Knowledge Bases

In Ontolearn we represent a knowledge base by the class KnowledgeBase which contains two main class attributes, an ontology AbstractOWLOntology and a reasoner AbstractOWLReasoner. It also contains the class and properties hierarchy as well as other Ontology-related attributes required for the Structured Machine Learning library.

Knowledge Base vs Ontology

These terms may be used interchangeably sometimes but in Ontolearn they are not the same thing, although they share a lot of similarities. An ontology in owlapy, as explained here is the object where we load the OWL 2.0 ontologies from a .owl file containing the ontology in an RDF/XML or OWL/XML format. On the other side a KnowledgeBase is a class which combines an ontology and a reasoner together. Therefore, differently from the ontology you can use methods that require reasoning. You can check the methods for each in the links below:

In summary:

  • An instance of KnowledgeBase contains an ontology and a reasoner and is required to run a learning algorithm.

  • The ontology object can load an OWL 2.0 ontology, be modified using the ontology manager and saved.

  • Although they have some similar functionalities, there are a lot of other distinct functionalities that each of them has.

Create an Object of KnowledgeBase

Let us show how you can initialize an object of KnowledgeBase. We consider that you have already an OWL 2.0 ontology (containing .owl extension).

The simplest way is to use the path of your .owl file as follows:

from ontolearn.knowledge_base import KnowledgeBase

kb = KnowledgeBase(path="file://KGs/Family/father.owl")

What happens in the background is that the ontology located in this path will be loaded in the AbstractOWLOntology object of kb as done here.

In our recent version you can also initialize a knowledge base using a dataset hosted in a triplestore. Since that knowledge base is mainly used for executing a concept learner, we cover that matter more in depth in Use Triplestore Knowledge Base section of Concept Learning.

Ignore Concepts

During concept learning which we describe later, you may need to avoid trivial solutions from being learned. So in Ontolearn you have the opportunity to ignore specific concepts. Since we pass a KnowledgeBase object to the concept learner, we set this ignored concept using the method ignore_and_copy of the KnowledgeBase class.

We don’t have such concept in our example ontology KGs/Family/father.owl but suppose that there is a class(concept) “Father” that we want to ignore, because we are trying to learn this a meaningful class expression for ‘Father’ using other classes(e.g. male, female, ∃ hasChild.⊤… ). So we need to ignore this concept before fitting a model (model fitting is covered in concept learning). It can be done as follows:

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

iri = IRI('http://example.com/father#', 'Father')
father_concept = OWLClass(iri)
concepts_to_ignore = {father_concept}  # you can add more than 1

new_kb = kb.ignore_and_copy(ignored_classes=concepts_to_ignore)

In this example, we have created an instance of OWLClass by using an IRI. On the other side, an instance of IRI is created by passing two parameters which are the namespace of the ontology and the remainder ‘Father’.

Accessing Individuals

You may need to work with individuals of a knowledge base. We cover different ways of accessing them.

Let us give a simple example of how to get the individuals that are classified by an OWLClassExpression. As a class expression, we will simply use the concept ‘male’.

NS = 'http://example.com/father#'
male_concept = OWLClass(IRI(NS,'male'))

male_individuals = kb.individuals(male_concept)

Note that the namespace has to match the Namespace/IRI that is defined in the Ontology.

male_individuals will contain all the individuals of type ‘male’. Keep in mind that OWLClass inherit from OWLClassExpression. Depending on the reasoner that the kb object is using the results may differ slightly but in case of a small dataset like the one we are using for this example, the results do not change.

If you don’t give any argument than this method returns all the individuals in the ontology:

all_individuals = kb.individuals()

You can as well get all the individuals using:

all_individuals_set  = kb.all_individuals_set()

The difference is that individuals() return type is Iterable[OWLNamedIndividual] and all_individuals_set() return type is frozenset(OWLNamedIndividual).

In case you need your result as frozenset, individual_set method is a better option then the individuals method:

male_individuals_set = kb.individuals_set(male_concept)

Or you can even combine both methods:

male_individuals_set = kb.individuals_set(male_individuals)

Evaluate a Concept

When using a concept learner, the generated concepts (class expressions) for a certain learning problem need to be evaluated to see the performance. To do that you can use the method evaluate_concept of KnowledgeBase. It requires the following arguments:

  1. a concept to evaluate: OWLClassExpression

  2. a quality metric: AbstractScorer

  3. the encoded learning problem: EncodedLearningProblem

The evaluation should be done for the learning problem that you used to generate the concept. The main result of the evaluation is the quality score describing how well the generated concept is doing on the job of classifying the positive individuals. The concept learners do this process automatically.

