### RELATIONAL SCIENCE: A SYNTHESIS

*John Kineman*

#### Abstract

This paper proposes a synthesis of two avenues of development of relational complexity theory that have followed the work of Robert Rosen (1934-1998). These avenues are: (1) further development of Rosen’s causal entailment in category theory (Rosen 1978 Rosen 1985 Rosen 1991 Rosen 1999 Louie 2009); and (2) contextual entailment based on Rosen’s modeling relation (Rosen 1985 Rosen 1991 Rosen 1999 Kineman 2007 Kineman 2008 Kineman Banathy and Rosen 2007 Kineman and Kumar 2007). These two tracks represent different theory structures that have not been fully integrated to date. Category theory describes causes in terms of entailments expressed as mappings between sets of a domain and co-domain. Modeling relations describe a complementarity between descriptive and, as argued here, prescriptive potentials of a system and their natural realizations; mediated by information relations. The synthesis presented here combines these two theory tracks to bring their mathematical and graphical systems of analysis into correspondence with each other and with a natural interpretation of causality. Such a synthesis requires asking if the current causal mapping algebra is sufficiently comprehensive to describe natural modeling relations, or alternatively, if the application of modeling relations as a fundamental analysis of nature requires additional algebraic elements.

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