Knowledge Representation and Validation in a Decision Support System: Introducing a Variability Modelling Technique - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 40

The proposed method guides the decision maker step by step (in each choice). If the
decision maker's choice is invalid, the choice is immediately rejected and corrective actions
are suggested, see Example 1. Moreover, notselect predicate can be assigned to some choices
according to decision maker's selection, see Example 2. The notselect predicate prevents the
decision maker from future errors; see Table 3: Rule 9.

? select (decrease level).

You have to deselect high level

Table 4. Example 1

? select ( non promotion decision ).
Yes
notselect (positive performance)
added to knowledge base.

Table 5. Example 2

4.2 Validate decision repository
4.2.1 Logical inconsistency detection
Inconsistency occurs from contradictions in constraint dependency rules. It is a very
complicated problem. Inconsistency has different forms and it can occur between: groups
(as example: (A and B) require (D and C) and (D and C) exclude (A and B)), group and
individual (as example: (A and B) require D and D excludes (A and B)), or between
individuals only (as example : (A require s B and B requires C and C excludes A)). A, B, C
and D could be choices or decision points.
In this paper, we suggest rules to detect logical inconsistency between individuals. The rules
that can be used to detect logical inconsistency (between individuals) are categorized in
three groups. Each group contains two rules.
Group 1
In this group, we discuss the constraint dependency relation between two decisions from
the same type (decision point or choice).
The first decision requires the second one while the second decision excludes the first one.
The logical inconsistency between two decisions could be indirect, e.g. A requires B and B
requires C and C excludes A. Therefore, to transfer the logical inconsistency to be directly
within two decisions, we define these transfer rules:
i. ∀ x,y,c:type(x,choice) ∧ type(y,choice) ∧ type(c,choice) ∧ requires_c_c(x,y) ∧

requires_c_c(y,c) ⟹

requires_c_c(x,c).
ii. ∀ x,y,c:type(x,decisionpoint) ∧ type(y,decisionpoint) ∧ type(c,decisionpoint) ∧ requires_dp_dp(x,y) ∧
requires_dp_dp(y,c) ⟹ requires_dp_dp(x,c).
The following rules detect inconsistency in group 1:
i. ∀ x,y:type(x,choice) ∧ type(y,choice) ∧ requires_c_c(x,y) ∧ excludes_c_c(y,x) ⟹ error.
If the choice x requires the choice y which means selection of x leads to selection of y (Rule
1). In addition, choice y excludes the choice x which means if y selected, x must not be
selected (Rule 2). This is an error.