2nd/10_Wiki/Topics/General Knowledge/Description-Logics.md

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

id	title	category	status	canonical_id	aliases	duplicate_of	source_trust_level	confidence_score	verification_status	tags	raw_sources	last_reinforced	github_commit	tech_stack
wiki-2026-0508-description-logics	Description Logics	10_Wiki/Topics	verified	self	P-REINFORCE-AUTO-088907 DL ALC SROIQ	none	A	0.92	applied	logic knowledge-representation ontology owl semantic-web		2026-05-10	pending	language framework python owlready2+hermit

Description Logics

매 한 줄

"매 decidable fragment of first-order logic". 매 Description Logics (DL) 은 concept (class), role (property), individual 을 formal language 로 표현하여 ontology reasoning 의 mathematical foundation. 매 OWL 2 (Web Ontology Language) 는 SROIQ(D) DL 의 syntactic dialect — 매 2026 의 Knowledge Graph + LLM grounding 의 backbone.

매 핵심

매 DL family (expressivity)

• AL (Attributive Language): atomic concept, conjunction, universal restriction.
• ALC: AL + full negation. 매 baseline.
• ALCN: ALC + cardinality.
• SHIQ: + role hierarchy, inverse role, qualified cardinality.
• SROIQ: SHIQ + role chain, self-restriction, nominal — OWL 2 DL 의 base.

매 reasoning task

• Subsumption: C ⊑ D (concept inclusion).
• Consistency: ontology 의 모순 검증.
• Instance check: a ∈ C.
• Classification: 전체 concept hierarchy 의 compute.
• Realization: 매 individual 의 most-specific class.

매 응용

1. Biomedical ontology (SNOMED CT, GO) — drug-disease reasoning.
2. Knowledge graph 의 schema validation (Wikidata, Schema.org).
3. LLM grounding — RAG 의 ontology-constrained retrieval.
4. Configuration management — feature compatibility reasoning.

💻 패턴

패턴 1: ALC concept 정의 (Owlready2)

from owlready2 import *

onto = get_ontology("http://example.org/family.owl")

with onto:
    class Person(Thing): pass
    class Parent(Person): pass
    class hasChild(Person >> Person): pass

    class Mother(Parent):
        equivalent_to = [Parent & ~onto.search(is_a=onto.Male)[0]]
        # ALC: Mother ≡ Parent ⊓ ¬Male

패턴 2: SROIQ role chain (grandparent)

with onto:
    class hasGrandchild(Person >> Person):
        # role chain: hasChild ∘ hasChild ⊑ hasGrandchild
        property_chain = [[hasChild, hasChild]]

패턴 3: Reasoner 실행 (HermiT)

from owlready2 import sync_reasoner_hermit

with onto:
    sync_reasoner_hermit(infer_property_values=True)

# inferred axioms inspect
for cls in onto.classes():
    print(cls, "⊑", cls.is_a)

패턴 4: Tableau algorithm (mini ALC)

def alc_satisfiable(concept, world=None):
    """Naive tableau for ALC C ⊓ ¬C unsatisfiability check."""
    world = world or {"individuals": {}, "constraints": []}
    if concept[0] == "AND":
        for sub in concept[1:]:
            if not alc_satisfiable(sub, world):
                return False
        return True
    if concept[0] == "NOT":
        atom = concept[1]
        if ("ATOM", atom) in world["constraints"]:
            return False  # clash
        world["constraints"].append(("NOT_ATOM", atom))
        return True
    if concept[0] == "ATOM":
        if ("NOT_ATOM", concept[1]) in world["constraints"]:
            return False
        world["constraints"].append(("ATOM", concept[1]))
        return True
    # ∃R.C, ∀R.C handled by spawning fresh individual ...

패턴 5: SPARQL over OWL inference

PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX :    <http://example.org/family#>

SELECT ?gp ?gc WHERE {
  ?gp :hasGrandchild ?gc .  # inferred via property_chain
}

패턴 6: LLM-grounded ontology query

import anthropic
from owlready2 import get_ontology

client = anthropic.Anthropic()
onto = get_ontology("./family.owl").load()

def grounded_answer(question: str) -> str:
    classes = [c.name for c in onto.classes()]
    response = client.messages.create(
        model="claude-opus-4-7-20260301",
        max_tokens=512,
        system=f"Use only these ontology classes: {classes}. Answer with class names.",
        messages=[{"role": "user", "content": question}]
    )
    return response.content[0].text

매 결정 기준

상황	Approach
Web ontology / Linked Data	OWL 2 DL (SROIQ) + Protégé
Lightweight inference	OWL 2 EL (medical) or RL (rule-based)
Real-time reasoning	RDFS + custom rules (avoid full DL)
Research / proof-of-concept	ALC + custom tableau
Fact-heavy KG (Wikidata)	SHACL validation > full DL reasoning
LLM grounding	EL/RL profile + SPARQL

기본값: OWL 2 EL (tractable PTIME) + HermiT/ELK reasoner.

🔗 Graph

• 부모: Logic · Knowledge Representation
• Adjacent: Knowledge-Graphs

🤖 LLM 활용

언제: ontology design review, axiom suggestion, SPARQL 생성, RAG 의 ontology-grounded prompt. 언제 X: 매 reasoning soundness 의 결정 — DL reasoner (HermiT, ELK) 의 영역. LLM 은 hint only.

❌ 안티패턴

• Open-world misunderstanding: 매 absent fact 가 false 라 가정 — DL 은 OWA (open world).
• Unique Name Assumption 가정: 매 individual a ≠ b 자동 아님 — differentFrom 명시 필요.
• Undecidable extension: 매 SROIQ 의 추가 expressivity (full datatype reasoning) → 결정불가.
• Reasoner 없이 inference: 매 axiom 만 작성 + 매 reasoner 미실행 → no inferred triples.

🧪 검증 / 중복

• Verified (Baader et al. "DL Handbook", W3C OWL 2 spec, Owlready2 docs).
• 신뢰도 A.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — substantive content + 2026 stack (Owlready2, HermiT, LLM grounding)