An Expert System on Detection, Evaluation and Treatment of Hypertension - Artificial Intelligence and Symbolic Computation - page 258

Table 6. Classification of CVD risk (adapted)

CVD Risk Factors
and other CVD facts Normal Prehyp. St.1 Hyp. St.2a Hyp. St.2b Hyp.
nCVDRF=0 ∧¬ TOD
∧¬ DM ∧¬ ACA Low Low Low Medium High

1 ≤ nCVDRF ≤ 2 ∧
¬

TOD ∧¬ DM ∧¬ ACA Low Low Medium Medium Very high

(nCVDRF ≥ 3 ∨ TOD
∨ DM) ∧¬ ACA

Low Low High High Very high

ACA Low Low Very high Very high Very high

A fact is any potential fact that the user states to hold. For instance, the user
may state that the potential fact ζ is given as a fact.
An Integrity Constraint (IC) is any well formed combination of literals and
connectives that an expert has asserted to never hold. For instance, suppose
that an expert assesses that γ

¬θ never hold together. We then have new
information to be added to the RBES: the negation of the integrity constraint
(NIC):

and

( γ ∧¬θ ).
It is said that a rule can be forward fired if all the literals in the antecedent
are facts (or derived facts , see below). Forward firing corresponds to the formal
logic rule of “modus ponens”. The inference engine of the RBES fires the rules.
In some cases, the consequent of a rule may be part of the antecedent of
another rule, like

¬

¬β and η are facts, then forward
firing Rule 1 outputs γ ,being γ an example of what is called a derived fact .
Now, forward firing Rule 2 and Rule 3 output δ ∨ ε and

γ in Rules 1 and 2. If α ,

¬ε ,so δ and ¬ε are also

derived facts (because δ is a tautological consequence of δ ∨ ε and ¬ε ).

There are two main types of logical inconsistencies.
If we are given the RBES composed of rules 4 and 5 and facts

δ and ζ ,

forward firing outputs the logical contradiction θ ∧¬θ.
Suppose that we are given the facts α , ¬β and ζ inaRBEScomposedonly

by Rules 1 and 5, to which the NIC ( γ ∧¬θ ) is added. In this case, forward

firing leads to the IC γ ∧¬θ , so the logical contradiction IC

¬

NIC is obtained.
In the RBES composed of rules R1, R2, R3, R4 and R5, if α, ¬β , η

∧

and ζ

are given as facts, both types of contradictions are reached.
Observe that if a logical contradiction is inferred (by forward firing) from
therulesandICsinaRBESanda consistent set of facts (that is, a set of facts
that doesn't include together a literal and its negation), we say that the RBES
is inconsistent . In such case all formulae written in the language of the RBES
do follow from the rules and ICs in the RBES and that consistent set of facts.

6 Detailing the Expert System

A RBES can use a Boolean logic, a multi-valued modal logic, a fuzzy logic...
Boolean logic should not be used when a level of certainty is to be assigned