Geometric Embedding for Knowledge Graph Rule Induction

The patent introduces Venn diagrams and Carroll's diagrams as intermediary representations that bridge geometric embeddings and logical rules. These diagrams serve as mediators that translate continuous geometric data into discrete logical structures, enabling existential rule capture without directly manipulating complex geometric data. The diagrams act as an intermediate layer that simplifies the reasoning process while preserving the semantic relationships embedded in the geometric representations.

The patent replaces traditional symbolic logic manipulation with geometric reasoning operations. Instead of manually constructing logical rules from symbolic representations, the system uses geometric transformations and spatial relationships to automatically derive existential rules. This substitution of mechanical symbolic manipulation with geometric computation simplifies the overall process while improving the ability to capture existential dependencies.

The patent implements a self-service mechanism where the system automatically generates logical rules from geometric embeddings without requiring manual intervention. The geometric representations inherently encode the logical relationships, and the system autonomously extracts existential rules by analyzing spatial relationships and transformations. This self-service approach maintains rule precision while dramatically improving productivity by eliminating manual rule writing.

The patent performs preliminary encoding of logical relationships during the knowledge graph construction phase by using geometric embeddings that inherently capture existential dependencies. By pre-encoding the logical structure in the geometric representation, the system eliminates the need for subsequent manual rule writing, as the rules can be directly extracted from the embedded geometric data through automated analysis.