Views, mappings and functions: Essential definitions to the conceptual graph theory
This paper introduces functions to the conceptual graph theory. To that effect, certain definitions need to be revised. For instance, the join operation and its associated definitions, vital to any conceptual-graph based system, must be redefined. In order to do so, the notions of views and mappings must be introduced. Views allow focal points to be defined over graphs. Certain operations act upon these focal points: joining two graphs u1 and u2 is originally based on compatible projections (π1 and π2 respectively) from a common generalization v. π1v and π2v are in fact focal points from which the join operation will proceed. Defining different join operations using views and mappings provide for a unique definitional framework unifying the definition of external, internal, elementary and extended join operations. Finally, in order to join graphs which may include functions, compatible projections must be replaced by functionally compatible projections. This paper formally defines these new projections.
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