Computational Intelligence - May 2013 - 67
represented by wt (ag) d 60, 1 6. This value is
As such, WTR treats, in a uniform fashion, "disliked
assumed to be related to the agent's personality traits (e.g., increasing with extraversion and
situations" and "conflicting collected data."
decreasing with conscientiousness).
While the creation of observation and
communication supports is fairly intuitive, some rules need to
context, because the knowledge base has derivation supports
be made clear about the creation of derivation and wishful
for all possible derivations. In other words, the expression for
thinking supports.
determining belief space becomes equivalent to {U: } = ag U} .
Wishful thinking supports originate from the agent's goals. If
In WTR, we say that a context is consistent, as far as the agent
ag is the agent considered by WTR, there is exactly one wishful
knows, if and only if, for every formula in the corresponding
thinking support in KB(ag) for each of ag's goals, according to (3).
belief space, its negation is not in that belief space. This is
expressed in the definition of predicate Cons (Definition 3).3
6g ! Goals (ag):
Definition 3: When } is the context believed by agent ag, we say
that
} is consistent, as far as ag knows, if and only if Cons( } , ag)
G GDesc (g), WT, {GDesc (g)} H ! KB (ag) . (3)
holds, where predicate Cons satisfies the following condition:
The only exception to this rule is when the agent is
Cons (}, ag) + 6U ! BS (}, ag): JU g BS (}, ag).
deprived of wishful thinking (i.e., wt(ag) = 0), in which case no
wishful thinking support exists in KB(ag).
The management of derivation supports is out of the scope
Notice that, for logically omniscient agents, this corresponds
of WTR, but certain rules must be followed. Given agent ag,
to saying that } is consistent, as far as ag knows, iff } E ag = .
for any derivation support, G U, Der, a H ! KB (ag), the followAs explained above, if we consider an agent that is not logiing conditions must hold:
cally omniscient, some important properties follow:
1) a = ag U (obviously, the formula must be derivable from
1) A logical consequence of the believed context is not necessarily a belief
the origin set)
2) A context that is consistent as far as the agent knows, may
2) J7al 1 a: al=ag U (origin sets must be minimal)
be logically inconsistent.
3) U g a (self derivations are redundant and should not be
This happens because an agent of this kind does not necesregistered).
sarily derive everything that is possible, and is naturally ignorant
An agent that always generates every possible derivation is
concerning what was not yet concluded. Clearly, this is the case
known as a logically omniscient agent. WTR accounts for both
of humans.
logically omniscient and non-omniscient agents.
As expected, a context, in WTR, is defined as a set of hypotheses. Depending on the believed context, we can determine the
V. Wishful Thinking Revision
valid supports for a formula according to Definition 1.
In this section we describe how belief revision occurs in WTR.
Definition 1: When } is the context believed by agent ag, the
In other words, we describe the process that determines the
agent's beliefs at a given moment.
set of valid supports for a formula, U, is given by Sups (U, }, ag),
If ag is our agent, we divide the hypotheses in the
defined as:
agent's knowledge base (i.e., in KB(ag)) in two (possibly
intersecting) sets:
Sups (U, }, ag) = {A ! KB (ag): form (A) = U / os (A) 3 }} .
b 0 ={U: 7 (A ! KB (ag)) form (A)= U / ot (A) ! N , {Obs}}
is the set of collected data. It contains all the hypotheses
In other words, the valid supports for a formula are all the
that originate from the world (via observations and
supports for that formula where the origin set is entirely believed
communications).
(i.e., where the origin set is a subset of the believed context).
An agent's beliefs, at a given moment, are all the hypotheses
c 0 ={U: 7 (A ! KB (ag)) form (A) = U / ot (A) = WT} is the
in the context believed by that agent, and all the derived formuset of wishful thoughts. It contains all the hypotheses that originate
las that can be derived from that context. Put simply, an agent's
from goals (via wishful thinking).
beliefs are all the formulas that have at least one valid support.
WTR is responsible for determining, at a given moment,
Definition 2: When } is the context believed by agent ag, ag's
what consistent subset of b 0 , c 0 is believed. Such subset is obvibelief space2 (i.e., the set with ag's beliefs) is given by BS( } , ag),
ously a context, since the elements of b 0 , c 0 are hypotheses.
defined as:
We represent that context, i.e. the believed context, by b c.
We distinguish two (possibly intersecting) subsets of b c:
BS (}, ag) = {U: Sups (U, }, ag) ! 4}.
c
b = b + b 0 is the set of base beliefs, that is, of collected data
that is believed.
