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    Jena is a Java framework for building Semantic Web applications. It provides a programmatic environment for RDF, RDFS and OWL, SPARQL and includes a rule-based inference engine.

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    #------------------------------------------------------------------
# OWL rule set v0.1
# This rule set is design to implement owl(f)lite using pure
# tabled backward chaining. It is experimental and not fully debugged.
# $Id: owl-b.rules,v 1.7 2004/07/02 08:08:21 der Exp $
#------------------------------------------------------------------

#------------------------------------------------------------------
# RDFS Axioms
#------------------------------------------------------------------

-> (rdf:type      rdfs:range rdfs:Class).
-> (rdfs:Resource  rdf:type  rdfs:Class).
-> (rdfs:Literal   rdf:type  rdfs:Class).
-> (rdf:Statement  rdf:type  rdfs:Class).
-> (rdf:nil        rdf:type  rdf:List).
-> (rdf:subject    rdf:type  rdf:Property).
-> (rdf:object     rdf:type  rdf:Property).
-> (rdf:predicate  rdf:type  rdf:Property).
-> (rdf:first      rdf:type  rdf:Property).
-> (rdf:rest       rdf:type  rdf:Property).
        
-> (rdfs:subPropertyOf rdfs:domain rdf:Property).
-> (rdfs:subClassOf rdfs:domain rdfs:Class).
-> (rdfs:domain rdfs:domain rdf:Property).
-> (rdfs:range rdfs:domain rdf:Property).
-> (rdf:subject rdfs:domain rdf:Statement).
-> (rdf:predicate rdfs:domain rdf:Statement).
-> (rdf:object rdfs:domain rdf:Statement).
-> (rdf:first rdfs:domain rdf:List).
-> (rdf:rest rdfs:domain rdf:List).

-> (rdfs:subPropertyOf rdfs:range rdf:Property).
-> (rdfs:subClassOf rdfs:range rdfs:Class).
-> (rdfs:domain rdfs:range rdfs:Class).
-> (rdfs:range rdfs:range rdfs:Class).
-> (rdf:type rdfs:range rdfs:Class).
-> (rdfs:comment rdfs:range rdfs:Literal).
-> (rdfs:label rdfs:range rdfs:Literal).
-> (rdf:rest rdfs:range rdf:List).

-> (rdf:Alt rdfs:subClassOf rdfs:Container).
-> (rdf:Bag rdfs:subClassOf rdfs:Container).
-> (rdf:Seq rdfs:subClassOf rdfs:Container).
-> (rdfs:ContainerMembershipProperty rdfs:subClassOf rdf:Property).

-> (rdfs:isDefinedBy rdfs:subPropertyOf rdfs:seeAlso).

-> (rdf:XMLLiteral rdf:type rdfs:Datatype).
-> (rdfs:Datatype rdfs:subClassOf rdfs:Class).

#------------------------------------------------------------------
# RDFS Closure rules
#------------------------------------------------------------------

# This one could be omitted since the results are not really very interesting!
#[rdf1: (?x ?p ?y) -> (?x rdf:type rdfs:Resource)]
#[rdf1b: (?x ?p ?y), notLiteral(?y) -> (?y rdf:type rdfs:Resource)]
#[rdf4: (?x ?p ?y) -> (?p rdf:type rdf:Property)]
#[rdfs7b: (?a rdf:type rdfs:Class) -> (?a rdfs:subClassOf rdfs:Resource)] 


[rdfs2:  bound(?c)   (?p rdfs:domain ?c) (?x ?p ?y)  -> (?x rdf:type ?c)] 
[rdfs2:  unbound(?c) (?x ?p ?y), (?p rdfs:domain ?c) -> (?x rdf:type ?c)] 

[rdfs3:  bound(?c)   (?p rdfs:range ?c) (?x ?p ?y) -> (?y rdf:type ?c)] 
[rdfs3:  unbound(?c) (?x ?p ?y), (?p rdfs:range ?c) -> (?y rdf:type ?c)] 

[rdfs5a: unbound(?c) (?a rdfs:subPropertyOf ?b), (?b rdfs:subPropertyOf ?c) -> (?a rdfs:subPropertyOf ?c)] 
[rdfs5a: bound(?c)   (?b rdfs:subPropertyOf ?c)  (?a rdfs:subPropertyOf ?b)-> (?a rdfs:subPropertyOf ?c)] 

[rdfs5b: (?a rdf:type rdf:Property) -> (?a rdfs:subPropertyOf ?a)] 

[rdfs6:  unbound(?q) (?a ?p ?b) (?p rdfs:subPropertyOf ?q) -> (?a ?q ?b)] 
[rdfs6:  bound(?q)   (?p rdfs:subPropertyOf ?q) (?a ?p ?b) -> (?a ?q ?b)] 

