"""Logical operators — elemental reasoning primitives. Tests the model's capacity for basic logical operations in text form: - negation: Verify whether a candidate is a correct logical negation - conjunction: Evaluate conjunction/disjunction statements from text facts - conditional: Decide whether a conclusion follows from a rule + fact These are building blocks for reasoning-heavy benchmarks. Format (ICL): Input: [text logic problem] Output: True or False (varies by category — see demos) """ import random from typing import Dict, List, Any from tasks.base_task import BaseTask, TaskConfig class LogicalOpsTask(BaseTask): """Elemental logical-operators task.""" TASK_NAME = "logical_ops" CATEGORY_DATA: Dict[str, List[Dict[str, str]]] = { "negation": [ {"input": "Statement: All robots can move.\nCandidate negation: Some robots cannot move.\nIs the candidate a correct logical negation?", "output": "True"}, {"input": "Statement: All apples are red.\nCandidate negation: No apples are red.\nIs the candidate a correct logical negation?", "output": "False"}, {"input": "Statement: Some birds can swim.\nCandidate negation: No birds can swim.\nIs the candidate a correct logical negation?", "output": "True"}, {"input": "Statement: Some books are heavy.\nCandidate negation: Some books are not heavy.\nIs the candidate a correct logical negation?", "output": "False"}, {"input": "Statement: The lamp is on.\nCandidate negation: The lamp is not on.\nIs the candidate a correct logical negation?", "output": "True"}, {"input": "Statement: The lamp is on.\nCandidate negation: The lamp is off and broken.\nIs the candidate a correct logical negation?", "output": "False"}, {"input": "Statement: Everyone passed the test.\nCandidate negation: Not everyone passed the test.\nIs the candidate a correct logical negation?", "output": "True"}, {"input": "Statement: Everyone passed the test.\nCandidate negation: No one passed the test.\nIs the candidate a correct logical negation?", "output": "False"}, {"input": "Statement: No cars are electric.\nCandidate negation: Some cars are electric.\nIs the candidate a correct logical negation?", "output": "True"}, {"input": "Statement: No cars are electric.\nCandidate negation: All cars are electric.\nIs the candidate a correct logical negation?", "output": "False"}, {"input": "Statement: The gate is closed.\nCandidate negation: The gate is open.\nIs the candidate a correct logical negation?", "output": "False"}, {"input": "Statement: The gate is closed.\nCandidate negation: The gate is not closed.\nIs the candidate a correct logical negation?", "output": "True"}, ], "conjunction": [ {"input": "Fact A is True. Fact B is True.\nClaim: A AND B.\nIs the claim true?", "output": "True"}, {"input": "Fact A is True. Fact B is False.\nClaim: A AND B.\nIs the claim true?", "output": "False"}, {"input": "Fact A is False. Fact B is True.\nClaim: A OR B.\nIs the claim true?", "output": "True"}, {"input": "Fact A is False. Fact B is False.\nClaim: A OR B.\nIs the claim true?", "output": "False"}, {"input": "Fact A is True. Fact B is False.\nClaim: NOT B.\nIs the claim true?", "output": "True"}, {"input": "Fact A is True. Fact B is False.\nClaim: NOT A.\nIs the claim true?", "output": "False"}, {"input": "Fact A is True. Fact B is True. Fact C is False.\nClaim: A AND B AND C.\nIs the claim true?", "output": "False"}, {"input": "Fact A is True. Fact B is True. Fact C is False.\nClaim: A AND (B OR C).\nIs the claim true?", "output": "True"}, {"input": "Fact A is False. Fact B is False. Fact C is True.\nClaim: (A OR B) AND C.\nIs the claim true?", "output": "False"}, {"input": "Fact A is False. Fact B is False. Fact C is True.\nClaim: A OR (B OR C).\nIs the claim true?", "output": "True"}, {"input": "Fact A is True. Fact B is False.\nClaim: (A AND B) OR A.\nIs the claim true?", "output": "True"}, {"input": "Fact A is True. Fact B is False.\nClaim: (A OR B) AND B.\nIs the claim true?", "output": "False"}, ], "conditional": [ {"input": 'Rule: If it rains, the ground gets wet.\nFact: It rains.\nConclusion: The ground gets wet.\nDoes the conclusion logically follow?', "output": "True"}, {"input": 'Rule: If it rains, the ground gets wet.\nFact: It does not rain.\nConclusion: The ground gets wet.\nDoes the conclusion logically follow?', "output": "False"}, {"input": 'Rule: If the switch is on, the lamp lights up.\nFact: The switch is on.\nConclusion: The lamp lights up.\nDoes the conclusion logically follow?', "output": "True"}, {"input": 'Rule: If the switch is on, the lamp lights up.\nFact: The lamp lights up.\nConclusion: The switch is on.\nDoes the conclusion logically follow?', "output": "False"}, {"input": 'Rule: If a number is even, it is divisible by 2.\nFact: 14 is even.\nConclusion: 14 is divisible by 2.\nDoes the conclusion logically follow?', "output": "True"}, {"input": 'Rule: If a number is even, it is divisible by 2.\nFact: 15 is not even.\nConclusion: 15 is not divisible by 2.\nDoes the conclusion logically follow?', "output": "False"}, {"input": 'Rule: If a file is deleted, it is unavailable.\nFact: The file is deleted.\nConclusion: The file is unavailable.\nDoes the conclusion logically follow?', "output": "True"}, {"input": 'Rule: If a file is deleted, it is unavailable.\nFact: The file is unavailable.\nConclusion: The file is deleted.\nDoes the conclusion logically follow?', "output": "False"}, {"input": 'Rule: If a student studies, they pass this quiz.\nFact: Mina studies.