Computational Intelligence - May 2013 - 66
We assume that all agents in the current world are uniquely
identified by their name. We represent the set of names of the
agents by N, where N + " Obs, WT, Der , =Y
0.
If ag is the agent using WTR, our model assumes that its internal state contains, among other items, the following information:
❏ The agent's knowledge base, represented by KB(ag)
❏ The agent's goals, represented by Goals(ag)
❏ For each other agent agi, the subjective credibility that our
agent associates with agi, represented by Cred(ag, agi)
❏ The agent's wishful thinking coefficient, represented
by wt(ag).
The knowledge base is where the agent keeps a record of
reasons to believe in propositions. This information is important because WTR abandons all beliefs that lose their justifications. Moreover, the knowledge base keeps information about
the origins of basic beliefs, which is used by WTR to measure
belief strength.
The representation we use, for the reasons stored in the
knowledge base, is based on the representation defined by
Martins and Shapiro, in the SWM logic [14], to record dependencies among formulas. Given an agent ag, KB(ag) is a set of
supports, defined as triplets with the form U, T, a , where:
❏ U d L ag is the support's formula and represents the proposition that is being supported;
❏ T d " Obs, WT, Der , , N is the support's origin tag and
indicates how U got in the knowledge base, in other words,
what kind of reason supports belief in the proposition represented by U ;
❏ a 3 L ag is the support's origin set and contains the formulas
that U depends on, in this support (important for keeping
track of the formulas that support derivations).
If A = U, T, a is a support, we define form (A) = U,
ot (A) = T, and os(A) = a. A can be of four kinds, depending on its origin tag, T:
If T = Obs A is called an observation support. This means
that the proposition represented by U was
observed by the agent.
If T = WT A is called a wishful thinking support. This
means that the proposition represented by U
originated, by wishful thinking, from one of
the agent's goals.
If T = Der A is called a derivation support. This means
that the proposition represented by U was
derived from other formulas.
If T d N A is called a communication support. This means
that the proposition represented by U was
communicated by the agent of name T.
We point out that the same formula may have more than
one support in the knowledge base. For instance, the agent may
be informed of a fact, represented by U , by two different
agents and also observe that fact. This would correspond to
three separate supports with formula U : two communication
supports and one observation support.
Furthermore, observation, communication and wishful
thinking supports are all called non-derivation supports. Formulas
66
IEEE ComputatIonal IntEllIgEnCE magazInE | may 2013
that occur in derivation supports are known as derived formulas,
and formulas that occur in non-derivation supports are known
as hypotheses. Notice that a formula can be both a derived formula and a hypothesis, if there is at least one derivation support
and one non-derivation support with that formula.
When A is a derivation support, its origin set is the set of
hypotheses underlying this specific derivation of form ^Ah . If
A is a non-derivation support, its origin set is " form (A) , .
For instance, suppose that agent ag's knowledge base contains only three supports, as shown in (1).
KB (ag) = {G A, Obs, {A} H ,
G A " B, Peter, {A " B} H ,
G B " C, Susan, {B " C} H} .
(1)
In other words, there are three hypotheses: A, A " B and
B " C. The first was observed by the agent, the second was
communicated by agent Peter, and the third was communicated
by agent Susan.
If the agent combines the first two hypotheses to derive B,
this originates a derivation support with the origin set
" A, A " B , (the hypotheses underlying the derivation). If, then,
the agent combines the newly derived formula (B) with the
third hypothesis (B " C ) to derive C, this originates another
derivation support with the origin set " A, A " B, B " C , .
After these two derivations take place, the agent's knowledge
base contains five supports, shown in (2).
KB (ag) = {G A, Obs, {A} H ,
G A " B, Peter, {A " B} H ,
G B " C, Susan, {B " C} H ,
G B, Der, {A, A " B} H ,
G C, Der, {A, A " B, B " C} H} .
(2)
Now we move to the second item in the agent's internal
state, namely the agent's goals. We recall that WTR aims at
modeling wishful thinking within the scope of goal satisfaction.
Hence, whatever the agent wants to be true, that is meant to be
captured by WTR, must be expressed in terms of goals.
We represent by Goals(ag) the set of goals of agent ag and,
for every g d Goals(ag), we write:
❏ GDesc( g) d L ag to represent the goal's description, that is,
the formula representing the proposition that the agent
wants to be true
❏ GImp( g) d @ 0, 1 6 to represent the goal's importance, that
is, the weight that the agent associates with the goal.
WTR assumes that the agent associates a value of subjective
credibility with each of the other agents in the current world.
The value of subjective credibility that an agent ag 1 associates
with another agent ag2 reflects the degree to which ag 1 believes
in what ag2 communicates, and is represented by Cred( ag 1, ag 2 )
d @ 0, 1 6. This may start as a default value, and evolve based on
the interactions between ag1 and ag2.
The wishful thinking coefficient of an agent, ag, reflects the
degree to which ag is susceptible to wishful thinking, and is
Table of Contents for the Digital Edition of Computational Intelligence - May 2013
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