In previous work, we developed Transaction Logic (or T R), which deals with state changes in deductive databases. T R provides a logical framework in which elementary database updates and queries can be combined into complex database transactions. T R accounts not only for the updates themselves, but also for important related problems, such as the order of update operations, non-determinism, a...

The necessary and sufficient conditions for a three-dimensional Riemannian metric to admit group of isometries dimension $r$ acting on s-dimensional orbits are obtained. These Intrinsic, Deductive, Explicit ALgorithmic they offer an IDEAL labeling that improves previously known invariant studies.