Date: 03 Mar 2000

Thinking in Cycles

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Abstract

A new axiomization of the intuitive concept of partial cyclic orders is proposed and the appropriateness is motivated from pragmatic as well as mathematical perspectives. There is a close relation to Petri net theory since the set of basic circuits of a safe and live synchronization graph naturally gives rise to a cyclic order. As a consequence cyclic orders provide a simple technique for safety-oriented specification where safety (in the sense of net theory) is achieved by relying on the fundamental concept of cyclic causality constraints avoiding the risk of an immediate and directed causality relation. From a foundational point of view cyclic orders provide a basis for a theory of nonsequential cyclic processes and new insights into C.A.Petri’s concurrency theory. By the slogan measurement as control cyclic orders can serve as a tool for the construction of cyclic measurement scales, spatial and temporal knowledge representation and reasoning being only some applications. New results in this article include a characterization of global orientability (implementability) by weak F-density (the existence of a true cut).