added patrick's theses

_theses_dir/PK_Explain_Negative.md

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+---
+title: 'Explaining Missing Entailments from Ontologies'
+layout: default
+description: 'In this project, you will develop methods for explaining missing entailments from ontologies.'
+topic: 'Ontologies and Reasoning' 
+keywords: 
+    - 'Ontologies'
+    - 'Explainability'
+    - 'Reasoning'
+    - 'Logics'
+    - 'Description Logics'
+supervisor: 'Patrick Koopmann'
+contact: 'p.k.koopmann@vu.nl'
+degree: 'M.Sc./B.Sc.'
+description_link: '/theses_dir/PK_Explain_Negative'
+---
+
+## Thesis title:  Explaining Missing Entailments from Ontologies
+*Supervisor: Patrick Koopmann (p.k.koopmann@vu.nl)*
+
+Ontologies are an important representation formalism for symbolic AI
+systems. Ontologies that are formulated in OWL allow to usage of
+reasoning systems such as HermiT or ELK to infer implicit information
+from an ontology, or from a dataset that is combined with the ontology.
+Different to inferences performed by sub-symbolic AI systems,
+decisions made by such a reasoner are in a way "explainable by
+design", because all inferences can be explained solely based on the
+information available in the ontology.
+
+But what do you do if the reasoner does not infer the expected result,
+how do you explain missing entailments? In the research literature,
+there are currently two main approaches to provide such explanations:
+1) counterexamples and 2) abduction. A counterexample explains a
+missing entailment by showing a scenario that is fully consistent with
+the ontology, but which makes it very clear that the expected
+entailment does not hold. Abduction by contrast explains the missing
+entailment by offering a fix, an extension to the current ontology
+that would produce the desired inference. In this project, you will
+choose one of these two techniques, and then develop and evaluate
+extensions/modifications of current methods for computing such
+explanations, towards making them more efficient or producing better
+explanations.
+
+
+The supervisor will give an introduction to the topic
+(foundations of description logics, counterexamples, abduction) at the 
+beginning of the project. To get an idea, you can consult the
+following paper, which explains and discusses abduction-based
+explanations on an example:
+
+https://lat.inf.tu-dresden.de/research/papers/2023/ABFKK-DL23.pdf
+
+Don't be afraid to contact the supervisor if you would like to
+have more information on this project or would like to discuss it in
+more detail in person.

_theses_dir/PK_Explain_Positive.md

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+---
+title: 'Explaining Entailments from Ontologies'
+layout: default
+description: 'In this project, you will investigate and develop alternative ways of explaining reasoning with ontologies.'
+topic: 'Ontologies and Reasoning'
+keywords: 
+    - 'Ontologies'
+    - 'Explainability'
+    - 'Reasoning'
+    - 'Logics'
+    - 'Description Logics'
+supervisor: 'Patrick Koopmann'
+contact: 'p.k.koopmann@vu.nl'
+degree: 'M.Sc./B.Sc.'
+description_link: '/theses_dir/PK_Explain_Positive'
+---
+
+## Thesis title:  Explaining Entailments from Ontologies
+*Supervisor: Patrick Koopmann (p.k.koopmann@vu.nl)*
+
+Ontologies are an important representation formalism for symbolic AI
+systems. Ontologies that are formulated in OWL allow to usage of
+reasoning systems such as HermiT or ELK to infer implicit information
+from an ontology, or from a dataset that is combined with the ontology.
+Different to inferences performed by sub-symbolic AI systems,
+decisions made by such a reasoner are in a way "explainable by
+design", because all inferences can be explained solely based on the
+information available in the ontology. However, in practice,
+explanations provided to users by the state-of-the-art are not always
+so easy to understand. Recently, we have been developing newer
+techniques towards different types of explanations, that are supposed
+to make reasoning with ontologies truly explainable in practice. In
+this project, you will investigate alternative inference systems that
+can be used to create better explanations. In particular, you will
+develop a system of inference rules that can be used to produce more
+user-friendly explanations.
+
+The supervisor will give an introduction to the topic
+(foundations of description logics, rule-based reasoning) at the
+beginning of the project. To get an idea, you can consult the
+following paper, that describes the current proof-based explanation
+services in practice:
+
+https://imld.de/cnt/uploads/evee-evonne-dl2022.pdf
+
+Don't be afraid to contact the supervisor if you would like to
+have more information on this project or would like to discuss it in
+more detail in person.

_theses_dir/PK_Hypotheses.md

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+---
+title: 'Automated Hypothesis Generation using ABox Abduction'
+layout: default
+description: 'This project is about generating, with the help of ontologies, hypotheses for unexpected observations.'  
+topic: 'Ontologies and Reasoning' 
+keywords: 
+    - 'Ontologies'
+    - 'Logics'
+    - 'Reasoning'
+supervisor: 'Patrick Koopmann'
+contact: 'p.k.koopmann@vu.nl'
+degree: 'B.Sc.'
+description_link: '/theses_dir/PK_Hypotheses'
+---
+
+## Thesis title:  Automated Hypothesis Generation using ABox Abduction
+*Supervisor: Patrick Koopmann (p.k.koopmann@vu.nl)*
+
+This project looks at the following problem: we have an ontology, as
+well as some data in the form of a knowledge graph of ABox. This
+contains our background knowledge about some domain such as medicine,
+or a context from robotics. We are then given a set of facts that do
+not follow from what we know according to our background knowledge -
+an observation that is somehow unexpected, for instance a description
+of symptoms of a patient or of an unexpected situation encountered by
+a robot. We then want to generate a hypothesis in the form of a set of
+facts that would explain the observation if added to the background
+knowledge. To avoid trivial answers, we assume that there is also a
+special vocabulary for explanations provided. This means, we want to
+compute a hypothesis that uses only terms from that vocabulary, but
+may refer also to unknown objects. This problem is called
+signature-based ABox abduction. The aim of this project is to develop
+a new method for signature-based ABox abduction based on some recent
+theoretical results of this problem.
+
+
+
+The supervisor will give an introduction to the topic and the proposed
+idea at the beginning of the project. 
+You can contact the supervisor if you would like to
+have more information on this project or would like to discuss it in
+more detail in person.
+

