#------------------------------------------------------------------
# OWL micro rule set v0.1
# This rule set is designed to implement owl(f)lite using the hybrid
# rule system (mixture of forward and backward chaining).
#
# This differs from the normal OWL rule set in several ways.
#  - no equality reasoning (sameAs, FunctionalProperty ...)
#  - omits the someValuesFrom => bNode entailments.
#  - avoids any guard clauses which would break the find() contract.
#  - TGC for subClass hierarchies, all subClassOf derivations are forward.
#  - omits use of prototypes and relies on explicit rules for subClassOf 
#    derivations this may lead to additional incompletenesses
#
# $Id: owl-fb.rules,v 1.45 2004/03/02 13:38:53 der Exp $
#------------------------------------------------------------------

#------------------------------------------------------------------
# Tabling directives
#------------------------------------------------------------------

#-> tableAll().

-> table(rdf:type).
-> table(rdfs:subClassOf).
-> table(rdfs:range).
-> table(rdfs:domain).
-> table(owl:equivalentClass).

#------------------------------------------------------------------
# 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
#------------------------------------------------------------------

[rdf1and4: (?x ?p ?y) -> (?p rdf:type rdf:Property)]

[rdfs7b: (?a rdf:type rdfs:Class) -> (?a rdfs:subClassOf rdfs:Resource)] 

[rdfs2:  (?p rdfs:domain ?c) -> [(?x rdf:type ?c) <- (?x ?p ?y)] ] 
[rdfs3:  (?p rdfs:range ?c)  -> [(?y rdf:type ?c) <- (?x ?p ?y)] ] 
[rdfs5b: (?a rdf:type rdf:Property) -> (?a rdfs:subPropertyOf ?a)] 
[rdfs6:  (?p rdfs:subPropertyOf ?q), notEqual(?p,?q) -> table(?p, ?q), [ (?a ?q ?b) <- (?a ?p ?b)] ] 
[rdfs7:  (?a rdf:type rdfs:Class) -> (?a rdfs:subClassOf ?a)]
[rdfs10: (?x rdf:type rdfs:ContainerMembershipProperty) -> (?x rdfs:subPropertyOf rdfs:member)] 

[rdfs2-partial: (?p rdfs:domain ?c) -> (?c rdf:type rdfs:Class)]
[rdfs3-partial: (?p rdfs:range ?c)  -> (?c rdf:type rdfs:Class)]

[rdfs9-alt:  (?a rdf:type ?y) <- bound(?y) (?x rdfs:subClassOf ?y), (?a rdf:type ?x) ] 
[rdfs9-alt:  (?a rdf:type ?y) <- unbound(?y) (?a rdf:type ?x) (?x rdfs:subClassOf ?y) ] 

#------------------------------------------------------------------
# RDFS iff extensions needed for OWL
#------------------------------------------------------------------

[rdfs2a: (?x rdfs:domain ?z) <- bound(?x), (?x rdfs:domain ?y), (?y rdfs:subClassOf ?z) ]
[rdfs2a: (?x rdfs:domain ?z) <- unbound(?x), (?y rdfs:subClassOf ?z), (?x rdfs:domain ?y) ]
[rdfs3a: (?x rdfs:range  ?z) <- bound(?x), (?x rdfs:range  ?y), (?y rdfs:subClassOf ?z) ]
[rdfs3a: (?x rdfs:range  ?z) <- unbound(?x), (?y rdfs:subClassOf ?z), (?x rdfs:range  ?y) ]

[rdfs12a: (rdf:type rdfs:subPropertyOf ?z), (?z rdfs:domain ?y) -> (rdfs:Resource rdfs:subClassOf ?y)]
[rdfs12a: (rdfs:subClassOf rdfs:subPropertyOf ?z), (?z rdfs:domain ?y) -> (rdfs:Class rdfs:subClassOf ?y)]
[rdfs12a: (rdfs:subPropertyOf rdfs:subPropertyOf ?z), (?z rdfs:domain ?y) -> (rdf:Property rdfs:subClassOf ?y)]

