Detecting truth, just on parts
Zolt\'an Kov\'acs, Tom\'as Recio, M. Pilar V\'elez
TL;DR
This paper presents a computational algebraic geometry method for automatically detecting propositions that are simultaneously true and false in certain instances, demonstrated through implementation in GeoGebra.
Contribution
It introduces a rigorous, algorithmic criterion for identifying contradictory propositions in dynamic geometry, advancing automated reasoning capabilities.
Findings
Effective detection of contradictory propositions demonstrated in GeoGebra
Algorithmic criterion proven to be rigorous and reliable
Potential applications in automated reasoning and geometry verification
Abstract
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.
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Taxonomy
TopicsPolynomial and algebraic computation · Constraint Satisfaction and Optimization · Logic, programming, and type systems