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Exercise 2. Four cases for one question

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# Exercise 2. Four cases for one question

An exercise for the [four states](/tutorials/four-states/) page. The
package is the same as on the page, without a single new symbol: the
rare-collections room norm and three relations.

**Setup.** Pick four cases so that the question "is Ivanova admitted to
the rare-collections room" receives in turn all four answers: `TRUE_ONLY`,
`FALSE_ONLY`, `BOTH`, `NEITHER`. The package must not be changed. Only
facts may change.

**Hint.** The norm derives only a positive access. Where, then, would a
denial and a contradiction come from, if there are no more rules?

Below is the solution. Try it yourself first.

## Solution

The page's package, same version:

```law
language "law.core" version "0.2";
package tutorial.archive version "0.2.0";
namespace "urn:law:tutorial:archive";

entity Person;

relation in_researcher_registry(p: Person) kind institutional;
relation accredited(p: Person) kind institutional;
relation may_enter_rare_room(p: Person) kind institutional;

rule RareRoomAccess strict {
    for p: Person;
    when in_researcher_registry(p) and accredited(p);
    then may_enter_rare_room(p);
}
```

Four cases:

| Case | Facts | Answer on `may_enter_rare_room(ivanova)` |
|---|---|---|
| 1 | registry, accreditation | `TRUE_ONLY` — the norm fired |
| 2 | case record `not may_enter_rare_room(ivanova)` | `FALSE_ONLY` — the denial fed by the case |
| 3 | registry, accreditation, the same negative record | `BOTH` — the norm and the record argue |
| 4 | nothing | `NEITHER` |

The key to cases 2 and 3: the case may state the norm's **head itself**,
not just premises, and in either polarity. Law does not ask "whether one
may": a negative access record is as much a case fact as a registry
record. The norm is not cancelled thereby. In case 3 it fires, and its
conclusion stands next to the case record, hence the answer is `BOTH`,
not "the record won".

## Check

All four rows of the table execute on this package. A fifth
case for self-check: the registry exists, accreditation holds two
records, "yes" and "no". Access here is `NEITHER`, already covered on
the page: a `BOTH`-state premise does not count as established.

What the exercise teaches. Telling apart two sources of denial: a norm
with a negative head, covered on the next page, and a case record. While
the package lacks the first, `FALSE_ONLY` comes only from the second.