[rdfs12b: (rdfs:subClassOf rdfs:subPropertyOf ?z), (?z rdfs:range ?y) -> (rdfs:Class rdfs:subClassOf ?y)]
[rdfs12b: (rdfs:subPropertyOf rdfs:subPropertyOf ?z), (?z rdfs:range ?y) -> (rdf:Property rdfs:subClassOf ?y)]

[rdfsder1: (?p rdfs:range ?z) <- (?p rdfs:subPropertyOf ?q), notEqual(?p, ?q), (?q rdfs:range ?z)]
[rdfsder2: (?p rdfs:domain ?z) <- (?p rdfs:subPropertyOf ?q), notEqual(?p, ?q), (?q rdfs:domain ?z)]

#------------------------------------------------------------------
# OWL axioms
#------------------------------------------------------------------

-> (owl:FunctionalProperty rdfs:subClassOf rdf:Property).
-> (owl:ObjectProperty rdfs:subClassOf rdf:Property).
-> (owl:DatatypeProperty rdfs:subClassOf rdf:Property).
-> (owl:InverseFunctionalProperty rdfs:subClassOf owl:ObjectProperty).
-> (owl:TransitiveProperty rdfs:subClassOf owl:ObjectProperty).
-> (owl:SymmetricProperty rdfs:subClassOf owl:ObjectProperty).

-> (rdf:first rdf:type owl:FunctionalProperty).
-> (rdf:rest rdf:type owl:FunctionalProperty).

-> (owl:oneOf rdfs:domain owl:Class).

-> (owl:Class rdfs:subClassOf rdfs:Class).
-> (owl:Restriction rdfs:subClassOf owl:Class).

-> (owl:Thing rdf:type owl:Class).
-> (owl:Nothing rdf:type owl:Class).

-> (owl:equivalentClass rdfs:domain owl:Class).
-> (owl:equivalentClass rdfs:range  owl:Class).

-> (owl:disjointWith rdfs:domain owl:Class).
-> (owl:disjointWith rdfs:range  owl:Class).

-> (owl:sameAs rdf:type owl:SymmetricProperty).

# These are true but mess up the Ont API's notion of declared properties
#-> (owl:sameAs rdfs:domain owl:Thing).
#-> (owl:sameAs rdfs:range  owl:Thing).
#-> (owl:differentFrom rdfs:domain owl:Thing).
#-> (owl:differentFrom rdfs:range  owl:Thing).

-> (owl:onProperty rdfs:domain owl:Restriction).
-> (owl:onProperty rdfs:range  owl:Property).

-> (owl:OntologyProperty rdfs:subClassOf rdf:Property).
-> (owl:imports rdf:type owl:OntologyProperty).
-> (owl:imports rdfs:domain owl:Ontology).
-> (owl:imports rdfs:range  owl:Ontology).

-> (owl:priorVersion rdfs:domain owl:Ontology).
-> (owl:priorVersion rdfs:range  owl:Ontology).

-> (owl:backwardCompatibleWith rdfs:domain owl:Ontology).
-> (owl:backwardCompatibleWith rdfs:range  owl:Ontology).

-> (owl:incompatibleWith rdfs:domain owl:Ontology).
-> (owl:incompatibleWith rdfs:range  owl:Ontology).

-> (owl:versionInfo rdf:type owl:AnnotationProperty).

# These properties are derivable from the definitions
#-> (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:differentFrom rdf:type owl:SymmetricProperty).
-> (owl:disjointWith rdf:type owl:SymmetricProperty).

-> (owl:intersectionOf rdfs:domain owl:Class).

#------------------------------------------------------------------
# OWL Rules
#------------------------------------------------------------------

[thing1: (?C rdf:type owl:Class) -> (?C rdfs:subClassOf owl:Thing), (owl:Nothing rdfs:subClassOf ?C)]

#------------------------------------------------------------------
# Class equality
#------------------------------------------------------------------

# equivalentClass
[equivalentClass1: (?P owl:equivalentClass ?Q) 
						-> (?P rdfs:subClassOf ?Q), (?Q rdfs:subClassOf ?P) ]
						
[equivalentClass2: (?P owl:equivalentClass ?Q) <-  (?P rdfs:subClassOf ?Q), (?Q rdfs:subClassOf ?P) ]
						
