Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

present in the consequent part;
Augment the derived consequent predicates(clauses) in the DB-file;
For each of the antecedent and consequent clauses of the rule
If the place representing that clause is absent from the FPN
Then augment the place in the FPN;
End For;
Augment a transition tri for that rule PRi , such that the antecedent
and consequent clauses of the rule are input and output places of
the transition tri;
End If;
End While;
Until augmentation of places or transitions in FPN is terminated;
End.
Time-complexity: The estimated worst case time-complexity of the FPNformation
algorithm is found to be
TFPN = (Npr 2 / 2) [ Pp . N pr / 3 + V 2 ]
where Npr , Pp and V represent the number of PR in the knowledge-base, the
maximum number of predicates per PR and the maximum number of
variables per PR respectively.
10.2.2 Reachability Analysis and Cycle Identification
While analyzing FPNs, reachability of places [7], [1] and reachability of
markings [28] are commonly used. In this chapter, the concept of reachability
of places, as defined below, is used for identifying cycles in the FPN.
Definition 10.2: If pi ∈ I(tra) and pj ∈ O(tra) then pj is immediately
reachable from pi.. Again, if pj is immediately reachable from pi and pk is
immediately reachable from pj , then pk is reachable from pi. The reachability
property is the reflexive, transitive closure of the immediate reachability
property [9]. We would use IRS (pi) and RS (pi) operators to denote the set of
places immediately reachable and reachable from the place pi respectively.
Moreover, if pj ∈ [IRS{IRS(IRS... k-times (p i)}], denoted by IRS k (pi),
then pj is reachable from pi with a degree of reachability k. For reachability
analysis two connectivity matrices [12] are defined.
Definition10.3: A place to transition connectivity (PTC) matrix Q is a
binary matrix whose elements qjk = 1 if pk ∈ I (trj ), otherwise qjk = 0. If the
FPN has n places and m transitions, then the Q matrix is of (m × n)
dimension.