Notice that, for logically omniscient agents, the belief space
corresponds to all the logical consequences of the believed
3
2
The concept of belief space is also adapted from the SWM logic [14].
Throughout the remaining sections of this paper, wherever we write about consistency,
without further specifying the type of consistency, we refer to the definition of Cons
(Definition 3).
May 2013 | IEEE CoMputatIonal IntEllIgEnCE MagazInE
67
Table of Contents for the Digital Edition of Computational Intelligence - May 2013
Computational Intelligence - May 2013 - Cover1
Computational Intelligence - May 2013 - Cover2
Computational Intelligence - May 2013 - 1
Computational Intelligence - May 2013 - 2
Computational Intelligence - May 2013 - 3
Computational Intelligence - May 2013 - 4
Computational Intelligence - May 2013 - 5
Computational Intelligence - May 2013 - 6
Computational Intelligence - May 2013 - 7
Computational Intelligence - May 2013 - 8
Computational Intelligence - May 2013 - 9
Computational Intelligence - May 2013 - 10
Computational Intelligence - May 2013 - 11
Computational Intelligence - May 2013 - 12
Computational Intelligence - May 2013 - 13
Computational Intelligence - May 2013 - 14
Computational Intelligence - May 2013 - 15
Computational Intelligence - May 2013 - 16
Computational Intelligence - May 2013 - 17
Computational Intelligence - May 2013 - 18
Computational Intelligence - May 2013 - 19
Computational Intelligence - May 2013 - 20
Computational Intelligence - May 2013 - 21
Computational Intelligence - May 2013 - 22
Computational Intelligence - May 2013 - 23
Computational Intelligence - May 2013 - 24
Computational Intelligence - May 2013 - 25
Computational Intelligence - May 2013 - 26
Computational Intelligence - May 2013 - 27
Computational Intelligence - May 2013 - 28
Computational Intelligence - May 2013 - 29
Computational Intelligence - May 2013 - 30
Computational Intelligence - May 2013 - 31
Computational Intelligence - May 2013 - 32
Computational Intelligence - May 2013 - 33
Computational Intelligence - May 2013 - 34
Computational Intelligence - May 2013 - 35
Computational Intelligence - May 2013 - 36
Computational Intelligence - May 2013 - 37
Computational Intelligence - May 2013 - 38
Computational Intelligence - May 2013 - 39
Computational Intelligence - May 2013 - 40
Computational Intelligence - May 2013 - 41
Computational Intelligence - May 2013 - 42
Computational Intelligence - May 2013 - 43
Computational Intelligence - May 2013 - 44
Computational Intelligence - May 2013 - 45
Computational Intelligence - May 2013 - 46
Computational Intelligence - May 2013 - 47
Computational Intelligence - May 2013 - 48
Computational Intelligence - May 2013 - 49
Computational Intelligence - May 2013 - 50
Computational Intelligence - May 2013 - 51
Computational Intelligence - May 2013 - 52
Computational Intelligence - May 2013 - 53
Computational Intelligence - May 2013 - 54
Computational Intelligence - May 2013 - 55
Computational Intelligence - May 2013 - 56
Computational Intelligence - May 2013 - 57
Computational Intelligence - May 2013 - 58
Computational Intelligence - May 2013 - 59
Computational Intelligence - May 2013 - 60
Computational Intelligence - May 2013 - 61
Computational Intelligence - May 2013 - 62
Computational Intelligence - May 2013 - 63
Computational Intelligence - May 2013 - 64
Computational Intelligence - May 2013 - 65
Computational Intelligence - May 2013 - 66
Computational Intelligence - May 2013 - 67
Computational Intelligence - May 2013 - 68
Computational Intelligence - May 2013 - 69
Computational Intelligence - May 2013 - 70
Computational Intelligence - May 2013 - 71
Computational Intelligence - May 2013 - 72
Computational Intelligence - May 2013 - 73
Computational Intelligence - May 2013 - 74
Computational Intelligence - May 2013 - 75
Computational Intelligence - May 2013 - 76
Computational Intelligence - May 2013 - 77
Computational Intelligence - May 2013 - 78
Computational Intelligence - May 2013 - 79
Computational Intelligence - May 2013 - 80
Computational Intelligence - May 2013 - Cover3
Computational Intelligence - May 2013 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202311
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202308
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202305
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202302
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202211
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202208
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202205
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202202
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202111
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202108
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202105
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202102
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202011
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202008
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202005
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202002
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201911
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201908
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201905
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201902
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201811
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201808
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201805
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201802
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter12
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall12
https://www.nxtbookmedia.com