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+---
+id: wiki-2026-0508-belief-revision
+title: Belief Revision
+category: 10_Wiki/Topics
+status: verified
+canonical_id: self
+aliases: [AGM Belief Revision, Belief Update, Knowledge Revision]
+duplicate_of: none
+source_trust_level: A
+confidence_score: 0.9
+verification_status: applied
+tags: [logic, ai, knowledge-representation, philosophy, reasoning]
+raw_sources: []
+last_reinforced: 2026-05-10
+github_commit: pending
+tech_stack:
+  language: Python
+  framework: Prolog / answer-set
+---
+
+# Belief Revision
+
+## 매 한 줄
+> **"매 새로운 information 의 도입 시 의 existing belief set 의 minimal & rational adjustment"**. Alchourrón–Gärdenfors–Makinson (1985) AGM 의 axiomatization, 2026 modern application 의 LLM tool-use feedback loop, knowledge graph fact retraction, multi-agent debate.
+
+## 매 핵심
+
+### 매 3 operations (AGM)
+- **Expansion** (K + φ): new fact 의 단순 의 add — consistency 의 maintain 의 X.
+- **Contraction** (K − φ): φ 의 remove + minimal collateral 의 retract.
+- **Revision** (K * φ): φ 의 add + consistency 의 preserve (= contract ¬φ then expand φ).
+
+### 매 AGM postulates (revision)
+- (K*1) closure under logical consequence
+- (K*2) success: φ ∈ K*φ
+- (K*3,4) prior-information preservation when consistent
+- (K*5) consistency preservation
+- (K*6) extensionality
+- (K*7,8) sub-expansion / super-contraction
+
+### 매 응용
+1. LLM RAG correction — retrieved chunk 의 contradict 의 시 의 selective discount.
+2. Knowledge graph 의 fact retraction — Wikidata edit 의 propagation.
+3. Truth maintenance system — Prolog assertz/retract 의 reasoned.
+4. Multi-agent debate — counter-evidence 의 belief 의 revise.
+
+## 💻 패턴
+
+### AGM revision (epistemic entrenchment ordering)
+```python
+from dataclasses import dataclass, field
+from typing import Set, Callable
+
+@dataclass
+class BeliefBase:
+    beliefs: Set[str] = field(default_factory=set)
+    entrenchment: Callable[[str], float] = lambda b: 0.5
+    
+    def expand(self, phi: str) -> "BeliefBase":
+        return BeliefBase(self.beliefs | {phi}, self.entrenchment)
+    
+    def contract(self, phi: str) -> "BeliefBase":
+        """Remove phi + minimal beliefs needed to break entailment."""
+        if not self.entails(phi):
+            return self
+        # Levi identity: remove the least entrenched supporting set
+        candidates = self._supporting_sets(phi)
+        chosen = min(candidates, key=lambda s: sum(self.entrenchment(b) for b in s))
+        return BeliefBase(self.beliefs - chosen, self.entrenchment)
+    
+    def revise(self, phi: str) -> "BeliefBase":
+        """Levi identity: K*φ = (K − ¬φ) + φ."""
+        return self.contract(f"¬({phi})").expand(phi)
+    
+    def entails(self, phi: str) -> bool: ...
+    def _supporting_sets(self, phi: str) -> list[set[str]]: ...
+```
+
+### TMS (truth maintenance system) sketch
+```python
+class JTMS:
+    """Justification-based TMS — Doyle 1979."""
+    def __init__(self):
+        self.nodes = {}        # belief -> {in/out, justifications}
+        self.justifications = []  # (consequent, antecedents)
+    
+    def add_justification(self, consequent, antecedents):
+        self.justifications.append((consequent, antecedents))
+        self._propagate(consequent)
+    
+    def retract(self, belief):
+        self.nodes[belief] = "out"
+        for cons, ants in self.justifications:
+            if belief in ants:
+                self._propagate(cons)
+```
+
+### LLM RAG with contradiction-aware revision
+```python
+def rag_with_revision(query: str, kb, llm) -> str:
+    chunks = kb.retrieve(query, k=8)
+    contradictions = detect_contradictions(chunks)  # NLI model
+    if contradictions:
+        # Trust hierarchy: official-doc > recent > popular
+        ranked = rank_by_trust(chunks)
+        chunks = resolve(ranked, contradictions)
+    return llm.generate(query, context=chunks)
+```
+
+### Multi-agent debate revision
+```python
+class DebatingAgent:
+    def __init__(self, beliefs: BeliefBase):
+        self.kb = beliefs
+    
+    def respond(self, opponent_claim: str, evidence: list[str]) -> str:
+        # Strong evidence => revise; weak => maintain
+        strength = self._evidence_strength(evidence)
+        if strength > 0.7 and self.kb.entails(f"¬({opponent_claim})"):
+            self.kb = self.kb.revise(opponent_claim)
+            return f"Revised. Now accepting {opponent_claim}."
+        return self._counter_argument(opponent_claim)
+```
+
+### Bayesian-AGM hybrid (graded revision)
+```python
+def graded_revise(prior_prob: dict, phi: str, llh_ratio: float) -> dict:
+    """Soft AGM via Bayes-style update with belief mass."""
+    return {b: p * (llh_ratio if b == phi else 1) for b, p in prior_prob.items()}
+```
+
+## 매 결정 기준
+| 상황 | Approach |
+|---|---|
+| Crisp logical KB | AGM contract+expand |
+| Probabilistic graded belief | Bayesian update |
+| Tracked justifications | JTMS / ATMS |
+| Streaming evidence | online graded revision |
+| Defeasible reasoning | default logic / circumscription |
+
+**기본값**: knowledge graph fact handling 의 default — AGM revision + entrenchment by source trust.
+
+## 🔗 Graph
+- 부모: [[Bayes-Theorem]] · [[Bayesian-Updating]]
+- 변형: [[Inference-Coupled Persistence]]
+- 응용: [[Multi-agent-System]] · [[Knowledge-Extraction-Protocol]]
+- Adjacent: [[Hypostatic-Abstraction]] · [[Sociology of Knowledge]]
+
+## 🤖 LLM 활용
+**언제**: RAG contradiction handling, knowledge graph maintenance, multi-agent debate orchestration.
+**언제 X**: pure prediction task — full Bayesian 의 sufficient.
+
+## ❌ 안티패턴
+- **Naive overwrite**: new fact 의 blind 의 replace — collateral inconsistency 의 generate.
+- **Recency bias only**: 가장 recent = correct 의 X. trust hierarchy 의 필수.
+- **Symmetric trust**: official source 와 user note 의 same weight 의 X.
+- **Justification-free retraction**: dependent inference 의 stale 의 leave.
+
+## 🧪 검증 / 중복
+- Verified (Alchourrón, Gärdenfors, Makinson 1985 *On the Logic of Theory Change*; Hansson *A Textbook of Belief Dynamics*).
+- 신뢰도 A.
+
+## 🕓 Changelog
+| 날짜 | 변경 |
+|---|---|
+| 2026-05-08 | Phase 1 |
+| 2026-05-10 | Manual cleanup — AGM postulates, JTMS, RAG contradiction, multi-agent debate |