I have the axiom: individual A does not like what individual B likes. Then, there are the properties, like and dislike. I want to be inferred that when someone does not like something then he dislikes it.
I have added that like and dislike are disjoint but I don't know how to go further using Protege.
If you do not insist on inferring object properties, there is a workaround using the covering axiom which sort of closes the world.
Let's say we have a :Person_A and if he/she doesn't like something, then he/she dislikes it. The focus needs to be changed to the things that :Person_A likes or dislikes. They would belong to the class :ThingsThatAHasAttitudeTo.
First, it is important to declare a property for both liking and disliking.
:dislikes rdf:type owl:ObjectProperty ;
rdfs:subPropertyOf :hasAttitude ;
owl:inverseOf :isDislikedBy .
:hasAttitude rdf:type owl:ObjectProperty .
:isDislikedBy rdf:type owl:ObjectProperty ;
rdfs:subPropertyOf :isLikedOrDislikedBy .
:isLikedBy rdf:type owl:ObjectProperty ;
rdfs:subPropertyOf :isLikedOrDislikedBy ;
owl:inverseOf :likes .
:isLikedOrDislikedBy rdf:type owl:ObjectProperty .
:likes rdf:type owl:ObjectProperty ;
rdfs:subPropertyOf :hasAttitude .
Then, if you have an enumerated class containing only the individual Person_A,
:PersonClass_A rdf:type owl:Class ;
owl:equivalentClass [ rdf:type owl:Class ;
owl:oneOf ( :PersonClass_A
)
] .
the following restrictions would be needed, for things liked:
:ThingsThatALikes rdf:type owl:Class ;
owl:equivalentClass [ owl:intersectionOf ( :ThingsThatAHasAttitudeTo
[ rdf:type owl:Restriction ;
owl:onProperty :isLikedBy ;
owl:someValuesFrom :PersonClass_A
]
) ;
rdf:type owl:Class
] .
... and for things disliked:
:ThingsThatADislikes rdf:type owl:Class ;
owl:equivalentClass [ rdf:type owl:Class ;
owl:unionOf ( [ owl:intersectionOf ( :ThingsThatAHasAttitudeTo
[ rdf:type owl:Restriction ;
owl:onProperty :isDislikedBy ;
owl:someValuesFrom :PersonClass_A
]
) ;
rdf:type owl:Class
]
[ owl:intersectionOf ( :ThingsThatAHasAttitudeTo
[ rdf:type owl:Restriction ;
owl:onProperty :isLikedOrDislikedBy ;
owl:someValuesFrom :PersonClass_A
]
) ;
rdf:type owl:Class
]
)
] .
And last, it is important to cover the class :ThingsThatAHasAttitudeTo
:ThingsThatAHasAttitudeTo rdf:type owl:Class ;
rdfs:subClassOf [ rdf:type owl:Class ;
owl:unionOf ( :ThingsThatADislikes
:ThingsThatALikes
)
] .
The classes needs to be disjoint and the individuals different.
With these definitions, if there are individuals that are members of the class :ThingsThatAHasAttitudeTo, for those of them that is not asserted that :Person_A likes, they will be inferred as members of the class :ThingsThatADislikes.