[equivalentClass3: (?P owl:sameAs ?Q), (?P rdf:type owl:Class), (?Q rdf:type owl:Class) 
						-> (?P owl:equivalentClass ?Q) ]
		
#------------------------------------------------------------------
# Property rules
#------------------------------------------------------------------

# 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) ]

# SymmetricProperty

[symmetricProperty1: (?P rdf:type owl:SymmetricProperty) -> table(?P),
                     [symmetricProperty1b: (?X ?P ?Y) <- (?Y ?P ?X)] ]


# inverseOf
[inverseOf1: (?P owl:inverseOf ?Q) -> (?Q owl:inverseOf ?P) ]

[inverseOf2: (?P owl:inverseOf ?Q) -> table(?P), table(?Q), [inverseOf2b: (?X ?P ?Y) <- (?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) ]

[inverseof5:  (?P owl:inverseOf ?Q) (?P rdfs:range ?C) -> (?Q rdfs:domain ?C)]
[inverseof6:  (?P owl:inverseOf ?Q) (?P rdfs:domain ?C) -> (?Q rdfs:range ?C)]

# TransitiveProperty

[transitiveProperty1: (?P rdf:type owl:TransitiveProperty) -> table(?P),
#			[transitiveProperty1b:  (?A ?P ?C) <- (?A ?P ?B), (?B ?P ?C)] ]
			[transitiveProperty1b:  (?A ?P ?C) <- bound (?C), (?B ?P ?C), (?A ?P ?B)] 
			[transitiveProperty1b:  (?A ?P ?C) <- unbound (?C), (?A ?P ?B) (?B ?P ?C)] 
			]
						
# Object properties 

[objectProperty: (?P rdf:type owl:ObjectProperty) ->
						(?P rdfs:domain owl:Thing) (?P rdfs:range owl:Thing) ]
						
#------------------------------------------------------------------
# Declaration of main XSD datatypes
#------------------------------------------------------------------

-> (xsd:float rdf:type rdfs:Datatype).
-> (xsd:double rdf:type rdfs:Datatype).
-> (xsd:int rdf:type rdfs:Datatype).
-> (xsd:long rdf:type rdfs:Datatype).
-> (xsd:short rdf:type rdfs:Datatype).
-> (xsd:byte rdf:type rdfs:Datatype).
-> (xsd:unsignedByte rdf:type rdfs:Datatype).
-> (xsd:unsignedShort rdf:type rdfs:Datatype).
-> (xsd:unsignedInt rdf:type rdfs:Datatype).
-> (xsd:unsignedLong rdf:type rdfs:Datatype).
-> (xsd:decimal rdf:type rdfs:Datatype).
-> (xsd:integer rdf:type rdfs:Datatype).
-> (xsd:nonPositiveInteger rdf:type rdfs:Datatype).
-> (xsd:nonNegativeInteger rdf:type rdfs:Datatype).
-> (xsd:positiveInteger rdf:type rdfs:Datatype).
-> (xsd:negativeInteger rdf:type rdfs:Datatype).
-> (xsd:boolean rdf:type rdfs:Datatype).
-> (xsd:string rdf:type rdfs:Datatype).
-> (xsd:anyURI rdf:type rdfs:Datatype).
-> (xsd:hexBinary rdf:type rdfs:Datatype).
-> (xsd:base64Binary  rdf:type rdfs:Datatype).
-> (xsd:date rdf:type rdfs:Datatype).
-> (xsd:time rdf:type rdfs:Datatype).
-> (xsd:dateTime rdf:type rdfs:Datatype).
-> (xsd:duration rdf:type rdfs:Datatype).
-> (xsd:gDay rdf:type rdfs:Datatype).
-> (xsd:gMonth rdf:type rdfs:Datatype).
-> (xsd:gYear rdf:type rdfs:Datatype).
-> (xsd:gYearMonth rdf:type rdfs:Datatype).
-> (xsd:gMonthDay rdf:type rdfs:Datatype).

#-> (xsd:integer rdfs:subClassOf xsd:decimal).

-> hide(rb:xsdBase).
-> hide(rb:xsdRange).
-> hide(rb:prototype).

