I am having problems with DL Queries that are based on object property cardinality and I am not sure if I am doing something wrong, or there is something wrong with HermiT.
First of all, I've attached a very simple ontology which demonstrates my problem. There are only two individuals A and B and the object property hasSomething. A hasSomething B is true.
The following DL Query returns A as a result:
hasSomething min 1
While the query
hasSomething exactly 1
cannot be satisfied.
Does anyone have an idea why the first one works and the second doesn't?
@prefix : <http://www.semanticweb.org/cg/ontologies/2015/9/untitled-ontology-3#> .
@prefix owl: <http://www.w3.org/2002/07/owl#> .
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix xml: <http://www.w3.org/XML/1998/namespace> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@base <http://www.semanticweb.org/cg/ontologies/2015/9/untitled-ontology-3> .
<http://www.semanticweb.org/cg/ontologies/2015/9/untitled-ontology-3> rdf:type owl:Ontology .
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#
# Object Properties
#
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### http://www.semanticweb.org/cg/ontologies/2015/9/untitled-ontology-3#hasSomething
:hasSomething rdf:type owl:ObjectProperty .
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#
# Classes
#
#################################################################
### http://www.semanticweb.org/cg/ontologies/2015/9/untitled-ontology-3#SimpleClass
:SimpleClass rdf:type owl:Class .
#################################################################
#
# Individuals
#
#################################################################
### http://www.semanticweb.org/cg/ontologies/2015/9/untitled-ontology-3#A
:A rdf:type owl:NamedIndividual ;
:hasSomething :B .
### http://www.semanticweb.org/cg/ontologies/2015/9/untitled-ontology-3#B
:B rdf:type owl:NamedIndividual .
### Generated by the OWL API (version 3.5.1) http://owlapi.sourceforge.net
The query cannot be fulfilled because of the Open World Assumption (OWA).
From the OWL2 Primer:
If some fact is not present in a database, it is usually considered false (the so-called closed-world assumption) whereas in the case of an OWL 2 document it may simply be missing (but possibly true), following the open-world assumption.
csnyluas, who is a protegé contributor / maintainer gave the following answer:
This is correct. Because of the open world assumption (OWA) in OWL, from your assertions the reasoner cannot infer that A has no other "hasSomething" relationships to other individuals than B.
If you would modify your ontology to state that A is of type SimpleClass, and that SimpleClass is subclass of "hasSomething exactly 1", then the reasoner would return A as instance of both "hasSomething min 1" and "hasSomething exactly 1".