task_symbolic__truth_table__expression_from_rows_label

1) Identity

1. Domain: symbolic
2. Scene id: truth_table
3. Scene: truth_table
4. Task id: task_symbolic__truth_table__expression_from_rows_label
5. Objective: select the Boolean expression that produces the completed output column.

Program Contract

Program: truth_table.expression_from_rows_label(scene=truth_table, scope=input_rows_plus_completed_output_column_and_expression_options, output=option_letter)

Candidate set: the four visible expression option cards labeled W..Z. Operands: the visible A, B, C input rows, the completed P output column, and candidate expressions. Operation: compare each candidate expression's truth values over the shown rows to the completed P column. Output binding: answer is the selected candidate label. Annotation witnesses: a scalar bbox around the selected expression option card. Query ids: single.

Reasoning Operations

Families: logical_composition, formula_evaluation, matching

2) Scene + Task Contract

1. The table uses variables A, B, and C with fixed row order 000..111.
2. The P column shows completed truth values for all rows.
3. Candidate labels W..Z do not collide with input variables A, B, and C.
4. Exactly one candidate expression has the same truth pattern as column P.
5. Values use 1 for true and 0 for false.
6. answer_gt.type: string
7. annotation_gt.type: bbox
8. Annotation schema: bbox

3) Prompt Contract

1. Bundle: symbolic_truth_table_v1
2. scene_key: truth_table
3. task_key: expression_from_rows_label
4. Modes: answer_only, answer_and_annotation
5. Prompt text comes from the external prompt bundle.

4) Trace Contract

1. execution_trace.truth_table_metadata.truth_pattern records the visible P column from top to bottom.
2. execution_trace.truth_table_metadata.candidate_expressions records each candidate expression and whether it matches the output column.
3. render_map.cell_bboxes_px contains table-cell projections.
4. render_map.item_bboxes_px contains expression-option card projections.
5. projected_annotation mirrors the selected option bbox.

5) Determinism + Tests

1. Deterministic generation and rendering from instance_seed.
2. Options are sampled with one unique final answer.
3. Behavior tests: tests/test_symbolic_truth_table_tasks.py