-> (xsd:byte rb:xsdBase xsd:decimal).
-> (xsd:short rb:xsdBase xsd:decimal).
-> (xsd:int rb:xsdBase xsd:decimal).
-> (xsd:long rb:xsdBase xsd:decimal).
-> (xsd:unsignedByte rb:xsdBase xsd:decimal).
-> (xsd:unsignedShort rb:xsdBase xsd:decimal).
-> (xsd:unsignedInt rb:xsdBase xsd:decimal).
-> (xsd:unsignedLong rb:xsdBase xsd:decimal).
-> (xsd:integer rb:xsdBase xsd:decimal).
-> (xsd:nonNegativeInteger rb:xsdBase xsd:decimal).
-> (xsd:nonPositiveInteger rb:xsdBase xsd:decimal).
-> (xsd:byte rb:xsdBase xsd:decimal).
-> (xsd:float rb:xsdBase xsd:float).
-> (xsd:decimal rb:xsdBase xsd:decimal).
-> (xsd:string rb:xsdBase xsd:string).
-> (xsd:boolean rb:xsdBase xsd:boolean).
-> (xsd:date rb:xsdBase xsd:date).
-> (xsd:time rb:xsdBase xsd:time).
-> (xsd:dateTime rb:xsdBase xsd:dateTime).
-> (xsd:duration rb:xsdBase xsd:duration).

# Describe range (base type, signed, min bits)
-> (xsd:byte    rb:xsdRange xsd(xsd:integer,1,8)).
-> (xsd:short   rb:xsdRange xsd(xsd:integer,1,16)).
-> (xsd:int     rb:xsdRange xsd(xsd:integer,1,32)).
-> (xsd:long    rb:xsdRange xsd(xsd:integer,1,64)).
-> (xsd:integer rb:xsdRange xsd(xsd:integer,1,65)).
							
-> (xsd:unsignedByte    rb:xsdRange xsd(xsd:integer,0,8)).
-> (xsd:unsignedShort   rb:xsdRange xsd(xsd:integer,0,16)).
-> (xsd:unsignedInt     rb:xsdRange xsd(xsd:integer,0,32)).
-> (xsd:unsignedLong    rb:xsdRange xsd(xsd:integer,0,64)).
-> (xsd:nonNegativeInteger rb:xsdRange xsd(xsd:integer,0,65)).

#------------------------------------------------------------------
# Identify restriction assertions
#------------------------------------------------------------------

[restriction1: (?C owl:onProperty ?P), (?C owl:someValuesFrom ?D)
	-> (?C owl:equivalentClass some(?P, ?D))]
		
[restriction2: (?C owl:onProperty ?P), (?C owl:allValuesFrom ?D)
	-> (?C owl:equivalentClass all(?P, ?D))]
		
[restriction3: (?C owl:onProperty ?P), (?C owl:minCardinality ?X)
	-> (?C owl:equivalentClass min(?P, ?X))]
		
[restriction4: (?C owl:onProperty ?P), (?C owl:maxCardinality ?X)
	-> (?C owl:equivalentClass max(?P, ?X)) ]
		
[restriction5: (?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))]
       					
[hasValueRec: (?C owl:onProperty ?P), (?C owl:hasValue ?V)
	-> (?C owl:equivalentClass hasValue(?P, ?V)) ]
						

## TODO do we need the early restriction propagation rules in this configuration?

# Equality propagation

[restrictionEq1: (?R1 owl:equivalentClass some(?P, ?C)) (?R2 owl:equivalentClass some(?P, ?C))
					notEqual(?R1, ?R2) -> (?R1 owl:equivalentClass ?R2) ]
[restrictionEq2: (?R1 owl:equivalentClass all(?P, ?C)) (?R2 owl:equivalentClass all(?P, ?C))
					notEqual(?R1, ?R2) -> (?R1 owl:equivalentClass ?R2) ]
[restrictionEq3: (?R1 owl:equivalentClass min(?P, ?C)) (?R2 owl:equivalentClass min(?P, ?C))
					notEqual(?R1, ?R2) -> (?R1 owl:equivalentClass ?R2) ]
[restrictionEq4: (?R1 owl:equivalentClass max(?P, ?C)) (?R2 owl:equivalentClass max(?P, ?C))
					notEqual(?R1, ?R2) -> (?R1 owl:equivalentClass ?R2) ]
[restrictionEq5: (?R1 owl:equivalentClass card(?P, ?C)) (?R2 owl:equivalentClass card(?P, ?C))
					notEqual(?R1, ?R2) -> (?R1 owl:equivalentClass ?R2) ]
[restrictionEq6: (?R1 owl:equivalentClass hasValue(?P, ?C)) (?R2 owl:equivalentClass hasValue(?P, ?C))
					notEqual(?R1, ?R2) -> (?R1 owl:equivalentClass ?R2) ]
					
