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

Petri nets [5]. It, however, does not mean that Petri nets can be used as an
automated tool for FOL based reasoning only. In fact, Petri nets can be used
for reasoning with a rule based system or (and) can be extended to handle
uncertainties modeled with stochastic and fuzzy techniques. A separate
chapter on fuzzy Petri nets thus has been covered in the book, keeping in mind
its increasing demand in knowledge engineering. Let us now represent the
following FOL clauses by a Petri net.
FOL clauses
Rule1: Father (X,Y) Son (Y,X) ∨ Daughter (Y,X).
Rule2: Daughter (Y,X) ∧ Female (X) Mother (X,Y).
The Petri net of 8.13 describes the above rules. It is to be noted that the
variables are recorded against the arc. The argument of the valid predicate
recorded against the arc is called an arc function. The input arc functions of a
transition are positive, while the output arc functions are negative.
Reasoning: For reasoning, one has to assign the atomic clauses in the Petri
net. For instance let us assume that we are given the following clauses:
Rule3: Father (d, r)
Rule4: ¬Son (r, d)
Rule5: ¬Mother (k, l)
Rule6: Female (k)
The arguent of the above clauses along with the sign of the predicates
is assigned as tokens (inside places) in the Petri net (vide fig. 8.14). The
following rules of transition firing are then used to derive the resulting
instances.
1. A transition is enabled in the forward direction, if all its input places
and all but one of its output places possess properly signed tokens with
‘consistent variable bindings’. Consistent variable bindings are checked
by the following procedure:
i) The value of signed variables in the arc function is bound with the
signed tokens of the associated places.
ii) The above process is repeated for all the arc functions associated with
the transition.