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questions we want to answ
person having a belief say
say that he knows it?
In order to answer these
that some nomenclature.
wer along this section are the following: When woul
that the belief is justified? When would this same per
ld a
rson
e questions, we will introduce four definitions, and bef
fore
Nomenclature
. Let
A
be an
set of Boolean connectives
and
the set of formulae (f
1988, p.157) that
contain
modus ponens.
must also
time
t
. We do not assume
consistent belief base.
is
Now imagine that we h
evaluate its naturalness at
related to
, and are salien
we are particularly conscio
trains, then intuitively
wo
my belief about the beauti
already have some such not
individual,
L
the smallest language (containing a comp
s) in which all the beliefs that
A
can have are expressib
formulated over
L
) of some logic. We suppose (with Gro
ns the propositional tautologies and that it is closed un
o be compact.
lete
ble,
ove,
nder
ular
is a
is the belief-system of
A
at a particu
that
is logically closed, i.e., a theory. Rather
i
the empty set.
have a belief that is not tautological,
, and we wan
a time
t
against those others of our beliefs,
,
that
nt at the moment of the evaluation, salient in the sense t
ous of them at
t
. For instance, imagine that
is ab
ould contain all of my relevant beliefs about trains, but
iful hair of my neighbor. Definition 1. assumes that
tion of salience.
nt to
are
that
bout
not
we
y) Let
⊆ Γ
be the salient set of beliefs related to
t
elief
is
acceptable
for
A
at
t
if Con(
,
), that is
a
tion, and one of the following cases holds:
Definition 1.
(Acceptability
does not include
. The be
do not imply a contradict
1.1.
;
1.2.
and
. W
relative to
;
1.3.
,
, and
necessarily in ) exp
..., p
n
}
, and
of the acceptability of
that
and
f
We say here that
is a
witness
of the acceptability of
{
p
1
, ..., p
n
} non-empty, finite set of potential beliefs (
ressed as literals in
L
, such that
{
p
1
, ..., p
n
}
,
{
p
1
, ..., p
n
}
.
As before, we call {
p
1
, ..., p
n
} a
witn
relative to
.
eptable then ¬
could also be acceptable, as acceptabi
We will clarify this notion in Definition 4. when we wo
tification which, as we will see, is stronger than the not
(not
{
p
1
,
ness
Observe that if
is acc
is a rather weak notion. W
introduce the notion of just
of acceptability.
In the case thus of Con
belief,
, if we are able
together with a set of
sim
ility
ould
tion
n(
,
) and
, we say that we have an
accepta
to semantically infer
either from
alone, or from
mple assumptions
satisfying certain properties (specif
able
m
fied