#[restrictionPropagate1: (?C owl:equivalentClass ?R), (?D rdfs:subClassOf ?C)
#                                -> (?D rdfs:subClassOf ?R) ]
#[restrictionPropagate2: (?C owl:equivalentClass ?R), (?D owl:equivalentClass ?C) 
#                                -> (?D owl:equivalentClass ?R) ]


#------------------------------------------------------------------
# One direction of unionOf
#------------------------------------------------------------------

[unionOf1:  (?C owl:unionOf ?L) -> listMapAsSubject(?L, rdfs:subClassOf ?C) ]

# Note could also add relation between two unionOf's if we add a listSubsumes primitive

#------------------------------------------------------------------
# Intersection of (instance reasoning is done by the translation hook)
#------------------------------------------------------------------

[intersectionOf1:  (?C owl:intersectionOf ?L) -> listMapAsObject(?C rdfs:subClassOf ?L) ]

#------------------------------------------------------------------
# someValuesFrom - recognition direction only
#------------------------------------------------------------------
    
[someRec2: (?C owl:equivalentClass some(?P, ?D)) ->
     [someRec2b: (?X rdf:type ?C) <- (?X ?P ?A) (?A rdf:type ?D) ] ]
    
[someRec2b: (?C owl:equivalentClass some(?P, ?D)), (?D rdf:type rdfs:Datatype)->
     [someRec2b: (?X rdf:type ?C) <- (?X ?P ?A), isDType(?A, ?D) ] ]

# In the absence of prototype and bNode introduction rules we have to manually
# code in additional subclass relationships

[restriction-inter-MnS: (?P rdfs:range ?D), (?C rdfs:subClassOf min(?P, 1)) 
						-> (?C rdfs:subClassOf some(?P, ?D)) ]
						
#------------------------------------------------------------------
# allValuesFrom (main rule is in Mini, this just does minimal subclass propagation
#------------------------------------------------------------------

[allRec1: (?C rdfs:subClassOf max(?P, 1)), (?C rdfs:subClassOf some(?P, ?D))
						-> (?C rdfs:subClassOf all(?P, ?D)) ]

[allRec2: (?P rdf:type owl:FunctionalProperty), (?C rdfs:subClassOf some(?P, ?C))
						 -> (?C rdfs:subClassOf all(?P, ?C)) ]
    
[allRec4: (?P rdf:type owl:FunctionalProperty), (?C owl:equivalentClass all(?P, ?D))
                         -> [ (?X rdf:type ?C) <- (?X ?P ?Y) (?Y rdf:type ?D) ] ]
    
[allRec5: (?C rdfs:subClassOf max(?P, 1)) (?C owl:equivalentClass all(?P, ?D))
                         -> [ (?X rdf:type ?C) <- (?X ?P ?Y) (?Y rdf:type ?D) ] ]
    
[restriction-inter-RA-T: (?P rdfs:range ?C), (?D owl:equivalentClass all(?P, ?C)) 
						-> (owl:Thing rdfs:subClassOf ?D) ]
						
[restriction-inter-AT-R: (owl:Thing rdfs:subClassOf all(?P, ?C)) 
						-> (?P rdfs:range ?C), (?P rdf:type owl:ObjectProperty) ]
						
#------------------------------------------------------------------
# Restricted support for hasValue, even though that is beyond OWL/lite
#------------------------------------------------------------------

# hasValue
[hasValueIF: (?C owl:equivalentClass hasValue(?P, ?V)) -> 
								[ (?x ?P ?V) <- (?x rdf:type ?C) ]
								[ (?x rdf:type ?C) <- (?x ?P ?V) ]
								]

#------------------------------------------------------------------
# Nothing
#------------------------------------------------------------------
    
