# Counting a course's examiners
#
# Wittgenstein participates in the philosophy course that Russell and
# Wittgenstein both teach. Participants are students, and a teacher who is not
# a student is an examiner. Every course with a participant also needs some
# examiner, so that rule's conclusion has a blank node. Russell already
# satisfies it, so eyeron introduces no fresh examiner and counts exactly one.
# The example shows scoped negation, an existential that is introduced only
# when no known fact satisfies it, and a count over the result.
# See https://arxiv.org/abs/2607.28778

@prefix log: <http://www.w3.org/2000/10/swap/log#> .
@prefix list: <http://www.w3.org/2000/10/swap/list#> .
@prefix : <https://example.org/course#> .

# Facts
:philosophy :teacher :russell .
:philosophy :teacher :wittgenstein .
:philosophy :participant :wittgenstein .

# Participants are students.
{
    ?course :participant ?person .
} => {
    ?person a :Student .
} .

# A teacher who is not a student is an examiner.
{
    ?course :teacher ?person .
    ?scope log:notIncludes {
        ?person a :Student .
    } .
} => {
    ?course :examiner ?person .
} .

# A course with a participant has some examiner.
{
    ?course :participant ?person .
} => {
    ?course :examiner _:examiner .
} .

# Count the examiners of each course with a participant.
{
    ?course :participant ?anyone .
    (?examiner {
        ?course :examiner ?examiner .
    } ?examiners) log:collectAllIn ?scope .
    ?examiners list:length ?count .
} => {
    ?course :numberOfExaminers ?count .
} .