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 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. But the incompleteness theorem (as generalized by Rosser) relies on the assumption of consistency! This paper proves a generalization of the Gödel/Rosser incompleteness theorem: strongly paraconsistent 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 self-provable, every strongly paraconsistent theory in Direct Logic has an inconsistency!

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Carl Hewitt

Logical Necessity of Inconsistency

References

• Carl Hewitt (2006a) The repeated demise of logic programming and why it will be reincarnated What Went Wrong and Why: Lessons from AI Research and Applications. Technical Report SS-06-08. AAAI Press. March 2006.
• Carl Hewitt (2006b) What is Commitment? Physical, Organizational, and Social COIN@AAMAS’06.
• Carl Hewitt (2007a) What is Commitment? Physical, Organizational, and Social (Revised) Pablo Noriega .et. al. editors. LNAI 4386. Springer-Verlag. 2007.
• Carl Hewitt (2007b) Large-scale Organizational Computing requires Unstratified Paraconsistency and Reflection COIN@AAMAS’07.
• Carl Hewitt (2008a). The downfall of mental agents in the implementation of large software systems What went wrong? Special Issue on “What Went Wrong and Why” Dan Shapiro and Mehmet Göker (eds.) AAAI Magazine. Summer 2008 (to appear).
• Carl Hewitt (2008b). ORGs (Organizations of Restricted Generality): Strong Paraconsistency and Participatory Behavioral Model Checking Discussed at MALLOW’07.
• Carl Hewitt (2008c) Common sense for concurrency and strong paraconsistency using unstratified inference and reflection Discussed in seminars at Edinburgh LFCS 11th September 2007 and Stanford Logic Group 26 September 2007.
• Carl Hewitt (2008d) Large-scale Organizational Computing requires Unstratified Reflection and Strong Paraconsistency Coordination, Organizations, Institutions, and Norms in Agent Systems III. Jaime Sichman, Pablo Noriega, Julian Padget and Sascha Ossowski (ed.). Springer-Verlag