[nothing1: (?C rdfs:subClassOf min(?P, ?n)) (?C rdfs:subClassOf max(?P, ?x))
           lessThan(?x, ?n)  ->  (?C owl:equivalentClass owl:Nothing) ]
           
[nothing3: (?C rdfs:subClassOf owl:Nothing) ->  (?C owl:equivalentClass owl:Nothing) ]

[nothing4: (?C owl:oneOf rdf:nil) -> (?C owl:equivalentClass owl:Nothing) ]
           
#------------------------------------------------------------------
# Disjointness
#------------------------------------------------------------------

[distinct1: (?X owl:differentFrom ?Y) <- 
    (?C owl:disjointWith ?D), (?X rdf:type ?C), (?Y rdf:type ?D)   ]

# Exploding the pairwise assertions is simply done procedurally here.
# This is better handled by a dedicated equality reasoner any.
[distinct2: (?w owl:distinctMembers ?L) -> assertDisjointPairs(?L) ]

						
#------------------------------------------------------------------
# min cardinality
#------------------------------------------------------------------

[minRec: (?C owl:equivalentClass min(?P, 1)), notEqual(?P, rdf:type) ->
    [min2b: (?X rdf:type ?C) <- (?X ?P ?Y)] ]

#------------------------------------------------------------------
# max cardinality 1
#------------------------------------------------------------------

[maxRec: (?C owl:equivalentClass max(?P, 1)), (?P rdf:type owl:FunctionalProperty)
		-> (owl:Thing rdfs:subClassOf ?C) ]

#------------------------------------------------------------------
# max cardinality 0
#------------------------------------------------------------------

# For completeness this requires iff version of rdfs:domain working forwards which it does not just now
[maxRec2: (?C owl:equivalentClass max(?P, 0)), (?P rdfs:domain ?D), (?E owl:disjointWith ?D)
	-> (?E owl:equivalentClass ?C)]
	
[cardRec1: (?C owl:equivalentClass card(?P, 0)), (?P rdfs:domain ?D), (?E owl:disjointWith ?D)
	-> (?E owl:equivalentClass ?C)]
	
#------------------------------------------------------------------
# cardinality 1
#------------------------------------------------------------------

[restriction-inter-CFP: (?C owl:equivalentClass card(?P, 1)), (?P rdf:type owl:FunctionalProperty) ->
     (?C owl:equivalentClass min(?P, 1)) ]

[restriction6: (?C owl:equivalentClass min(?P, ?X)), (?C owl:equivalentClass max(?P, ?X)) 
       					-> (?C owl:equivalentClass card(?P, ?X))]

#------------------------------------------------------------------
# Validation rules. These are dormant by default but are triggered
# by the additional of a validation control triple to the graph.
#------------------------------------------------------------------

[validationDomainMax0: (?v rb:validation on()), (?C rdfs:subClassOf max(?P, 0)), (?P rdfs:domain ?C)  ->
    (?P rb:violation error('inconsistent property definition', 'Property defined with domain which has a max(0) restriction for that property (domain)', ?C) )
]

[validationMax0: (?v rb:validation on()), (?C rdfs:subClassOf max(?P, 0))  -> 
    [max2b: (?X rb:violation error('too many values', 'Value for max-0 property (prop, class)', ?P, ?C))
    			<- (?X rdf:type ?C), (?X ?P ?Y) ] ]

[validationMaxN: (?v rb:validation on()), (?C rdfs:subClassOf max(?P, ?N)) ->
    [max2b: (?X rb:violation error('too many values', 'Too many values on max-N property (prop, class)', ?P, ?C))
    			<- (?X rdf:type ?C), countLiteralValues(?X, ?P, ?M), lessThan(?N, ?M)  ] ]

[validationIndiv: (?v rb:validation on())  ->
	[validationIndiv: (?X rb:violation error('conflict', 'Two individuals both same and different, may be due to disjoint classes or functional properties', ?Y)) 
				<- (?X owl:differentFrom ?Y), (?X owl:sameAs ?Y) ] ]
				
[validationIndiv2: (?v rb:validation on()) (?X owl:disjointWith ?Y) -> 
	[validationIndiv: (?I rb:violation error('conflict', 'Individual a member of disjoint classes', ?X, ?Y)) 
				<- (?I rdf:type ?X), (?I rdf:type ?Y)] ]

