Introduction to Dialectical Nets

Abstract: This paper initiates the dialectical approach to net theory. This approach views nets as special, but very important and natural, dialectical systems. By following this approach, a suitably generalized version of nets, called dialectical nets, can be defined in terms of the "fundamental contradiction" inherent in the structure of closed preorders. Dialectical nets are the least conceptual upper bound subsuming the notions of Petri nets, Kan quantification and transition systems. The nature of dialectical nets is that of logical dynamics, and is succinctly defined and summarized in the statement that "dialectical nets are transition systems relativized to closed preorders, and hence are general predicate transformers".