Information Technology Reference
In-Depth Information
To sum up, the belief that
of an agent
A
at a time
t
is knowledge at
t
for some
agent
B
from the second person perspective if, and only if,
B
is convinced at
t
that
A
will behave according to
.
2.3
The Third Person Perspective
The third person perspective is that of an observer who draws attention to the
dynamic of an individual
A
's belief-system (i.e. what the salient set of beliefs related
to a belief are at any time) given the evolution of the situation in which the particular
belief is elicited. In particular, we have in mind two sort of contexts: one in which the
observer has actually witnessed the evolution of the situation and the reactions of
A
(witness-case), and another in which the observer predicts what is going to happen
(prediction-case). We say that
A
's belief that
shows a successful behavior for
B
from
the third person perspective at a time
t
if
A
's belief that
˕
is successful for
B
at
t
from
the first person perspective (given the idea held by
B
of
A
's belief-system), and the
evolution (witness-case) or
natural
evolution (prediction-case) of the situation does
not present a challenge to it, that is, the situation evolves in a way in which none of
the new items added to the set of salient beliefs undermines
A
's belief that
˕
˕
.
Let us introduce an example in order to clarify our proposal:
A
is a teacher in a school. He witnesses the following situation in the playground:
At the corner of the main building is student
S1
. Running towards him is
S2
. After a
couple of minutes
S1
and
S2
have moved out from the sight of the teacher who then
hears someone crying. The teacher believes that '
S1
is crying' (
˕
).
Suppose that the salient set of beliefs of
A
related to
˕
at the time the teacher sees
the scene t
0
is:
= {'
S2
was running towards
S1
', 'Someone is crying', '
S2
hates
S1
', '
S2
is a violent boy', '
S1
has reported
S2
's bad behavior', 'if
S2
heard about the report, he
would hit
S1
', 'if
S1
were hit, he would cry'}. In this case, on the one hand γ
{'
S2
has heard about the report'}
ϕ, and hence ˕
is
acceptable
(see section 2.1), and on
the other hand,
¬
ʳ
˕
is not
acceptable
for
A
at the same time
t
0
given
ʳ
. Thus the belief
˕
is knowledge for
A
at
t
0
from the first person perspective. But is
A
's belief also
knowledge for
A
at
t
0
from the third person perspective?
The situation evolves in such a way that, when
A
hears the cry, he runs towards it.
Once there, at
t
1
,
A
observes that
S1
lies on the ground crying, while
S2
is calmly
talking to someone else.
A
is puzzled. The fact that
S2
is calmly talking to another
student causes the introduction into
' = γ
{'
S2
seems to be calmly talking to another student', 'after hitting a person one is excited'}.
The teacher would have needed more
credulity
at
t
0
in order to get
ʳ
at
t
1
of at least two new beliefs:
ʳ
out of the new
salient set of beliefs: γ
{'S2 has heard about the report', 'S2 is pretending to be
calm'}
ϕ. That is,
d
(˕, ʳ) <
d
(˕, γ
). In this case (witness-case) the belief that ˕
,
was not knowledge at
t
0
for the teacher from the third person perspective. The teacher
would not say at
t
1
that he knew at
t
0
that
S1
was crying.
The previous example is, as we have just pointed out, a witness-case example. Let
us talk now for a while about the prediction-cases. In these cases the observer, the
evaluator of the belief, predicts the evolution of the situation. So the question to raise
is: What is the evolution which the observer will predict? When is a situation said to
˕