[rdfs7:  (?a rdf:type rdfs:Class) -> (?a rdfs:subClassOf ?a)]

[rdfs8:  unbound(?c) (?a rdfs:subClassOf ?b) (?b rdfs:subClassOf ?c) -> (?a rdfs:subClassOf ?c)] 
[rdfs8:  bound(?c)   (?b rdfs:subClassOf ?c) (?a rdfs:subClassOf ?b) -> (?a rdfs:subClassOf ?c)] 

[rdfs9:  bound(?y)   (?x rdfs:subClassOf ?y) (?a rdf:type ?x) -> (?a rdf:type ?y)] 
[rdfs9:  unbound(?y) (?a rdf:type ?x) (?x rdfs:subClassOf ?y) -> (?a rdf:type ?y)] 

[rdfs10: (?x rdf:type rdfs:ContainerMembershipProperty) -> (?x rdfs:subPropertyOf rdfs:member)] 

#------------------------------------------------------------------
# RDFS iff extensions needed for OWL
#------------------------------------------------------------------
[rdfs2a: (?x rdfs:domain ?y), (?y rdfs:subClassOf ?z) -> (?x rdfs:domain ?z)]
[rdfs3a: (?x rdfs:range  ?y), (?y rdfs:subClassOf ?z) -> (?x rdfs:range  ?z)]

#------------------------------------------------------------------
# OWL axioms
#------------------------------------------------------------------

-> (rdf:first rdf:type owl:FunctionalProperty).
-> (rdf:rest rdf:type owl:FunctionalProperty).

-> (rdfs:domain owl:SymmetricProperty owl:ObjectProperty).
-> (rdfs:domain owl:TransitiveProperty owl:ObjectProperty).
-> (rdfs:domain owl:InverseFunctionalProperty owl:ObjectProperty).

-> (rdfs:range owl:ObjectProperty owl:Thing).
-> (rdfs:domain owl:ObjectProperty owl:Thing).

-> (owl:Class rdfs:subClassOf rdfs:Class).
-> (owl:Restriction rdfs:subClassOf owl:Class).

# Omitted since this owl:Class is likelty to die anyway.
#-> (rdfs:Class rdfs:subClassOf owl:Class).

-> (owl:Thing rdf:type owl:Class).

# These might need to be pre-expanded in the initial rule set
-> (owl:equivalentProperty rdf:type owl:SymmetricProperty).
-> (owl:equivalentProperty rdf:type owl:TransitiveProperty).
-> (owl:equivalentClass rdf:type owl:SymmetricProperty).
-> (owl:equivalentClass rdf:type owl:TransitiveProperty).
-> (owl:sameIndividualAs rdf:type owl:SymmetricProperty).
-> (owl:sameIndividualAs rdf:type owl:TransitiveProperty).
-> (owl:sameIndividualAs owl:equivalentProperty owl:sameAs).
-> (owl:differentFrom rdf:type owl:SymmetricProperty).

-> (owl:intersectionOf rdfs:domain owl:Class).

#------------------------------------------------------------------
# OWL Rules
#------------------------------------------------------------------

#------------------------------------------------------------------
# Class rules
# (Note: compiling intersectionOf to an n+1 rule set is done procedurally)
#------------------------------------------------------------------

# Identify restriction assertions

[restriction1: (?C rdf:type owl:Restriction), (?C owl:onProperty ?P), (?C owl:someValuesFrom ?D)
						-> (?C owl:equivalentClass some(?P, ?D))]
						
[restriction2: (?C rdf:type owl:Restriction), (?C owl:onProperty ?P), (?C owl:allValuesFrom ?D)
						-> (?C owl:equivalentClass all(?P, ?D))]
						
[restriction3: (?C rdf:type owl:Restriction), (?C owl:onProperty ?P), (?C owl:minCardinality ?X)
						-> (?C owl:equivalentClass min(?P, ?X))]
		
[restriction4: (?C rdf:type owl:Restriction), (?C owl:onProperty ?P), (?C owl:maxCardinality ?X)
						-> (?C owl:equivalentClass max(?P, ?X))]
		
[restriction5: (?C rdf:type owl:Restriction), (?C owl:onProperty ?P), (?C owl:cardinality ?X)
						-> (?C owl:equivalentClass card(?P, ?X)), 
						   (?C rdfs:subClassOf min(?P, ?X)), 
						   (?C rdfs:subClassOf max(?P, ?X)) ]
		
[restriction6: (?C rdfs:subClassOf min(?P, ?X)), (?C rdfs:subClassOf max(?P, ?X)) 
       					-> (?C rdfs:subClassOf card(?P, ?X))]

