What is a structural representation? A proposal for an event-based representational formalism: Sixth Variation

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We outline a formalism for structural, or symbolic, representation, the necessity of which has been acutely felt not just in artificial intelligence and pattern recognition, but also in the natural sciences, particularly biology. At the same time, biology has been gradually edging to the forefront of sciences, although the reasons obviously have nothing to do with its state of formalization or maturity. Rather, the reasons have to do with the growing realization that the objects of biology are not only more important (to society) and interesting (to science), but that they also more explicitly exhibit the evolving nature of all objects in the Universe. It is this view of objects as evolving structural entities/processes that we aim to formally address here, in contrast to theubiquitous mathematical view of objects as points in some abstract space. In light of the above, the paper is addressed to a very broad group of scientists. One can gain an initial intuitive understanding of the proposed representation by generalizing the temporal process of the (Peano) construction of natural numbers: replace the single structureless unit out of which a number is built by multiple structural ones. An immediate and important consequence of the distinguishability (or multiplicity) of units in the construction process is that we can now see which unit was attached and when. Hence, the resulting (object) representation for the first time embodies temporal structural information in the form of a formative, or generative, object “history” recorded as a series of (structured) events. Each such event stands for a “standard” interaction of several objects/processes. We introduce the new concept of class representation via the concept of class generating system, which outputs structural entities belonging to that class. Hence, the concept of class is introduced as that of a class of similar structural entities, where the “similarity” of such entities is ensured by them being outputs of the same class generating system and hence having similar formative histories. In particular, such a concept of class representation implies that—in contrast to all existing formalisms—no two classes have elements in common. The evolving transformation system (ETS) formalism proposed here is the first one developed to support such a new vision of classes. Most important, since the operations that participated in the object’s construction are, for the first time, made explicit in the representation, it makes the inductive recovery of class representation (on the basis of object representation) much more reliable. As a result, ETS offers a formalism that outlines, for the first time, a tentative framework for understanding what a class is. Even this tentative framework makes it quite clear that the term “class” has been improperly understood, used, and applied: many, if not most, of the current “classes” should not be viewed as such. A detailed example of a class representation is included. In light of ETS, the classical discrete “representations” (strings, graphs) appear as incomplete special cases at best, the proper adaptation of which should incorporate corresponding formative histories, as is done here. The gradual emergence of ETS—including the concepts of structural object and class representations, the resulting radically different (temporal) view of “data”, as well as the associated inductive learning processes and the representational levels—points to the beginning of a new field, inductive informatics, which is intended as a class oriented rival to conventional information processing paradigms.