# equality rules 
# Inspired by "Bubo -Implementing OWL in rule-based systems"
# by Volz, Decker, Oberle.

@prefix : <#test>.
@prefix owl: <http://www.w3.org/2002/07/owl#>.
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix log: <http://www.w3.org/2000/10/swap/log#>.

# reflexivity
{?a = ?a}.   
# symmetry
{?a = ?b} log:implies {?b = ?a}.
# transitivity
{?a = ?b. ?b = ?c.} log:implies {?a = ?c}. 

# test data
:5 = {:2 :+ :3}.
# query: {:2 :+ :3} = ?n.
{:2 :+ :3} = {:3 :+ :2}.
# query: :5 = {:3 :+ :2}.
#        :5 = :5.

# triple rules
#{?a ?b ?c.?a = ?d.} log:implies {?d ?b ?c}.
#{?b ?a ?c.?a = ?d.} log:implies {?b ?d ?c}.
#{?c ?b ?a.?a = ?d.} log:implies {?c ?b ?d}.

# data
:John :owns :car. :John = :JD.
# query: :JD :owns :car.

# owl:sameClassAs
#{?c1 owl:sameClassAs ?c2. ?a a ?c1.} log:implies {?a a ?c2}.
#{?c1 owl:sameClassAs ?c2. ?a a ?c2.} log:implies {?a a ?c1}.
"{?c1 owl:sameClassAs ?c2} log:implies {?c2 owl:sameClassAs ?c1}.

# data
:mammals owl:sameClassAs :mammalia. :rat a :mammals.
# query :rat a :mammalia.

# owl:samePropertyAs
#{?p1 owl:samePropertyAs ?p2. ?a ?p1 ?b.} log:implies {?a ?p2 ?b}.
#{?p1 owl:samePropertyAs ?p2. ?a ?p2 ?b.} log:implies {?a ?p1 ?b}.
#{?p1 owl:samePropertyAs ?p2} log:implies {?p2 owl:samePropertyAs ?p1}.

# data
:rat :gives :milk.
:gives owl:samePropertyAs :produces.
# query: :rat :produces :milk.

# owl:disjointWith
{?c1 owl:disjointWith ?c2. ?a a ?c1. ?a a ?c2} log:implies {?a :inconsistency
"belongs to disjoint classes."}. 
#data 
:mammalia owl:disjointWith :reptilia. :snake a :reptilia.
# query: :snake a :mammalia.   

# owl:sameIndividualAs
{?x1 owl:sameIndividualAs ?x2} log:implies {?x1 = ?x2}.
{?x1 = ?x2} log:implies {?x1 owl:sameIndividualAs ?x2}.

# data
:John owl:sameIndividualAs :JD.  :JD a :person.
# query: :John a :person.

# owl:differentIndividualFrom
{?x1 owl:differentIndividualFrom ?x2. ?x1 = ?x2} log:implies {?x1 :inconsistency
"violation owl:differentIndividualFrom"}.

:Frank :differentIndividualFrom :Anna.
# query: :Frank :sameIndividualAs :Anna.