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in the knowledge representation for decision making. In our framework, the knowledge is
represented by a logical theory built upon an underlying logic-based language.
In this language we distinguish between several different categories of predicate symbols.
First of all, we use
goals
to represent the possible objectives of the decision making process.
For instance, the goal
fast
represents the objective of a buyer who would like to obtain a
quick answer. We will denote by
the set of predicate symbols denoting goals.
In the language we also want to distinguish symbols representing the
decisions
an agent can
adopt. For instance, in the procurement example a unary predicate symbol
s
(
x
)canbeused
to represent the decision of the buyer to select the service
x
. It is clear that a problem may
involve some decisions over different items, which will correspond to adopting many decision
predicate symbols (this is not the case in our running example). We will denote by
G
D
the set
of the predicate symbols for representing decisions.
In order to represent further knowledge about the domain under consideration, we will adopt
also a set of predicate symbols for
beliefs
, denoted by
B
. Furthermore, in many situations
the knowledge about a decision making problem may be incomplete, and it may require to
make assumptions to carry on the reasoning process. This will be tackled by selecting, in
the set
B
P
sm
). For instance,
in the procurement example, the decision made by the buyer may (and will indeed) depend
upon the way the buyer thinks the seller replies to the buyer's offer, either by accepting or by
rejecting it. This can be represented by a presumption
reply
(
, those predicate symbols representing
presumptions
(denoted by
)
x
,where
x
is either
accept
or
reject
.
In a decision making problem, we need to express
preferences
between different goals and the
reservation value
, that is the lowest (in terms of preference) set of goals under which the agent
cannot concede. For instance, in the procurement example, the buyer prefers to minimize
the price. Hence, its knowledge base should somehow represent the fact that the goal
fast
should be preferred to
cheap
. On the other hand, the buyer is prepared to concede on the
price in order to achieve an agreement with the seller, but it may be not ready to concede on
the delivery time which must be low. Hence, its knowledge base should somehow represent
the fact that these goals consist of its reservation value.
Finally, we allow the representation of explicit
incompatibilities
between goals and/or
decisions. For instance, different alternatives for the same decision predicate are incompatible
with each other, e.g.
s
(
a
)
. On the other hand, different goals
may
be
incompatible with one another. For instance,
cheap
is incompatible with
expensive
,
whereas
expensive
is not incompatible with
good
. Incompatibilities between goals and
between decisions will be represented through a binary relation denoted by
is incompatible with
s
(
b
)
.
The above informal discussion can be summarized by the definition of
decision framework
(Definition 8 below). For the sake of simplicity, in this definition, as well as in the rest of
the paper, we will assume some familiarity with the basic notions of logic languages (such
as terms, atomic formulae, clauses etc.) Moreover, we will not explicitly introduce formally
all the components of the underlying logic language, in order to focus our attention to those
components which are relevant to our decision making context. So, for instance, we assume
that the constants and function symbols over which terms are built (i.e. predicate arguments)
are given. Finally, given a set of predicate symbols
X
in the language, we will still use
X
to
denote the set of all possible atomic formulae built on predicates belonging to
X
.Ifnotclear
from the context, we will point out whether we refer to the predicate symbols in
X
rather than
to the atomic formulae built on
X
.
I
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