An Efficient Automated Geometry Reasoning Method via Knowledge Merging and Semi-Conditional Rules

This paper presents KM-SCR, a deductive-database system for automated geometry reasoning that aims to reduce redundant knowledge representation and inference overhead. First, a geometric-object merging mechanism consolidates collinear or coplanar objects and updates their associated relations, reducing redundant representations in the knowledge base. Second, a chain-of-equalities representation facilitates quantitative inference and supports algebraic reasoning through matrix-column compression and equation-system simplification. Third, semi-conditional rules divide rule-matching conditions into base conditions and remaining constraints, enabling staged candidate generation and constraint verification to reduce unnecessary matching operations. We establish the equivalence between semi-conditional rules and their original formulations at the rule-instance level and integrate the three mechanisms into an iterative reasoning workflow. Experiments on all 293 problems in FormalGeo7k-L6 show that KM-SCR solves 288 instances (98.29%), with a mean solving time of 4.06 s among successfully solved instances. On 40 sampled problems from each of levels L1–L5, the success rates range from 97.50% to 100.00%. Further analyses of theoretical inference space, actual rule instantiations, memory consumption, and solving time assess the effects of the proposed mechanisms on knowledge redundancy and inference efficiency.