# Needed for the case where ?R is a restriction literal and so does not appear in the subject position

[restrictionSubclass1: bound(?D) (?D owl:equivalentClass ?R), isFunctor(?R), 
											(?X rdf:type ?R)-> (?X rdf:type ?D)]
										
[restrictionSubclass1: unbound(?D) (?X rdf:type ?R), isFunctor(?R), 
								(?D owl:equivalentClass ?R) -> (?X rdf:type ?D)]
							
[restrictionSubclass2: bound(?R), isFunctor(?R), (?D owl:equivalentClass ?R), 
										   (?X rdf:type ?D) -> (?X rdf:type ?R)]
									   
[restrictionSubclass2: unbound(?R), (?X rdf:type ?D), (?D owl:equivalentClass ?R),
											isFunctor(?R) -> (?X rdf:type ?R)]

# Interactions between cardinalities and some/all

[restrictionProc1: (?X rdf:type, max(?P, 1)), (?X, rdf:type, some(?P, ?C)) 
						-> (?X rdf:type all(?P, ?C))]

[restrictionProc2a: unbound(?X), (?P rdf:type owl:FunctionalProperty), (?X, rdf:type, some(?P, ?C)) 
						-> (?X rdf:type all(?P, ?C))]

[restrictionProc2b: bound(?X),(?X, rdf:type, some(?P, ?C)), (?P rdf:type owl:FunctionalProperty), 
						-> (?X rdf:type all(?P, ?C))]

[restrictionProc4a: (?X rdf:type all(?P, ?C)), (?X ?P ?Y), notEqual(?P, rdf:type) 
						-> (?X rdf:type some(?P, ?C))]

[restrictionProc4b: unbound(?Y), (?X rdf:type all(?P, ?C)), (?X ?P ?Y), notEqual(?P, rdf:type) 
						-> (?Y rdf:type ?C)]

[restrictionProc4c: bound(?Y), (?X ?P ?Y), (?X rdf:type all(?P, ?C)), notEqual(?P, rdf:type) 
						-> (?Y rdf:type ?C)]       					
		
[restrictionProc5: (?P rdfs:range ?C), (?X ?P *), notFunctor(?C) -> (?X rdf:type some(?P, ?C))]

[restrictionProc6: (?D owl:equivalentClass all(?P, ?C)) (?P rdfs:range ?C)
						-> (owl:Thing rdfs:subClassOf ?D)]

[restrictionProc7: (?A rdf:type max(?P, 1)), (?A ?P ?B), (?A ?P ?C) -> (?B owl:sameIndividualAs ?C)]

[restrictionProc8: (?X rdf:type min(?P, 1)), (?X rdf:type max(?P, 0)) -> (?X rdf:type owl:Nothing)]

[restrictionProc9: (?X rdf:type max(?P, 0)) (?X ?P *) -> (?X rdf:type owl:Nothing)]

## Omitted 10 for now, requires prototype generation

[restrictionProc11: (?P rdf:type owl:FunctionalProperty), (?X rdf:type owl:Thing) 
						-> (?X rdf:type max(?P, 1))]
		
#[restrictionProc12: bound (?D), (?D rdf:type owl:Class), (?P rdfs:range ?C), notFunctor(?C)  
#						-> (?D rdfs:subClassOf all(?P, ?C)) ]
[restrictionProc12: bound(?P), (?P rdfs:range ?C), (?D rdf:type owl:Class), notFunctor(?C)  
						-> (?D rdfs:subClassOf all(?P, ?C)) ]
		
[restrictionProc13: (owl:Thing rdfs:subClassOf all(?P, ?C)) -> (?P rdfs:range ?C)]

#[restrictionProc13: (owl:Thing rdfs:subClassOf all(?P, ?C)) 
#						-> (?P rdfs:range ?C), (?P rdf:type owl:ObjectProperty)]

# There is a problem with this when used backward chaining -
# if we supported (* type *) matches then we are doing search over all data.
#[card3: (?X ?P ?V), (?V rdf:type ?C), notFunctor(?C) -> (?X rdf:type some(?P, ?C))]
[card3: bound(?P), bound(?X), (?X ?P ?V), (?V rdf:type ?C) -> (?X rdf:type some(?P, ?C))]

#------------------------------------------------------------------
# Disjointness and equivalence rules
#------------------------------------------------------------------

[distinct1: (?C owl:disjointWith ?D), (?X rdf:type ?C), (?Y rdf:type ?D) 
						-> (?X owl:differentFrom ?Y) ]