\nConclusion: Mina passes this quiz.\nDoes the conclusion logically follow?', "output": "True"}, {"input": 'Rule: If a student studies, they pass this quiz.\nFact: Leo does not pass this quiz.\nConclusion: Leo did not study.\nDoes the conclusion logically follow?', "output": "False"}, {"input": 'Rule: If the alarm rings, everyone evacuates.\nFact: The alarm rings.\nConclusion: Everyone evacuates.\nDoes the conclusion logically follow?', "output": "True"}, {"input": 'Rule: If the alarm rings, everyone evacuates.\nFact: Everyone evacuates.\nConclusion: The alarm rings.\nDoes the conclusion logically follow?', "output": "False"}, ], } CATEGORY_DEMOS: Dict[str, List[str]] = { "negation": [ "Input: Statement: All chairs are wooden.\nCandidate negation: Some chairs are not wooden.\nIs the candidate a correct logical negation?\nOutput: True", "Input: Statement: Some cups are clean.\nCandidate negation: No cups are clean.\nIs the candidate a correct logical negation?\nOutput: True", "Input: Statement: The window is open.\nCandidate negation: The window is not open.\nIs the candidate a correct logical negation?\nOutput: True", "Input: Statement: Everyone arrived early.\nCandidate negation: No one arrived early.\nIs the candidate a correct logical negation?\nOutput: False", "Input: Statement: The road is clear.\nCandidate negation: The road is blocked.\nIs the candidate a correct logical negation?\nOutput: False", ], "conjunction": [ "Input: Fact A is True. Fact B is True.\nClaim: A AND B.\nIs the claim true?\nOutput: True", "Input: Fact A is True. Fact B is False.\nClaim: A AND B.\nIs the claim true?\nOutput: False", "Input: Fact A is False. Fact B is True.\nClaim: A OR B.\nIs the claim true?\nOutput: True", "Input: Fact A is True. Fact B is False.\nClaim: NOT B.\nIs the claim true?\nOutput: True", "Input: Fact A is False. Fact B is False.\nClaim: A OR B.\nIs the claim true?\nOutput: False", ], "conditional": [ "Input: Rule: If the bell rings, class starts.\nFact: The bell rings.\nConclusion: Class starts.\nDoes the conclusion logically follow?\nOutput: True", "Input: Rule: If traffic is heavy, travel time increases.\nFact: Travel time increased.\nConclusion: Traffic was heavy.\nDoes the conclusion logically follow?\nOutput: False", "Input: Rule: If the key fits, the lock opens.\nFact: The key fits.\nConclusion: The lock opens.\nDoes the conclusion logically follow?\nOutput: True", "Input: Rule: If a file is saved, it can be reopened.\nFact: The file can be reopened.\nConclusion: The file was saved.\nDoes the conclusion logically follow?\nOutput: False", "Input: Rule: If the sensor triggers, the alarm sounds.\nFact: The sensor triggers.\nConclusion: The alarm sounds.\nDoes the conclusion logically follow?\nOutput: True", ], } def __init__(self, config: TaskConfig): super().__init__(config) def _load_data(self): import pandas as pd if self.config.in_memory_data: self.data = pd.DataFrame(self.config.in_memory_data) return rows: List[Dict[str, str]] = [] for category, examples in self.CATEGORY_DATA.items(): for ex in examples: rows.append({ "input": ex["input"], "output": ex["output"], "category_name": category, }) self.data = pd.DataFrame(rows) def build_prompt(self, instance: Dict[str, Any], num_shots: int = 5) -> str: category = instance.get("category_name", "negation") demos = self.CATEGORY_DEMOS.get(category, []) inst_input = instance.get("input", "") demos = [d for d in demos if inst_input not in d][:num_shots] prompt = "" for d in demos: prompt += d + "\n\n" if category == "conditional": prompt += f"Input: {inst_input}\nOutput:" else: prompt += f"Input: {inst_input}\nOutput:" return prompt def evaluate(self, predictions: List[str], split: str = "test", **kwargs) -> Dict[str, float]: ground_truth = self.get_ground_truth(split) task_data = self.get_split(split) if len(predictions) != len(ground_truth): raise ValueError( f"Prediction count ({len(predictions)}) != ground truth ({len(ground_truth)})" ) processed = [self.preprocess_prediction(p) for p in predictions] correct = sum( 1 for p, g in zip(processed, ground_truth) if p.lower().strip() == g.lower().strip() ) results: Dict[str, Any] = { "accuracy": correct / len(ground_truth), "correct": correct, "total": len(ground_truth), } cat_stats: Dict[str, Dict[str, int]] = {} for p, g, item in zip(processed, ground_truth, task_data): cat = item.get("category_name", "unknown") cat_stats.setdefault(cat, {"correct": 0, "total": 0}) cat_stats[cat]["total"] += 1 if p.lower().strip() == g.lower().strip(): cat_stats[cat]["correct"] += 1 for cat, s in cat_stats.items(): results[f"accuracy_{cat}"] = s["correct"] / s["total"] return results def get_ground_truth(self, split: str = "test") -> List[str]: rows = self.get_split(split) return [str(r.get("output", "")) for r in rows] def create_logical_ops_task( category: str = None, name: str = "logical_ops", ) -> LogicalOpsTask: """Create a LogicalOpsTask, optionally filtered to one category.""" data = None if category and category in LogicalOpsTask.CATEGORY_DATA: data = [ {**ex, "category_name": category} for ex in LogicalOpsTask.CATEGORY_DATA[category] ] name = f"logical_ops:{category}" config = TaskConfig( name=name, description="Logical operators (negation, conjunction, conditional)", data_format="memory", in_memory_data=data, input_column="input", output_column="output", evaluation_metrics=["accuracy"], metadata={"task_type": "logical_ops", "category": category}, ) return LogicalOpsTask(config)