8J
?"
∃∧
I7
J
∃%
2%3⇒#2%47
3
∃%
2%3∧#2%47
3
,
$5
5
!5
6
K
,
&
?K
5-
"
H
-
-0
-
"
-0
#
@"
,
$
H
IG,-
G5"
,J
$
LG,4G54
$
L-
GH-
2G,4G543
I&5'4$5'+'--J
I&
,4
E5'
,
J
,
I$,-
J
I
:5',J
IK,
,
J
$
LK,
$L!,
GH,
2K,
3
8
.5-
="H
I
5?'J
$.
L
&L0?-%
K?'L?="
GH∀%52
4%3
∧
∧
I
5
,J
I
,-
'5
J
,
,
E="H
I
,-
'
,J
GH∃%4'2%4'3
E
,%
H
IG5'
J
GH∀%
2%3∧5'2%3⇒
2%3
I8
5'
J
IK?'-
'?'J
I
,-
'
?'J
,
"
H
IK?'
5J
GH∀%4'22%3∧"M2'3∧52%4'3⇒2%4'33
∀%
2%3∧5'2%3⇒¬
2%3
¬∃ %
2%3∧5'2%3∧
2%3
¬∃ %
2%3∧5'2%3⇒
2%32L3
,
&'
?
""
"
IK?'-
'
?
,-
'J
I&
,
?-'?'
J
IK?'-
'"J
IK?',
'J
I'
J
,
- IK?'-
'
?
,-
'J
,NH∀%∃'
?2%4'3
,H∃'∀%
?2%4'3
"="
,
,%="*
I&--
?,
?,?J
I&
,
?-'?'
J
∃'∀%
?2%4'3
IK?'-
'"J
,
NH"
2%3
,
H∀%∃'"2'4%3
IK?',
'J
∀%,2%3⇒#'2%3
I'
J
∃%12%3∧ ∀'12'3⇒'<%
!5'
I%'J
IJ
I,
J
$
HC
"
H2%3(
"%
88,-H
88,2C
3
∀88,23⇒88,2233
"
H
∀C
≠23
∀,4,≠⇒2,3≠23
G
"H
∀,88,2,3⇒A24,3<,
∀,488,2,3∧88,23⇒A22,343<2A2,433
G
",-
'2,
4?
4,4,,-4
'
'43-
I1
"
,
"
"
,4'"
"
,
"
,4-'."
"
"
,J
IG'
,-
,
"
J
I
,
"
-,J
N !"'&&5
G,-?5
O +
?
-'
"4"
4
(
'
K
5
-
,
K
""
-,
'%,
"
,44
?4="
$
="
$
?
#
?5