Title: Extension of logical structures by safe extension of specialisation systems

Authors: Kiyoshi Akama, Ekawit Nantajeewarawat

Addresses: Division of Large-Scale Computational Systems, Information Initiative Center, Hokkaido University, Sapporo, Hokkaido 060-0811, Japan. ' Computer Science Program, Sirindhorn International Institute of Technology, Thammasat University, Rangsit Campus, Pathumthani 12121, Thailand

Abstract: A specialisation system provides an axiomatic structure for studying the common interrelations between various forms of extended atomic formulas and specialisation operations on them. We show how to generate a logical structure from a specialisation system and introduce the concept of safe extension of a logical structure as a process of extending the space of logical formulas while preserving their logical meanings. We establish a sufficient condition for safe extension of a logical structure based on safe extension of its underlying specialisation system. Under this condition, a logical structure generated from a safe extension of a specialisation system is always a safe extension of that generated directly from the source specialisation system. The work extends a foundation for developing a computation theory based on the equivalent transformation principle.

Keywords: logical structures; specialisation systems; knowledge representation; equivalent transformation; extended atomic formulas; common interrelations; atoms; substitutions.

DOI: 10.1504/IJAAC.2008.022185

International Journal of Automation and Control, 2008 Vol.2 No.2/3, pp.340 - 364

Published online: 22 Dec 2008 *

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