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preference information.
KB
A
P
records the preferences of
Ag
using clauses with pref-
erence based propositions as heads and bodies comprising factual propositions. Now
KB
Ag
F
KB
Ag
P
∪
p
Ag
denotes that the preferences of
Ag
are required for
p
Ag
to be
shown.
This reflects that a value judgement such as
Rolls Royce make the best cars
, cannot be
considered true
simpliciter
, but is true (or false) relative to an agent, and determined
using that agent's individual preferences. Next we may need to distinguish between the
knowledge base of an agent at the start of the dialogue, and the knowledge base of
that agent at the end of the dialogue. In our simple case, only
KB
A
F
changes during a
dialogue. While an agent may be persuaded to change its preferences, this is a higher
order persuasion in this paper and not a straightforward matter of simply adding to the
existing
KB
P
, as is the case with facts.
Definition 3.
Let the knowledge base of an agent
Ag
at the start of a dialogue be denoted
by
KB
Ag
0
, and its knowledge base after n steps of dialogue be denoted by
KB
Ag
n
.
We now introduce some further definitions needed for the protocol and strategy. Firstly,
agents need to be able to discuss the options under consideration within the dialogue
and the attributes of these options. For example, in a dialogue about where to go on hol-
iday, the options might cover different countries such as France and Spain with relevant
attributes including things such as the food and the weather. In the restaurant example
the various local restaurants will be the options and various features such as distance,
quality, type of cuisine, ambiance and the like are attributes of restaurants that agents
may use as reasons to choose between them. Furthermore, agents can give individual
weightings to these attributes to reflect their different tastes and aspirations.
Definition 4.
Let
O
be a set of options that agents can propose during the course of a
dialogue.
O
has an associated set of attributes
A
O
. An agent associates each
a
j
∈
A
O
with a weight
w
j
≥
0
to form a set of weights
W
.Eachset
W
is individual to an agent.
Next we need to be able to determine the truth value of attributes of options, e.g. stating
that the option Spain does indeed have the attribute of good weather, or that the Mogul
Palace serves Indian food. We also need to be able to determine the weight that an agent
assigns to an attribute of an option. The following two functions enable the above.
Definition 5.
Let
τ
:
O × A
O
→{
0
,
1
}
be a truth function that returns the truth value
given by
τ
(
O
i
,a
j
)
=
τ
ij
for option
O
i
∈ O
and attribute
a
j
∈ A
O
.
Definition 6.
Let
w
:
AG
be a weight function that returns the weight
w
(
Ag, a
j
)
=
w
Ag
(
a
j
)
of an attribute
a
j
for agent
Ag
×
A
O
→
N
∪{
0
}
∈
A
O
. Where the agent
Ag
is
clear from the context, we use
w
j
.
Next we introduce notation to enable us to refer to sets of attributes of options as deter-
mined by their truth status (as will be required in section 4). Thus, attributes of options
will fall within one the following disjoint sets:
verified true
,
verified false
,
unverified