Construct a learning problem

To evaluate a concept you need a learning problem. Firstly, we create two simple sets containing the positive and negative examples for the concept of ‘Father’. Our positive examples (individuals to describe) are stefan, markus, and martin. And our negative examples (individuals to not describe) are heinz, anna, and michelle.

from owlapy.owl_individual import OWLNamedIndividual

positive_examples = {OWLNamedIndividual(IRI.create(NS, 'stefan')),
                     OWLNamedIndividual(IRI.create(NS, 'markus')),
                     OWLNamedIndividual(IRI.create(NS, 'martin'))}

negative_examples = {OWLNamedIndividual(IRI.create(NS, 'heinz')),
                     OWLNamedIndividual(IRI.create(NS, 'anna')),
                     OWLNamedIndividual(IRI.create(NS, 'michelle'))}

Now the learning problem can be captured in its respective object, the positive-negative standard learning problem and encode it using the method encode_learning_problem of KnowledgeBase:

from ontolearn.learning_problem import PosNegLPStandard

lp = PosNegLPStandard(pos=positive_examples, neg=negative_examples)

encoded_lp = kb.encode_learning_problem(lp)

Now that we have an encoded learning problem, we need a concept to evaluate.

Construct a concept

Suppose that the class expression (¬female) ⊓ (∃ hasChild.⊤) was generated by CELOE for the concept of ‘Father’. We will see how that can happen later but for now we let’s construct this class expression manually:

from owlapy.owl_property import OWLObjectProperty
from owlapy.class_expression import OWLObjectSomeValuesFrom , OWLObjectIntersectionOf

female = OWLClass(IRI(NS,'female'))
not_female = kb.generator.negation(female)
has_child_property = OWLObjectProperty(IRI(NS, "hasChild"))
thing = OWLClass(IRI('http://www.w3.org/2002/07/owl#', 'Thing'))
exist_has_child_T = OWLObjectSomeValuesFrom(property=has_child_property, filler=thing)

concept_to_test = OWLObjectIntersectionOf([not_female, exist_has_child_T])

kb has an instance of ConceptGenerator which we use in this case to create the negated concept ¬female. The other classes OWLObjectProperty, OWLObjectSomeValuesFrom and OWLObjectIntersectionOf are classes that represent different kind of axioms in owlapy and can be found in owlapy.class_expression module. There are more kind of axioms there which you can use to construct class expressions like we did in the example above.

Evaluation and results

You can now evaluate the concept you just constructed as follows:

from ontolearn.metrics import F1

evaluated_concept = kb.evaluate_concept(concept_to_test, F1(), encoded_lp)

In this example we use F1-score to evaluate the concept, but there are more metrics which you can use including Accuracy, Precision and Recall.

You can now:

  • Print the quality:

    print(evaluated_concept.q) # 1.0

  • Print the set of individuals covered by the hypothesis:

    for ind in evaluated_concept.inds:
    print(ind) 

# OWLNamedIndividual(http://example.com/father#markus)
# OWLNamedIndividual(http://example.com/father#martin)
# OWLNamedIndividual(http://example.com/father#stefan)

  • Print the amount of them:

    print(evaluated_concept.ic) # 3

Obtaining axioms

You can retrieve Tbox and Abox axioms by using tbox and abox methods respectively. Let us take them one at a time. The tbox method has 2 parameters, entities and mode. entities specifies the owl entity from which we want to obtain the Tbox axioms. It can be a single entity, a Iterable of entities, or None.

The allowed types of entities are:

  • OWLClass

  • OWLObjectProperty

  • OWLDataProperty

Only the Tbox axioms related to the given entit-y/ies will be returned. If no entities are passed, then it returns all the Tbox axioms. The second parameter mode (str) sets the return format type. It can have the following values:

  1. 'native' -> triples are represented as tuples of owlapy objects.

  2. 'iri' -> triples are represented as tuples of IRIs as strings.

  3. 'axiom' -> triples are represented as owlapy axioms.

For the abox method the idea is similar. Instead of the parameter entities, there is the parameter individuals which accepts an object of type OWLNamedIndividuals or Iterable[OWLNamedIndividuals].

If you want to obtain all the axioms (Tbox + Abox) of the knowledge base, you can use the method triples. It requires only the mode parameter.

