variables.n3

@prefix : <urn:example:> .

# Examples form Dörthe Arndt "Implicit quantification made explicit"

:A a :B , :C. 

:Kurt :knows :Alice .

:Kurt :thinks { :Alice :is :Pretty } .

# A blank node means an existential
#  If something is a B, then there is something 
#  (maybe else) that is a B-able
{
    [] a :B .
}
=>
{
    # vv-* this is a new blank node
      [] :is :Bable . 
} .

# A blank node can also be named an its scope is limited to
# the parent premisse.
#  { SCOPE-A } => { SCOPE-B }
{
    _:x a :C .
}
=>
{
    # vvv-* this is a new blank node, not _:x in the premisse
      _:x :is :Cable .
} .

# A question mark means universal. Its scope
# is the *parent* premisse and conclusion. See next example
#  Everyone that Kurt knows also knows Kurt 
{
    :Kurt :knows ?W .
}
=> 
{
    ?W :knows :Kurt .
} . 

# When there is a combination of existentials
# and universals, then the universal is always
# interpreted outside the scope of the existentials
#
# For everyone (y) there is someone (x) that thinks
# that he/she (a member of y) is pretty.
#
# and not
#
# There is someone (x) that thinks everyone (y) is
# pretty.
#
# The scope of ?y is the outer graph plus conclusion
{
    _:x :thinks { ?y :is :Pretty } .
}
=> 
{
    ?y :isThoughtAs :Pretty .
} .

# When existentials are nested in the premis of a rule
# their scope is the premis and same for the conclusion.
#
# There is someone (_:x1) that thinks something other
# (_:x2) is Pretty.
{
    _:x1 :thinks { _:x2 :is :Pretty } .
}
=>
{
    [] :containsPretty true .
} .

# A statement
:ChateauxGreysac a :French , :Wine .
:Badenhortst a :SouthAfrican , :Wine .
:Croissant a :French, :Bread .

# A rule
{ ?X a :Wine } => { ?X :contains :Alcohol } .

# Reasoning about rules..
# One can reason about rules in N3. How should the
# universal ?X be interpreted in the example below?
# Is the scope of ?X in the examples below is limited
# to the inner implications? Or to the outer premisse
# and conclusion. The answer depends on the 
# implementation and was the core of Arndt-s research
{  
    # The ?X here is or not bounded to ...
    { ?X a :Wine } => { ?X :contains :Alcohol } 
}
=> 
{
    # ..the ?X-s here?
    { ?X a :French } => { ?X :needs :ImportTax }
} .

# Test
{
    [] :is :Bable .
    [] :is :Cable .
    :Alice :knows :Kurt .
    :Alice :isThoughtAs :Pretty .
    [] :containsPretty true .

    # Don't test the rules about rules
}
=>
{
    :test :is true .
} .