Large-Scale Organizational Computing Requires Unstratified Reflection and Strong Paraconsistency
Organizational Computing is a computational model for using the principles, practices, and methods of human organizations. Organizations of Restricted Generality (ORGs) have been proposed as a foundation for Organizational Computing. ORGs are the natural
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Abstract. Organizational Computing is a computational model for using the principles, practices, and methods of human organizations. Organizations of Restricted Generality (ORGs) have been proposed as a foundation for Organizational Computing. ORGs are the natural extension of Web Services, which are rapidly becoming the overwhelming standard for distributed computing and application interoperability in Organizational Computing. The thesis of this paper is that large-scale Organizational Computing requires reflection and strong paraconsistency for organizational practices, policies, and norms. Strong paraconsistency is required because the practices, policies, and norms of large-scale Organizational Computing are pervasively inconsistent. By the standard rules of logic, anything and everything can be inferred from an inconsistency, e.g., “The moon is made of green cheese.” The purpose of strongly paraconsistent logic is to develop principles of reasoning so that irrelevances cannot be inferred from the fact of inconsistency while preserving all natural inferences that do not explode in the face of inconsistency. Reflection is required in order that the practices, policies, and norms can mutually refer to each other and make inferences. Reflection and strong paraconsistency are important properties of Direct Logic [Hewitt 2007] for large software systems. Gödel first formalized and proved that it is not possible to decide all mathematical questions by inference in his 1st incompleteness theorem. However, the incompleteness theorem (as generalized by Rosser) relies on the assumption of consistency! This paper proves a generalization of the Gödel/Rosser incompleteness theorem: theories of Direct Logic are incomplete. However, there is a further consequence. Although the semi-classical mathematical fragment of Direct Logic is evidently consistent, since the Gödelian paradoxical proposition is selfprovable, every theory in Direct Logic has an inconsistency! Keywords: Co-ordination, Concurrency, Direct Logic, Inconsistency, Institutions, Mental Agents, Norms, Organizational Computing, ORGs (Organizations of Restricted Generality), Norms, Paraconsistency, Policies, Practices, Reflection.
1 Introduction Organizational Computing is the metaphor of using an organizational model for computation; i.e., computers using the principles, methods and practices of human organizations. Organizations of Restricted Generality (ORGs) have been proposed as a foundation for Organizational Computing [Hewitt and Inman 1991]. ORGs are the J.S. Sichman et al. (Eds.): COIN 2007 Workshops, LNAI 4870, pp. 110–124, 2008. © Springer-Verlag Berlin Heidelberg 2008
Large-Scale Organizational Computing Requires Unstratified Reflection
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natural extension of Web Services, which are rapidly becoming the overwhelming standard for distributed computing and application interoperability in Organizational Computing. Microsoft, IBM, Oracle, SAP, and just about every Fortune 500 company are betting on Web Services. The plan of this paper is as follows:
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