The Scenario

A group of 20 persons spent the night in a manor. In the morning, Daphine, a young lady, went missing. Her dead body was found the following day in the cellar. The autopsy revealed the following facts:

• She died of a head injury caused by a blunt-force instrument.
• Her death happened between midnight and 8 am.
• She was not killed in the cellar, but her body was moved there afterwards.
• Goose down found in her wound proves that she died in bed in one of the bedrooms; unfortunately all beds have the same down pillows, and pillowcases were changed in the morning, so it is impossible to identify which bedroom.

The police interviewed all 19 suspects and collected their statements about who they saw in which room at which time. They also assessed each witness's reliability through a psychological evaluation.

Your mission: help the police discover who killed Daphine, using the power of provenance management and probabilistic databases.

Setup

This tutorial assumes a working ProvSQL installation (see getting-provsql). Download setup.sql <../../tutorial/setup.sql> and load it into a fresh PostgreSQL database:

psql -d mydb -f setup.sql

This creates four tables:

• person – the 20 persons present at the manor
• room – the rooms of the manor
• sightings – witness statements: who was seen where, and when
• reliability – the reliability score (between 0 and 1) of each witness

Step 1: Explore the Database

Familiarise yourself with the schema. In the psql client:

\d
\d sightings

At the start of every new session, set the search path so that ProvSQL functions can be called without the provsql. prefix:

SET search_path TO public, provsql;

Step 2: Build a Sightings Table

Design a query that retrieves, for every sighting: the time, the name of the person seen, the name of the witness, and the name of the room. Store the result in a new table s.

CREATE TABLE s AS
SELECT
  time,
  person.name  AS person,
  p2.name      AS witness,
  room.name    AS room
FROM sightings
  JOIN person       ON person  = person.id
  JOIN person AS p2 ON witness = p2.id
  JOIN room         ON room    = room.id;

Step 3: Enable Provenance

Activate provenance tracking on the table s using add_provenance:

SELECT add_provenance('s');

A hidden provsql column is added that holds a UUID provenance token for each tuple. Run a simple SELECT * FROM s – you will see this extra column in the output.

Create a provenance mapping that associates each provenance token with the name of the witness who made the sighting, using create_provenance_mapping:

SELECT create_provenance_mapping('witness_mapping', 's', 'witness');

The mapping is stored as an ordinary table – inspect it with SELECT * FROM witness_mapping;.

Step 4: Find Contradictions

Some witnesses are unreliable: the same person may be reported in two different rooms at the same time – an impossibility. Write a query that identifies all such contradictions.

SELECT s1.time, s1.person, s1.room
FROM s AS s1, s AS s2
WHERE s1.person = s2.person
  AND s1.time   = s2.time
  AND s1.room  <> s2.room;

Step 5: Display Provenance Formulas

Extend the previous query by adding sr_formula(provenance(), 'witness_mapping') to the SELECT clause to see which witnesses are responsible for each contradiction.

sr_formula displays the provenance token as a formula, substituting each leaf token with the mapped value from witness_mapping.

SELECT s1.time, s1.person, s1.room,
       sr_formula(provenance(), 'witness_mapping')
FROM s AS s1, s AS s2
WHERE s1.person = s2.person
  AND s1.time   = s2.time
  AND s1.room  <> s2.room;

Step 6: Build a Consistent Sightings Table

Create a table consistent_s containing all sightings except those identified as contradictions. Display its content along with the provenance formula for each tuple.

CREATE TABLE consistent_s AS
SELECT time, person, room FROM s
EXCEPT
SELECT s1.time, s1.person, s1.room
FROM s AS s1, s AS s2
WHERE s1.person = s2.person
  AND s1.time   = s2.time
  AND s1.room  <> s2.room;

SELECT *, sr_formula(provenance(), 'witness_mapping')
FROM consistent_s;

Step 7: Identify Suspects

The murder happened between midnight and 8 am in a bedroom. Create a suspects table containing every person who was seen (in a consistent sighting) in a bedroom during that window. Display the suspects along with their provenance formula.

CREATE TABLE suspects AS
SELECT DISTINCT person
FROM consistent_s
WHERE room LIKE '% bedroom'
  AND time BETWEEN '00:00:00' AND '08:00:00';

SELECT *, sr_formula(provenance(), 'witness_mapping')
FROM suspects;

Step 8: Count Confirming Sightings

Use the counting m-semiring to find how many sightings confirm that each person is a suspect. Add an integer column count to s, set it to 1 for all rows, and create a count_mapping. Then use sr_counting to display the count for each suspect.

ALTER TABLE s ADD COLUMN count int;
UPDATE s SET count = 1;

SELECT create_provenance_mapping('count_mapping', 's', 'count');

SELECT *, sr_counting(provenance(), 'count_mapping') AS c
FROM suspects
ORDER BY c;

Step 9: Assign Reliability Probabilities

Add a reliability float column to s and populate it with the reliability score of each sighting's witness. Then assign these scores as the probability of each provenance token using set_prob.

ALTER TABLE s ADD COLUMN reliability float;

UPDATE s
SET reliability = score
FROM reliability, person
WHERE reliability.person = person.id
  AND person.name = s.witness;

SELECT set_prob(provenance(), reliability) FROM s;

Step 10: Find the Murderer

The police needs a confidence of at least 0.99 before making an arrest. Use probability_evaluate to compute the probability that each suspect was truly present, and identify those above the threshold.

probability_evaluate accepts an optional second argument for the computation method:

• 'possible-worlds' – exact, by exhaustive enumeration
• 'monte-carlo' – approximate sampling (add a sample count as third argument)
• 'tree-decomposition' – exact, via tree decomposition of the Boolean circuit
• 'compilation' – d-DNNF compilation (add the tool name, e.g. 'd4', as third argument)

SELECT *,
       sr_formula(provenance(), 'witness_mapping'),
       probability_evaluate(provenance(), 'possible-worlds')
FROM suspects
WHERE probability_evaluate(provenance(), 'possible-worlds') > 0.99
  AND person <> 'Daphine';