# This one is best done backwards or with a dedicated equality reasoner
# Hacked for now just for completeness

# [distinct2: (* owl:distinctMembers ?L) -> assertDisjointPairs(?L) ]

# To be improved when resolve how to record contradictions

#[conflict1: (?X owl:sameIndividualAs ?Y), (?X owl:differentFrom ?Y) 
#						-> contradiction('same/different', ?X, ?Y) ]
		
#[conflict2: (?X rdf:type ?C), (?X rdf:type ?D), (?C owl:disjointWith ?D) 
#						-> contradiction('disjoint classes overlap', ?C, ?D, ?X) ]

#------------------------------------------------------------------
# Property rules
#------------------------------------------------------------------

# symmetric
[symmetricProperty1: bound(?P) (?P rdf:type owl:SymmetricProperty), (?X ?P ?Y) -> (?Y ?P ?X)]
[symmetricProperty1: unbound(?P), (?X ?P ?Y) (?P rdf:type owl:SymmetricProperty) -> (?Y ?P ?X)]

# equivalentProperty 

[equivalentProperty1: (?P owl:equivalentProperty ?Q) 
						-> (?P rdfs:subPropertyOf ?Q), (?Q rdfs:subPropertyOf ?P) ]
						
[equivalentProperty2: (?P rdfs:subPropertyOf ?Q), (?Q rdfs:subPropertyOf ?P) 
						-> (?P owl:equivalentProperty ?Q) ]
						
[equivalentProperty3: (?P owl:sameAs ?Q), (?P rdf:type rdf:Property), (?Q rdf:type rdf:Property) 
						-> (?P owl:equivalentProperty ?Q) ]
						
# equivalentClass
[equivalentClass1: (?P owl:equivalentClass ?Q) 
						-> (?P rdfs:subClassOf ?Q), (?Q rdfs:subClassOf ?P) ]
						
[equivalentClass2: (?P rdfs:subClassOf ?Q), (?Q rdfs:subClassOf ?P) 
						-> (?P owl:equivalentClass ?Q) ]
						
[equivalentClass3: (?P owl:sameAs ?Q), (?P rdf:type rdfs:Class), (?Q rdf:type rdfs:Class) 
						-> (?P owl:equivalentClass ?Q) ]

# inverseOf
[inverseOf1: (?P owl:inverseOf ?Q) -> (?Q owl:inverseOf ?P) ]

[inverseOf2: bound(?P), (?P owl:inverseOf ?Q), (?X ?P ?Y) -> (?Y ?Q ?X) ]
[inverseOf2: unbound(?P), (?X ?P ?Y), (?P owl:inverseOf ?Q) -> (?Y ?Q ?X) ]

[inverseOf3: (?P owl:inverseOf ?Q), (?P rdf:type owl:FunctionalProperty) 
						-> (?Q rdf:type owl:InverseFunctionalProperty) ]
		
[inverseOf4: (?P owl:inverseOf ?Q), (?P rdf:type owl:InverseFunctionalProperty) 
						-> (?Q rdf:type owl:FunctionalProperty) ]

# Transitive
[transitivePropery1: (?P rdf:type owl:TransitiveProperty), (?A ?P ?B), (?B ?P ?C) -> (?A ?P ?C)]

# sameIndividualAs
[sameIndividualAs1: (?P rdf:type owl:FunctionalProperty), (?A ?P ?B), (?A ?P ?C) 
                    -> (?B owl:sameIndividualAs ?C) ]
                    
[sameIndividualAs2: (?P rdf:type owl:InverseFunctionalProperty), (?A ?P ?B), (?C ?P ?B) 
                    -> (?A owl:sameIndividualAs ?C) ]
                    
[sameIndividualAs3: (?X owl:sameAs ?Y), (?X rdf:type owl:Thing), (?Y rdf:type old:Thing) 
                    -> (?X owl:sameIndividualAs ?Y) ]
                    

[sameIndividualAs4: bound(?Y), (?X owl:sameIndividualAs ?Y), (?X ?P ?V) -> (?Y ?P ?V) ]
[sameIndividualAs4: unbound(?Y), (?X ?P ?V) (?X owl:sameIndividualAs ?Y) -> (?Y ?P ?V) ]

[sameIndividualAs5: bound(?Y) (?X owl:sameIndividualAs ?Y), (?V ?P ?X) -> (?V ?P ?Y) ]
[sameIndividualAs5: unbound(?Y), (?V ?P ?X) (?X owl:sameIndividualAs ?Y) -> (?V ?P ?Y) ]

[sameIndividualAs6: (?X owl:sameIndividualAs ?Y) -> (?X rdf:type owl:Thing) ]

# Don't yet handle reflexivity of sameIndividualAs




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