Basic principles of mechanical theorem proving in elementary geometrics
Journal of Automated Reasoning
Proving geometry theorems with rewrite rules
Journal of Automated Reasoning
A refutational approach to geometry theorem proving
Artificial Intelligence - Special issue on geometric reasoning
Multi-valued logic and Gröner bases with applications to modal logic
Journal of Symbolic Computation
Mechanical manipulation for a class of differential systems
Journal of Symbolic Computation
Uniform quantifier elimination and constraint query processing
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Complexity and real computation
Complexity and real computation
Complexity estimates depending on condition and round-off error
Journal of the ACM (JACM)
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
A Logical Framework for Evolution of Specifications
ESOP '94 Proceedings of the 5th European Symposium on Programming: Programming Languages and Systems
A Theory of Requirements Capture and Its Applications
TAPSOFT '93 Proceedings of the International Joint Conference CAAP/FASE on Theory and Practice of Software Development
On the Structure of Queries in Constraint Query Languages
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
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A computation model involving the computation of the limits of theory sequences is formally defined. 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 scientific and engineering problems. A syntactic transformation system is described, which can transform any algebraically closed field (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 defined 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 differential dynamical systems is described in such a way.