You are a reasoning expert skilled in formal logic and semiotic analysis.Your task is to analyze a **complex logical proposition** from the RepublicQA dataset using the **Greimas Semiotic Square**. This framework decomposes a proposition into four logically interrelated positions: the original statement (S1), its semantic contrary (S2), and their respective logical negations (¬S1, ¬S2).

## Core Proposition Extraction

When analyzing the input question, first extract the core proposition:
- **Most importantly** If the question asks "Is the statement 'X' correct/true?", extract X as the core proposition **S1**
- If the question contains quoted text, use the quoted content as the core proposition
- **For nested quotes**: Extract only the innermost quoted statement
- Preserve the original wording exactly - do not add qualifiers or conditions
- Pay special attention to absolute claims (e.g., "always", "never", "all", "is defined as")
- **Maintain the logical structure**: If the original contains "X is always Y", keep the "always" in S1

## Context-Based Reasoning Priority

Before determining concept opposition, analyze the context to understand:
- What premises support or challenge the core proposition
- What logical tensions exist in the given context
- How the context frames the philosophical problem

## Concept Opposition Guidance

When extracting opposing concepts (A vs B), prioritize the following types of semantic opposition based on the context:

### 1. **Authority vs Independent Judgment** (HIGHEST PRIORITY for governance/obedience statements)
- obedience_to_authority vs moral_independent_judgment
- formal_compliance vs substantive_ethics
- rule_following vs principle_based_reasoning

### 2. **Absolutist vs Contextual** (HIGH PRIORITY for "always" statements)
- universal_application vs contextual_consideration
- absolute_rule vs situational_ethics
- invariant_principle vs circumstantial_judgment

### 3. **Moral Opposition**
- just vs unjust, good vs evil, right vs wrong
- virtuous vs vicious, moral vs immoral
- beneficial vs harmful

### 4. **Behavioral Opposition**
- help vs harm, benefit vs hurt, protect vs attack
- support vs oppose, assist vs hinder

### 5. **Relational Opposition**
- friend vs enemy, ally vs opponent
- insider vs outsider, member vs non-member

### 6. **Factual Opposition**
- truth vs lie, real vs virtual
- true vs false, right vs wrong

### Selection Priority
For statements involving justice, morality, or ethics:
- ✅ **Strong opposition**: benefiting vs harming, helping vs hurting, just vs unjust
- ❌ **Weak opposition**: interest of stronger vs interest of weaker
If no moral, relational, or behavioral opposition applies, use factual oppositions (e.g., true vs false).
Your task is to analyze a **complex logical proposition** from the RepublicQA dataset using the **Greimas Semiotic Square**. This framework decomposes a proposition into four logically interrelated positions: the original statement (S1), its semantic contrary (S2), and their respective logical negations (¬S1, ¬S2).
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Step 1 – Identify the core proposition

- **S1** must be **identical in wording and logic** to the original question statement.
- **S2** should be a **semantic contrary** to S1 — i.e., a proposition that **cannot be true at the same time** as S1, but **can be false simultaneously**.
- ⚠️ **Important**: Only when no meaningful contrary can be identified, use the **logical negation** of S1 as S2 (i.e., contradiction), and set `"S2_type": "contradictory"`.
- Use existing entities and predicates from the context — do **not** invent new ones.

- S2_type determination checklist:
    - If S1 and S2 **cannot be true simultaneously** but **can be false together** → `contrary`
    - If S2 is **exact logical negation** of S1 → `contradictory`

- ¬S1 and ¬S2 are strict logical negations of S1 and S2 respectively.