NOTE: The results of these methods are limited only to named and direct entities. That means that especially the axioms that contain anonymous owl objects (objects that don’t have an IRI) will not be part of the result set. For example, if there is a Tbox T={ C ⊑ (A ⊓ B), C ⊑ D }, only the latter subsumption axiom will be returned.

Sampling the Knowledge Base

Sometimes ontologies and therefore knowledge bases can get very large and our concept learners become inefficient in terms of runtime. Sampling is an approach to extract a portion of the whole knowledge base without changing its semantic and still being expressive enough to yield results with as little loss of quality as possible. OntoSample is a library that we use to perform the sampling process. It offers different sampling techniques which fall into the following categories:

  • Node-based samplers

  • Edge-based samplers

  • Exploration-based samplers

and almost each sampler is offered in 3 modes:

  • Classic

  • Learning problem first (LPF)

  • Learning problem centered (LPC)

You can check them here.

When operated on its own, Ontosample uses a light version of Ontolearn (ontolearn_light) to reason over ontologies, but when both packages are installed in the same environment it will use ontolearn module instead. This is made for compatibility reasons.

Ontosample treats the knowledge base as a graph where nodes are individuals and edges are object properties. However, Ontosample also offers support for data properties sampling, although they are not considered as “edges”.

Sampling steps:

  1. Initialize the sample using a KnowledgeBase object. If you are using an LPF or LPC sampler than you also need to pass the set of learning problem individuals (lp_nodes).

  2. To perform the sampling use the sample method where you pass the number of nodes (nodes_number) that you want to sample, the amount of data properties in percentage (data_properties_percentage) that you want to sample which is represented by float values form 0 to 1 and jump probability (jump_prob) for samplers that use “jumping”, a technique to avoid infinite loops during sampling.

  3. The sample method returns the sampled knowledge which you can store to a variable, use directly in the code or save locally by using the static method save_sample.

Let’s see an example where we use RandomNodeSampler to sample a knowledge base:

from ontosample.classic_samplers import RandomNodeSampler

# 1. Initialize KnowledgeBase object using the path of the ontology
kb = KnowledgeBase(path="KGs/Family/family-benchmark_rich_background.owl")

# 2. Initialize the sampler and generate the sample
sampler = RandomNodeSampler(kb)
sampled_kb = sampler.sample(30) # will generate a sample with 30 nodes

# 3. Save the sampled ontology
sampler.save_sample(kb=sampled_kb, filename="some_name")

Here is another example where this time we use an LPC sampler:

from ontosample.lpc_samplers import RandomWalkerJumpsSamplerLPCentralized
from owlapy.owl_individual import OWLNamedIndividual,IRI
import json

# 0. Load json that stores the learning problem
with open("examples/uncle_lp2.json") as json_file:
    examples = json.load(json_file)

# 1. Initialize KnowledgeBase object using the path of the ontology
kb = KnowledgeBase(path="KGs/Family/family-benchmark_rich_background.owl")

# 2. Initialize learning problem (required only for LPF and LPC samplers)
pos = set(map(OWLNamedIndividual, map(IRI.create, set(examples['positive_examples']))))
neg = set(map(OWLNamedIndividual, map(IRI.create, set(examples['negative_examples']))))
lp = pos.union(neg)

# 3. Initialize the sampler and generate the sample
sampler = RandomWalkerJumpsSamplerLPCentralized(graph=kb, lp_nodes=lp)
sampled_kb = sampler.sample(nodes_number=40,jump_prob=0.15)

# 4. Save the sampled ontology
sampler.save_sample(kb=sampled_kb, filename="some_other_name")

WARNING! Random walker and Random Walker with Prioritization are two samplers that suffer from non-termination in case that the ontology contains nodes that point to each other and form an inescapable loop for the “walker”. In this scenario you can use their “jumping” version to make the “walker” escape these loops and ensure termination.

To see how to use a sampled knowledge base for the task of concept learning check the sampling_example.py in examples folder. You will find descriptive comments in that script that will help you understand it better.

For more details about OntoSample you can see this paper.

Since we cannot cover everything here in details, see KnowledgeBase API documentation to check all the methods that this class has to offer. You will find convenient methods to access the class/property hierarchy, methods that use the reasoner indirectly and a lot more.

In the next guide we will walk through how to use concept learners to learn class expressions in a knowledge base for a certain learning problem.