Reasoning over OWL cardinality restriction - owl

Question

I think I still have a fundamental misunderstanding of OWL axioms :(.
Here is a small test ontology I created:
#prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
#prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
#prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
#prefix owl: <http://www.w3.org/2002/07/owl#> .
#prefix : <http://foobar.com/test/> .
: a owl:Ontology .
:prop1 a owl:DatatypeProperty .
:prop2 a owl:DatatypeProperty .
:Class1 owl:equivalentClass [
a owl:Restriction ;
owl:onProperty :prop1 ;
owl:cardinality "1"^^xsd:int
] .
:Ind1 a owl:NamedIndividual ;
:prop1 "value1"^^xsd:string .
:Class2 owl:equivalentClass [
a owl:Restriction ;
owl:onProperty :prop2 ;
owl:minCardinality "1"^^xsd:int
] .
:Ind2 a owl:NamedIndividual ;
:prop2 "value2"^^xsd:string .
When I run the Hermit reasoner in Protege over this, I get the expected result with :Ind2, that is it is a member of :Class2. But I am not getting the same for :Ind1 with regards to being a member of :Class1.
I am suspecting that this has to do with open world assumption and that it is possible that :Ind1 might still have another :prop1 assertion. So couple of questions:
Have I diagnosed the problem correctly?
Can I get an example of how I can get my goal for hermit to reason that :Ind1 is a member of :Class1 without explicitly making the assertion?
Thanks

Answer 1

Premise
OWL semantics is defined under open-world assumption, so you can't check if the cardinality for a certain property is exactly N, because there may be other property instances even if not declared.
More precisely, these are the checks that you can do:
Cardinality check
Possible answers
Sound
Complete
At-least N
Yes (if N or more)I don't know (otherwise)
Yes
No
Exactly N
No (if N+1 or more)I don't know (otherwise)
Yes
No
At-most N
No (if N+1 or more)I don't know (otherwise)
Yes
No
Solution
You can check if a cardinality is exactly 1 only if you explicitly state that "value1" is the only value for :Ind1. In this case :Ind1 will be part of :Class1.
In FOL:
∀x.(R(Ind1, x) → x = "value1")
In DL:
∃R⁻.{Ind1} ⊑ {"value1"}
In OWL2 (not tested):
:Ind1
a owl:NamedIndividual ;
a [ a owl:Restriction ;
owl:onProperty :prop1 ;
owl:allValuesFrom [ a rdfs:Datatype ;
owl:oneOf ( "value1"^^xsd:string )
]
] .

Answer 2

Thanks to #horcrux for providing the hint. What worked finally is to also declare the properties as owl:FunctionalProperty. Editing the property declarations to:
:prop1 a owl:DatatypeProperty, owl:FunctionalProperty .
:prop2 a owl:DatatypeProperty, owl:FunctionalProperty .
This does not require adding additional restrictions to each individual declaration.