Detecting truth, just on parts
This work addresses a specific issue in automated reasoning for dynamic geometry, but it appears incremental as it applies an existing mathematical approach to a new context without broad impact.
The paper tackles the problem of automatically detecting propositions that are simultaneously true and false across different instances, presenting an algorithmic criterion based on computational algebraic geometry and demonstrating its implementation in GeoGebra.
We introduce and discuss, through a computational algebraic geometry approach, the automatic reasoning handling of propositions that are simultaneously true and false over some relevant collections of instances. A rigorous, algorithmic criterion is presented for detecting such cases, and its performance is exemplified through the implementation of this test on the dynamic geometry program GeoGebra.