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Limits of theory sequences over algebraically closed fields and applications

✍ Scribed by Wei Li; Shilong Ma

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
306 KB
Volume
136
Category
Article
ISSN
0166-218X

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✦ Synopsis

A computation model involving the computation of the limits of theory sequences is formally deÿned. It is called procedure scheme. It provides an approach to build a new theory by the limit of some sequence of formal theories and also has potential applications to scientiÿc and engineering problems. A syntactic transformation system is described, which can transform any algebraically closed ÿeld (ALC) theory into a system of polynomial equations syntactically. The system provides a bridge to use the symbolic, algebraic computation techniques for studying the computational properties of procedure schemes. Some convergent procedure schemes are deÿned and investigated in the ALC. As applications of the framework, some procedure schemes in automated reasoning are designed, and a process of solving the center-focus problem for di erential dynamical systems is described in such a way.

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