---
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 |