2nd/10_Wiki/Topics/AI_and_ML/Beliefs.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-beliefs	Beliefs	10_Wiki/Topics	verified	self	신념 belief revision Bayesian belief knowledge confirmation bias doxastic logic	none	B	0.85	applied	epistemology beliefs knowledge bayesian confirmation-bias ai-belief doxastic-logic		2026-05-10	pending	language applicable_to epistemology / cognitive science Agent Beliefs RAG Trust Bias Mitigation

Beliefs

📌 한 줄 통찰

"매 mind 의 잠정적 결론". 매 evidence 의 objective ↔ subjective 의 confidence. 매 action 의 trigger. 매 AI 의 응용 — 매 agent 의 belief state, 매 RAG 의 trust scoring, 매 confirmation bias 의 detect.

📖 핵심

매 정의 (philosophical)

• Belief: 매 proposition 의 true 의 mental acceptance.
• Knowledge: 매 Justified True Belief (Plato).
• Gettier problem: JTB 가 X 의 case (Gettier 1963).
• → 매 knowledge 의 stricter (no luck / safety / sensitivity).

매 belief 의 type

1. Occurrent: 매 active conscious thought.
2. Dispositional: 매 stored, 매 retrieve 매 ready.
3. De dicto vs de re: 매 about-words vs about-thing.
4. Implicit / explicit: 매 articulate-able.

매 belief revision (AGM)

• Expansion: 매 add (no conflict).
• Contraction: 매 remove.
• Revision: 매 add + remove 매 conflicting.
• Postulates: 매 closure, success, consistency, ...

Bayesian belief

• 매 belief = 매 probability (degree of confidence).
• 매 update via Bayes (Cox theorem).
• 매 coherent.
• 매 modern AI 의 standard.

매 cognitive bias (belief 관련)

1. Confirmation bias: 매 belief 의 confirm 의 selective.
2. Belief perseverance: 매 disconfirming evidence 후 의 retain.
3. Backfire effect: 매 disconfirming evidence 의 strengthen.
4. Sunk cost: 매 commitment 의 belief 의 maintain.
5. Motivated reasoning: 매 want 의 believe.

매 AI / agent 의 응용

Belief state (POMDP)

• 매 partially observable.
• 매 belief = 매 distribution over state.
• 매 action 의 belief 의 update.

RAG trust score

• 매 retrieved document 의 belief.
• 매 confidence = recency × authority × consistency.

Multi-agent BDI (Belief-Desire-Intention)

• 매 belief: world state.
• 매 desire: goal.
• 매 intention: committed plan.
• 매 PRS, JADE.

LLM 의 belief

• 매 train 의 belief 의 instillation.
• 매 RLHF 의 alignment.
• 매 calibration: 매 P(true) 의 actual frequency.

매 epistemic logic

• 매 K_a φ: 매 agent a 의 knows φ.
• 매 B_a φ: 매 belief.
• 매 multi-agent: 매 common knowledge.
• 매 Aumann's agreement theorem: 매 rational 의 동의.

💻 패턴 (응용)

Bayesian belief update

def update_belief(prior, likelihood_true, likelihood_false, evidence):
    # P(H | E) = P(E | H) * P(H) / P(E)
    posterior_unnorm = likelihood_true * prior
    evidence_prob = likelihood_true * prior + likelihood_false * (1 - prior)
    return posterior_unnorm / evidence_prob

belief = 0.3  # 매 prior
belief = update_belief(belief, 0.9, 0.2, evidence=True)  # 매 0.66
belief = update_belief(belief, 0.9, 0.2, evidence=True)  # 매 0.90

POMDP belief state

class POMDPBelief:
    def __init__(self, n_states, prior):
        self.belief = prior  # np.array, sum=1
    
    def update(self, action, observation, T, O):
        # T: transition matrix, O: observation matrix
        new_belief = np.zeros_like(self.belief)
        for s_next in range(len(self.belief)):
            new_belief[s_next] = O[s_next, observation] * \
                sum(T[s, s_next, action] * self.belief[s] for s in range(len(self.belief)))
        new_belief /= new_belief.sum()
        self.belief = new_belief