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Step 2 – Build the Semiotic Square

Define the four positions as follows:

- **S1**: Original target proposition → FOL: (as close to formal logic as possible)
- **S2**: Semantic contrary to S1 (or contradiction if contrary is not available)
- **¬S1**: Logical negation of S1
- **¬S2**: Logical negation of S2

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Required Semantic Relationships:

- S1 ⊥ S2   S1 and S2 are **semantic contraries**, not mere negations (if available)
- S1 ⇒ ¬S2  and S2 ⇒ ¬S1
- ¬S1 ∪ ¬S2  covers the full semantic space

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## First-Order Logic Grammar:

The following grammar rules define the valid syntax for FOL expressions:

1. **Conjunction** (and): `expr1 ∧ expr2`
2. **Disjunction** (inclusive or): `expr1 ∨ expr2`
3. **Exclusive Disjunction** (xor): `expr1 ⊕ expr2`
4. **Negation** (not): `¬expr1`
5. **Implication** (if ... then): `expr1 → expr2`
6. **Biconditional** (if and only if): `expr1 ↔ expr2`
7. **Universal Quantifier** (for all x): `∀x (...)`
8. **Existential Quantifier** (there exists x): `∃x (...)`

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Below is an example:

Question: Is the statement "repaying a dept is always just" correct?

- concept_A: just
- concept_B: unjust

- S1  
  Statement: Repayment of debt is always just.  
  FOL: ∀x (Debt(x) ∧ Repaid(x) → Just(x))

- S2 
  Statement: Repaying depts to mentally incapacitated individuals is unjust.  
  FOL: ∀x (Deposit(x) ∧ MentallyIncapacitated(x) → ¬Just(Return(x)))

- ¬S1  
  Statement: Repayment of debt is not always just.  
  FOL: ∃x (Debt(x) ∧ Repaid(x) ∧ ¬Just(x))

- ¬S2  
  Statement: Returning depts to mentally incapacitated individuals is just.  
  FOL: ∃x (Dept(x) ∧ MentallyIncapacitated(x) ∧ Just(Return(x)))
"S2_type": "contrary"

Below is another example.

Question: Is the statement "repaying a dept is always just" correct?

- concept_A: just
- concept_B: unjust

- S1 
  Statement: Repayment of debt is always just.  
  FOL: ∀x (Debt(x) ∧ Repaid(x) → Just(x))

- S2  
  Statement: Repayment of debt is not always just. 
  FOL: ∃x (Debt(x) ∧ Repaid(x) ∧ ¬Just(x))

- ¬S1  
  Statement: Repayment of debt is not always just.  
  FOL: ∃x (Debt(x) ∧ Repaid(x) ∧ ¬Just(x))

- ¬S2  
  Statement: Repayment of dept is always just.  
  FOL: ∀x (Debt(x) ∧ Repaid(x) → Just(x))
"S2_type": "contradictory"

Below is another example.

Question: Is the statement "Justice is always the interest of the stronger" correct?

- concept_A: stronger
- concept_B: weaker

- S1  
  Statement: Justice is always the interest of the stronger.  
  FOL: ∀x (Justice(x) → InterestOfStronger(x))

- S2  
  Statement: Justice is always the interest of the weaker.  
  FOL: ∀x (Justice(x) → InterestOfWeaker(x))

- ¬S1  
  Statement: Justice is not always the interest of the stronger.  
  FOL: ∃x (Justice(x) ∧ ¬InterestOfStronger(x))

- ¬S2  
  Statement: Justice is not always the interest of the weaker.  
  FOL: ∃x (Justice(x) ∧ ¬InterestOfWeaker(x))

S2_type: contrary

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Now analyze the following statement using this framework.

Context:
{context}

Question:
{question}

Return your answer strictly in the format below.  
⚠️ Do **not** return anything outside this block — no markdown, no LaTeX, no extra commentary.
```json
{{
  "concept_A": "...",
  "concept_B": "...",
  "S1": {{
    "statement": "...",
    "FOL": "..."
  }},
  "S2": {{
    "statement": "...",
    "FOL": "..."
  }},
  "not_S1": {{
    "statement": "...",
    "FOL": "..."
  }},
  "not_S2": {{
    "statement": "...",
    "FOL": "..."
  }}
  "S2_type": "contrary" | "contradictory"
}}
```
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Always remember to output the type of s2!Based on the truth you should output the correct type.