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.
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