_theses_dir/PK_Learning.md

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+---
+title: 'Learning Concept Descriptions from Examples'
+layout: default
+description: 'In this project, you will use recent advancements on ontology reasoning to develop and evaluate a new method for learning conceptual (logic-based descriptions of groups of objects based on examples.'  
+topic: 'Ontologies and Reasoning' 
+keywords: 
+    - 'Ontologies'
+    - 'Learning'
+    - 'Reasoning'
+    - 'Logics'
+    - 'Description Logics'
+supervisor: 'Patrick Koopmann'
+contact: 'p.k.koopmann@vu.nl'
+degree: 'M.Sc./B.Sc.'
+description_link: '/theses_dir/PK_Learning'
+---
+
+## Thesis title:  Learning Concept Descriptions from Examples
+*Supervisor: Patrick Koopmann (p.k.koopmann@vu.nl)*
+
+The aim of this project is develop learning methods that can be used
+to aid the development of ontologies that are based on OWL or
+description logics. In particular, the problem to be solved can be
+stated as follows: given a dataset with some objects marked as
+positive and negative examples, find a logical description (using an
+ontology language) that describes all of the positive and none of the
+negative examples. While this sounds like a classical machine learning
+problem, the aim is to use logic-based techniques to solve this
+learning problem. For this, you will implement an further investigate
+a new idea for learning concept descriptions, which will explore
+recent tools for non-classical reasoning.
+
+The supervisor will give an introduction to the topic and the proposed
+idea at the beginning of the project. 
+You can contact the supervisor if you would like to
+have more information on this project or would like to discuss it in
+more detail in person.

_theses_dir/PK_Modules.md

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+---
+title: 'Extracting Sub-Ontologies'
+layout: default
+description: 'The aim of this project is to develop new heuristics to use existing tools that extract small parts from large ontologies.'  
+topic: 'Ontologies and Reasoning' 
+keywords: 
+    - 'Ontologies'
+    - 'Logics'
+supervisor: 'Patrick Koopmann'
+contact: 'p.k.koopmann@vu.nl'
+degree: 'B.Sc.'
+description_link: '/theses_dir/PK_Modules'
+---
+
+## Thesis title:  Extracting Sub-Ontologies
+*Supervisor: Patrick Koopmann (p.k.koopmann@vu.nl)*
+
+Ontologies are an important representation formalism for symbolic AI
+systems. Ontologies that are formulated in OWL allow to usage of
+reasoning systems such as HermiT or ELK to infer implicit information
+from an ontology, or from a dataset that is combined with the ontology.
+Modern ontologies are often very large, and can contain 10,000s and even
+100,000s of statements, which makes it hard to handle them. In many
+applications, not all of the content of an ontology is relevant, so
+that it would make sense to extract a smaller ontology to use instead
+of the original, large ontology. A subontology is a smaller and ideally
+simpler ontology that covers all relevant information from the
+ontology for a user-provided set of terms of interest. There are
+different techniques (module extraction, uniform interpolation) that
+can be used to extract subontologies. The aim of this project is to
+investigate and evaluate heuristics to improve the performance of
+these methods, or develop a new approach that works by combining them,
+with the aim of obtaining simpler ontologies and/or shorter
+computation times.   
+
+The supervisor will give an introduction to the topic and the proposed
+idea at the beginning of the project. 
+You can contact the supervisor if you would like to
+have more information on this project or would like to discuss it in
+more detail in person.

_theses_dir/PK_Optimizing.md

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+---
+title: 'Optimizing Concept Expressions'
+layout: default
+description: 'In this project, you will investigate how to automatically improve expressions found in an ontology.'  
+topic: 'Ontologies and Reasoning' 
+keywords: 
+    - 'Ontologies'
+    - 'Logics'
+supervisor: 'Patrick Koopmann'
+contact: 'p.k.koopmann@vu.nl'
+degree: 'B.Sc.'
+description_link: '/theses_dir/PK_Optimizing'
+---
+
+## Thesis title:  Optimizing Concept Expressions
+*Supervisor: Patrick Koopmann (p.k.koopmann@vu.nl)*
+
+Ontologies often contain expressions that are more complex than
+necessary. This is even more a problem with ontology content that is
+automatically generated, which appears in many applications. The aim
+of this project is to develop a method to optimize concept expressions
+by replacing them by equivalent expressions that are of minimal
+size. We recently developed a method that can do this for a language
+of rather limited expressivity. The student will extend this
+framework, possibly using techniques from concept learning.
+
+The supervisor will give an introduction to the topic and the proposed
+idea at the beginning of the project. 
+You can contact the supervisor if you would like to
+have more information on this project or would like to discuss it in
+more detail in person.
+