BDI agent

class BDIAgent:
    def __init__(self):
        self.beliefs = {}     # 매 facts about world
        self.desires = []     # 매 goals
        self.intentions = []  # 매 active plans
    
    def perceive(self, observations):
        for obs in observations:
            self.beliefs[obs.key] = obs.value
    
    def deliberate(self):
        # 매 desire selection based on belief
        feasible = [d for d in self.desires if self.is_feasible(d)]
        return max(feasible, key=lambda d: d.priority)
    
    def plan(self, goal):
        # 매 belief 기반 의 plan
        return planner.plan(self.beliefs, goal)
    
    def execute(self):
        if not self.intentions:
            goal = self.deliberate()
            self.intentions = self.plan(goal)
        action = self.intentions.pop(0)
        return action

LLM calibration

def calibration_check(model, eval_set):
    # 매 P(true) 의 declared confidence vs actual
    bins = [(0, 0.1), (0.1, 0.2), ..., (0.9, 1.0)]
    bin_correct = {b: [] for b in bins}
    
    for example in eval_set:
        response = model.generate(example.prompt + ' Reply with answer and confidence (0-1).')
        ans, conf = parse(response)
        actual = (ans == example.expected)
        for b in bins:
            if b[0] <= conf < b[1]:
                bin_correct[b].append(actual)
                break
    
    # 매 ECE (Expected Calibration Error)
    ece = sum(abs(np.mean(corr) - (b[0]+b[1])/2) * len(corr) / len(eval_set)
              for b, corr in bin_correct.items() if corr)
    return ece

→ 매 well-calibrated = ECE 낮음.

Confirmation bias detector

def detect_confirmation_bias(query, results, user_belief):
    # 매 user 의 belief 의 align 의 source 만 의 click?
    aligning = [r for r in results if r.aligns_with(user_belief)]
    clicked_aligning = sum(1 for r in aligning if r.clicked)
    clicked_total = sum(1 for r in results if r.clicked)
    
    if clicked_total == 0: return None
    bias_ratio = clicked_aligning / clicked_total
    return bias_ratio  # 매 > 0.7 = 매 strong confirmation bias

🤔 결정 기준

응용	Approach
Agent world model	POMDP belief
RAG trust	Source authority + consistency
Multi-agent	BDI
LLM calibration	ECE + temperature scaling
User UX	Diverse perspective + bias detect
Knowledge graph	Justified belief (provenance)

기본값: Bayesian belief + ECE calibration + diverse evidence.

🔗 Graph

• 부모: Epistemology · Cognitive-Science
• 변형: Knowledge · Justified-True-Belief · Bayesian-Belief · Doxastic-Logic
• 응용: POMDP · BDI-Agent · LLM-Calibration · RAG-Trust
• 비판: Confirmation-Bias · Belief-Perseverance · Motivated-Reasoning · Gettier-Problem
• Adjacent: Bayesian-Brain-Hypothesis · Multi-Agent-Systems · Aumann-Theorem

🤖 LLM 활용

언제: 매 agent design (belief state). 매 RAG trust scoring. 매 LLM calibration eval. 매 bias detection. 언제 X: 매 metaphysical claim 의 substitute. 매 single belief 의 deterministic system.

❌ 안티패턴

• Belief 의 binary: 매 confidence 의 lose.
• No update: 매 stale belief.
• Confirmation bias 의 ignore: 매 echo chamber.
• Calibration 무시: 매 over-confident model.
• Multiple agent 의 belief 의 share assumption: 매 multi-agent fail.
• Belief 의 hard-code: 매 update 의 X.

🧪 검증 / 중복

• Verified (Plato JTB, Gettier, AGM postulates, Bayesian).
• 신뢰도 B.
• Related: Bayesian-Statistics · Bayesian-Brain-Hypothesis · Confirmation-Bias · POMDP.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — JTB + AGM + Bayesian + POMDP / BDI + 매 calibration code