[validationIndiv3: (?v rb:validation on()) ->
	[validationIndiv: (?I rb:violation error('conflict', 'Individual a member of Nothing', ?I)) 
				<- (?I rdf:type owl:Nothing) ] ]

[validationDisjoint: (?v rb:validation on()) (?X owl:disjointWith ?Y)  ->
	[validationIndiv: (?X rb:violation warn('Inconsistent class', 'Two classes related by both subclass and disjoint relations', ?Y)) 
				<- (?X owl:disjointWith ?Y), (?X rdfs:subClassOf ?Y) ] ]

[validationDisjoint2: (?v rb:validation on()) (?X owl:disjointWith ?Y) ->
	[validationIndiv: (?C rb:violation warn('Inconsistent class', 'subclass of two disjoint classes', ?X, ?Y)) 
				<- (?X owl:disjointWith ?Y), (?C rdfs:subClassOf ?X) (?C rdfs:subClassOf ?Y) notEqual(?C, owl:Nothing) ] ]

[validationDTP: (?v rb:validation on()), (?P rdf:type owl:DatatypeProperty) ->
	[validationDTP: (?X rb:violation error('range check', 'Object value for datatype property (prop, value)', ?P, ?V))
				<- (?X ?P ?V), notLiteral(?V), notBNode(?V) ] ]

[validationOP: (?v rb:validation on()), (?P rdf:type owl:ObjectProperty) ->
	[validationDTP: (?X rb:violation warn('range check', 'Literal value for object property (prop, value)', ?P, ?V))
				<- (?X ?P ?V), isLiteral(?V) ] ]

[validationDTRange: (?v rb:validation on()), (?P rdfs:range ?R) (?R rdf:type rdfs:Datatype) ->
	[validationDTRange: (?X rb:violation error('range check', 'Incorrectly typed literal due to range (prop, value)', ?P, ?V))
				<- (?X ?P ?V), notDType(?V, ?R)  ] ]

[validationDTRange: (?v rb:validation on()), (?P rdfs:range rdfs:Literal)  ->
	[validationDTRange: (?X rb:violation error('range check', 'Incorrectly typed literal due to range rdsf:Literal (prop, value)', ?P, ?V))
				<- (?X ?P ?V), notLiteral(?V), notBNode(?V) ] ]

[validationAllFrom: (?v rb:validation on()), (?C rdfs:subClassOf all(?P, ?R)) (?R rdf:type rdfs:Datatype) ->
	[validationDTRange: (?X rb:violation error('range check', 'Incorrectly typed literal due to allValuesFrom (prop, value)', ?P, ?V))
				<- (?X ?P ?V), (?X rdf:type ?C), notDType(?V, ?R) ] ]

[validationAllFrom: (?v rb:validation on()), (?C owl:equivalentClass all(?P, rdfs:Literal)) -> 
	[validationDTRange: (?X rb:violation error('range check', 'Incorrectly typed literal due to allValuesFrom rdfs:Literal (prop, value)', ?P, ?V))
				<- (?X ?P ?V), (?X rdf:type ?C), notDType(?V, rdfs:Literal) 
				 ] ]

[validationNothing: (?v rb:validation on()), (?C owl:equivalentClass owl:Nothing) notEqual(?C, owl:Nothing) -> 
	(?C rb:violation warn('Inconsistent class', 'Class cannot be instantiated, probably subclass of a disjoint classes or of an empty restriction'))
]

[validationRangeNothing: (?v rb:validation on()), (?P rdfs:range owl:Nothing) -> 
	(?C rb:violation warn('Inconsistent property', 'Property cannot be instantiated, probably due to multiple disjoint range declarations'))
]

[validationOneOf: (?v rb:validation on()) (?C owl:oneOf ?L) ->
	[validationIndiv: (?X rb:violation warn('possible oneof violation', 'Culprit is deduced to be of enumerated type (implicicated class) but is not one of the enumerations\n This may be due to aliasing.', ?Y)) 
				<- (?X rdf:type ?C), notBNode(?X), listNotContains(?L, ?X) ] ]