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

It is to be noted that if- then operator of the knowledge has been represented in
the figure by tr1 and the antecedent-consequent pairs of knowledge have been
denoted by input (I) – output (0) places of tr1. Moreover, the arguments of the
predicates have been represented by arc functions.
22.5.2 Forward and Backward Firing
For computing a token at a place, the transition associated with the place is
required to be fired. Firing of a transition, however, calls for satisfaction of the
following criteria.
A transition tri is enabled,
(1) if all the places excluding at most one empty place, associated with the
transition tri , possess appropriately signed tokens, i.e., positive literals
for input and negative literals for output places.
(2) if the variables in the argument of the predicates, associated with the
input and output places of the transition, assume consistent bindings.
It means that a variable in more than one arc function, associated with a
transition, should assume unique value, which may be a constant or renamed
variable [7] and should not be contradictory. For instance, if variable X
assumes a value ‘a’ in one arc function and ‘b’ in another arc function of the
same transition, then they are inconsistent. The bindings of a variable X in an
arc function are evaluated by setting its value to the same positioned term in
the token, located in the connected place.
When a transition is enabled, we can ‘fire’ the transition. After firing,
tokens are generated as a result of resolution and are transferred to its
input/output place. It is to be noted that the value of the token at these places
is decided by the corresponding arc functions.
In the case of forward firing, the empty place is on the output side,
whereas in the case of backward firing, it must be at the input side of the
transitions.
Examples of forward and backward firing
The concept of forward and backward firing in Petri nets is illustrated below
with examples.