saracandu/implications

---
annotations_creators:
- no-annotation
language_creators:
- found
language:
- en
license:
- apache-2.0
multilinguality:
- monolingual
size_categories:
- 10K<n<100K
source_datasets:
- generated/synthetic
task_categories:
- text-classification
- other
---

# Implications

## Dataset Description

**Implications** is a synthetic dataset of logical formulas with Boolean variables and logical operators (`and`, `or`, `implies`).
Each example contains:

- `facts`: truth values assigned to variables (e.g., `a is true, b is false, ...`)
- `formula`: a linear formula without parentheses (e.g., `a and b implies c or d`)
- `num_operators`: the number of logical operators in the formula
- `gold_formula`: the overall truth value of the formula (`True` or `False`)

All duplicate `(facts, formula)` pairs have been removed to ensure that each combination is unique.

The dataset is designed for training models on **logical reasoning**, **linear probing**, or **LLMs** to predict the truth value of formulas.

---

## Data Fields

| Column | Type | Description |
|-----------------|---------|-------------|
| facts | string | Boolean values assigned to variables |
| formula | string | Linear formula without parentheses |
| num_operators | int | Number of logical operators in the formula |
| gold_formula | bool | Truth value of the full formula |

---

### `num_operators` counts (both in train and in test)

| num_operators | train_count | test_count |
|---------------|------------|-----------|
| 1 | 730 | 196 |
| 2 | 775 | 225 |
| 3 | 811 | 189 |
| 4 | 814 | 186 |
| 5 | 788 | 212 |
| 6 | 799 | 201 |
| 7 | 788 | 212 |
| 8 | 800 | 200 |
| 9 | 808 | 192 |
| 10 | 795 | 205 |
| 11 | 806 | 194 |
| 12 | 787 | 213 |
| 13 | 817 | 183 |
| 14 | 806 | 194 |
| 15 | 817 | 183 |
| 16 | 819 | 181 |
| 17 | 815 | 185 |
| 18 | 793 | 207 |
| 19 | 778 | 222 |
| 20 | 795 | 205 |

**Note:** All duplicate `(facts, formula)` pairs have been removed to ensure each example is unique.

---

## Example

```csv
facts,formula,num_operators,gold_formula
"a is true, b is false, c is true","a and b or c implies d",5,True
"p is false, q is true","p or q implies r",2,False