{
  "abstract": "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.",
  "abstract_shown": true,
  "affiliations": [
    "Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China",
    "Guangzhou University of Software, Guangzhou 510990, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Qixin Zhou",
      "orcid": "0009-0000-2470-5871"
    },
    {
      "affs": [
        0
      ],
      "name": "Siran Lei"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Ying Wang"
    },
    {
      "affs": [
        0
      ],
      "name": "Hao Guan",
      "orcid": "0000-0002-7859-5409"
    },
    {
      "affs": [
        0
      ],
      "name": "Yongsheng Rao",
      "orcid": "0000-0001-9615-3658"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/15yvc36j53gfr.bib",
  "cited_by": 0,
  "doi": "10.3390/math14214038",
  "fulltext_url": null,
  "id": "15yvc36j53gfr",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/4038",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/15yvc36j53gfr.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T00:20:49Z",
      "native_id": "10.3390/math14214038",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/4038"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "An Efficient Automated Geometry Reasoning Method via Knowledge Merging and Semi-Conditional Rules",
  "title_text": "An Efficient Automated Geometry Reasoning Method via Knowledge Merging and Semi-Conditional Rules",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T00:21:06Z",
  "url": "https://research.draconitic.com/paper/15yvc36j53gfr",
  "venue": "Mathematics",
  "versions": []
}