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

significant issues discussed in the chapter are 'backward reasoning' and
'reciprocity under bi-directional IFF' type reasoning. Backward reasoning has
been carried out with the help of a new definition of inverse fuzzy relational
matrix, Q, which when pre- or post-composed with a given relational matrix,
R, yields a matrix which is closest to the identity matrix, I, in a global sense.
The condition of reciprocity, which ensures regaining of fuzzy tokens [26] at
all places of the FPN after n-forward steps followed by n-backward steps of
reasoning (and vice versa), has been derived. Since the condition of
reciprocity imposes relationships between the structure of the FPN and its
relational matrices, determination of the matrices for a given network
topology, therefore, is a design problem. Networks whose relational matrices
support reciprocity conditions can generate tokens at all places consistently,
when the tokens of only a few terminal or non-terminal places are given. Such
networks may ideally be used for diagnostic problems, where the tokens of the
terminal places, representing measurement points, are known and the tokens
of the independent starting places, representing defects, are to be evaluated.
Another problem of interest, considered in the chapter, is the transformation
of a given primal FPN into its dual form, using the classical modus tollens
property of predicate logic. The dual FPN is useful for estimation of the
degree of precision of the negated predicates, when the degree of precision of
one or more negated predicates is known. Lastly, the principle of management
of contradiction of data and knowledge, hereafter called non-monotonic
reasoning, has been presented briefly in the chapter.
In section 10.2 of the chapter, an algorithm for formation of FPN is
presented along with an algorithm for detection of cycles in a FPN with the
help of reachability analysis. Section 10.3 is devoted to the state-space
formulation of the model and its stability analysis. Section 10.4 includes an
algorithm for forward reasoning. In section 10.5, the formulation of the
backward reasoning problem along with its solution with inverse fuzzy
relational matrix is presented. Reciprocity analysis under bi-directional IFF
type reasoning is presented in section 10.6. Details of primal to dual
transformation and its application are covered in section 10.7. The principles
of non-monotonic reasoning are presented in section 10.8. The conclusions
are summarized in section 10.9.
10.2 Structural Model of FPN and
Reachability Analysis
In this section, an algorithm for formation of FPN from a set of database and
knowledge base is presented. An analysis of reachability with special
reference to detection of cycles in a FPN is also included in this section.
Definition 10.1: A FPN is a directed bipartite graph with 9 tuples, formally
denoted by FPN = { P, D, N, Tr, t, th, I, O, Ri} where P ={p1 , ,p2 ,...., pn } is