Basic Usage

The main usage for owlapy is to use it for class expression construction. Class expression learning algorithms require such basic structure to work upon. Let’s walk through an example of constructing some class expressions.

In this example we will be using the family ontology, a simple ontology with namespace: http://example.com/family#. Here is a hierarchical diagram that shows the classes and their relationship:

         Thing
           |
        person
       /   |   
   male  female

It contains only one object property which is hasChild and in total there are six persons (individuals), of which four are males and two are females.

Atomic Classes

To represent the classes male, female, and person we can simply use the class OWLClass:

from owlapy.class_expression import OWLClass
from owlapy.iri import IRI

namespace = "http://example.com/family#"

male = OWLClass(IRI(namespace, "male"))
female = OWLClass(IRI(namespace, "female"))
person = OWLClass(IRI(namespace, "person"))

Notice that we created an IRI object for every class. IRI is used to represent an IRI. Every named entity requires an IRI, whereas Anonymous entities does not. However, in owlapy you can create an OWLClass by passing the IRI directly as a string, like so:

male = OWLClass("http://example.com/family#male")

Object Property

To represent the object property hasChild we can use the class OWLObjectProperty:

from owlapy.owl_property import OWLObjectProperty

hasChild = OWLObjectProperty("http://example.com/family#hasChild")

Tip: In owlapy the naming of the classes is made in accordance with the notations from OWL 2 specification but with the word “OWL” in the beginning. Example: “OWLObjectProperty” represents the notation “ObjectProperty”.

Complex class expressions

Now that we have these atomic entities, we can construct more complex class expressions. Let’s say we want to represent all individuals which are male and have at least 1 child.

We already have the concept of male. We need to find the appropriate class for the second part: “have at least 1 child”. In OWL 2 specification that would be ObjectMinCardinality. In owlapy, as we said, we simply add the word “OWL” upfront to find the correct class:

from owlapy.class_expression import OWLObjectMinCardinality

has_at_least_one_child = OWLObjectMinCardinality(
    cardinality = 1, 
    property = hasChild,
    filler = person
)

As you can see, to create an object of class OWLObjectMinCardinality is as easy as that. You specify the cardinality which in this case is 1, the object property where we apply this cardinality restriction and the filler class in case you want to restrict the domain of the class expression. In this case we used person.

Now let’s merge both class expressions together using OWLObjectIntersectionOf:

from owlapy.class_expression import OWLObjectIntersectionOf

ce = OWLObjectIntersectionOf([male, has_at_least_one_child])

Convert to SPARQL, DL or Manchester syntax

Owlapy is not just a library to represent OWL entities, you can also use it to convert owl expressions into other formats:

from owlapy import owl_expression_to_sparql, owl_expression_to_dl, owl_expression_to_manchester

print(owl_expression_to_dl(ce))
# Result: male ⊓ (≥ 1 hasChild.person)

print(owl_expression_to_sparql(ce))
# Result: SELECT DISTINCT ?x WHERE { ?x a <http://example.com/family#male> . { SELECT ?x WHERE { ?x <http://example.com/family#hasChild> ?s_1 . ?s_1 a <http://example.com/family#person> .  } GROUP BY ?x HAVING ( COUNT ( ?s_1 ) >= 1 ) } }

print(owl_expression_to_manchester(ce))
# Result: male and (hasChild min 1 person)

To parse a DL or Manchester expression to owl expression you can use the following convenient methods:

from owlapy import dl_to_owl_expression, manchester_to_owl_expression

print(dl_to_owl_expression("∃ hasChild.male", namespace))
# Result: OWLObjectSomeValuesFrom(property=OWLObjectProperty(IRI('http://example.com/family#','hasChild')),filler=OWLClass(IRI('http://example.com/family#','male')))

print(manchester_to_owl_expression("female and (hasChild max 2 person)", namespace))
# Result: OWLObjectIntersectionOf((OWLClass(IRI('http://example.com/family#','female')), OWLObjectMaxCardinality(property=OWLObjectProperty(IRI('http://example.com/family#','hasChild')),2,filler=OWLClass(IRI('http://example.com/family#','person')))))

More tools

Owlapy also provides some useful tools to work with OWL expressions. For example, you can use CESimplifier which is a syntactic class expression simplifier following the Unique Name Assumption (UNA) under Close world Assumption (CWA) to simplify class expressions. You can directly call the function simplify_class_expression which uses a predefined instance of CESimplifier. For interpretability, we will use concepts in description logic (DL) syntax to show the examples.

from owlapy import dl_to_owl_expression, owl_expression_to_dl
from owlapy.utils import simplify_class_expression

ce_dl = "(A ⊓ B) ⊓ (C ⊓ (B ⊔ (C ⊔ E)))"
ce_owl = dl_to_owl_expression(ce_dl, "http://example_namespace.org/")

ce_owl_simplified = simplify_class_expression(ce_owl)
ce_dl_simplified = owl_expression_to_dl(ce_owl_simplified)
print(ce_dl_simplified) # "A ⊓ B ⊓ C"

You can get the top-level Disjunctive Normal Form (DNF) or top-level Conjunctive Normal Form (CNF) as shown below:

from owlapy import dl_to_owl_expression, owl_expression_to_dl
from owlapy.utils import get_top_level_dnf, get_top_level_cnf

ce1_dl = "(A ⊔ B) ⊓ (A ⊔ C)"
ce2_dl = "(A ⊓ B) ⊓ (C ⊓ (B ⊔ (C ⊔ E)))"
ce1_owl = dl_to_owl_expression(ce1_dl, "http://example_namespace.org/")
ce2_owl = dl_to_owl_expression(ce2_dl, "http://example_namespace.org/")

ce1_owl_tl_dnf = get_top_level_dnf(ce1_owl)
ce2_owl_tl_cnf = get_top_level_dnf(ce2_owl)

ce1_dl_tl_dnf = owl_expression_to_dl(ce1_owl_tl_dnf)
ce2_dl_tl_cnf = owl_expression_to_dl(ce2_owl_tl_cnf)

print(ce1_dl_tl_dnf) # A ⊔ (A ⊓ B) ⊔ (A ⊓ C) ⊔ (B ⊓ C)
print(ce2_dl_tl_cnf) # (A ⊓ B ⊓ C) ⊔ (A ⊓ B ⊓ C ⊓ E)

Get the negation normal form (NNF) simply by calling get_nnf() directly from the class expression:

from owlapy import dl_to_owl_expression, owl_expression_to_dl

ce_dl = "¬(A ⊓ (B ⊔ C))"
ce_owl = dl_to_owl_expression(ce_dl, "http://example_namespace.org/")

ce_owl_nnf = ce_owl.get_nnf()
ce_dl_nnf = owl_expression_to_dl(ce_owl_nnf)

print(ce_dl_nnf) # (¬A) ⊔ ((¬B) ⊓ (¬C))

You can also measure the length of a class expression using OWLClassExpressionLengthMetric. You can set the weights for different types of constructors. We will continue with the default weights so we are going to call directly the function get_expression_length which uses a predefined instance of OWLClassExpressionLengthMetric:

from owlapy import dl_to_owl_expression
from owlapy.utils import get_expression_length

ce_dl = "(∀r_1.⊤) ⊓ (∀r_2.(¬C)) ⊓ (∃r_3.{i1 ⊔ i2 ⊔ i5}) ⊓ A"
ce_owl = dl_to_owl_expression(ce_dl, "http://example_namespace.org/")

length = get_expression_length(ce_owl)

print(length) # 14 

In these examples we showed a part of owlapy. You can explore the api documentation to learn more about all classes in owlapy and check more examples in the examples or tests directory