After successful completion of the course, students are able to...

• Write syntactically correct concepts, ontologies, and knowledge bases(KBs) in any of the following DLs:  EL, EL++, DL-Lite(_R/_A), ALC, and any extension of ALC that is a fragment of SROIQ. 
• Given a natural language description of a domain, write it as a DL ontology in the least expressive DL that can capture it. 
• Judge whether a DL axiom can be expressed in a target DLs from the ones above, and translate axioms between DLs when possible. 
• Sort the studied DLs by their ability to express a given axiom described in natural language. 
• Answer correctly given instances of the following decision problems, and illustrate negative instances with a counterexample: concept satisfiability(wrt general TBoxes/KBs), concept subsumption(wrt general TBoxes/KBs), instance checking, and KB consistency;  illustrating negative instances .
• Apply the tableaux algorithm to solve instances of KB consistency in expressive DLs from ALC to ALCIN. 
• Give tight upper bounds on the complexity of  KB consistency for all the studied DLs. 
• Solve instances of EL concept subsumption using TBox saturation.  
• Compute the perfect reformulation of a conjunctive query w.r.t. a DL-Lite TBox and evaluate the rewritten query over a given ABox.  
• For each DL studied in the course, describe how the KB satisfiability problem is solved by an existing dedicated reasoner.
• Define at least five non-classical DL reasoning problems; for two selected problems, name a technique that can be used to solve it, and state two complexity bounds(either upper or lower bounds, for any DL). 
• List at least five examples of extensions of DLs; for two of them, illustrate its use by means of  a KR example that cannot be adequately captured in standard DLs.  

Additionally, depending on the selected focus (F1: logifoundations or F2:OWL), the student is also able to:  

• prove hardness and membership in Exptime for concept satisfiability w.r.t. general TBoxes in the  DL ALC;
• prove soundness and completeness of the main algorithms studied in the lecture;
• classify DLs by the following properties:  finite model property, universal model property, tree(or forest) model property; 
• explain the classification above by means of counterexamples and proof sketches(with focus on proof techniques); and
  
• translate DL ontologies and KBs into first order theories using the standard translation; 

or able to:  

• name the OWL profiles and the DL that they correspond to;
  
• name at least one popular application area for each profile;
  
• name an exisitng reasoner for each profile and say which type of reaosning algorithm it implmenets;
  
• list at least three features of OWL not supported im standard DLs; and
  
• mention at least three developer tools for OWL. 

The students learn the basics of Description Logics (DLs), how they are used for writing ontologies, and how to do automated reasoning from such ontologies. The course covers basic DLs like ALC and its extensions (e.g., SHIQ and  SROIQ),  and the lightweight DLs of  the EL and DL-Lite families, along with the computational complexity of reasoning in different DLs and their basic model theory.  The students learn basics reasoning algorithms (particularly tableaux  for expressive DLs) and how to use them to solve classical reasoning problems like concept satisfiability, KB consistency, subsumption, and instance checking. Some non-standard reasoning tasks are discussed, including the basics of CQ answering. The course contents also include application areas of DL ontologies, the OWL standard and its relationship to DLs, and   existing OWL reasoners.  The students can choose to focus on either logical foundations on the one hand (model theory, relationships between DLs and other logics), or on the OWL standard and OWL reasoning.

The course contents consist of:

Five general units
B1: ALC and its extensions
B2: Reasoning with Tableaux 
B3: Complexity 
B4: The EL family
B5: The DL-Lite family  

One focus unit, to choose from: 
F1: Logic foundations 
F2:  the Web Ontology Languages OWL   

Three special topics
S1: DL reasoners
S2: Non-classical reasoning problems
S3: Extensions of DLs

The course is held in English.   

In SS 2021 the course will be offered as distance learning. It will implement ideas from flipped classroom and from mastery grading. 

For each unit, lecture materials will be posted online on a weekly basis,  including: 

• online videolectures (with slides or wihiteboard), and  -
• exercise sheets.

During the week, students watch the lectures and sketch solutions to some exercises of their own choice.  

In a weekely videoconference meeting selected exercises will be discussed, the students will propose solution strategies, and questions will be answered.   

After the weekly session the students will finish a selection of written exercises to submit. The students will receive feedback and have the opportunity to improve and resubmit their exercises during the entire semester.  

At the end of each block (3 units/topics), there will be an online quiz to assess the mastery of the contents; quizzes can be retaken on up to four occasions.   

During the semester, the students will carry out three small reading assignments (on subtopics of the special topics) of their choice, and for each topic do an informal 10-minute presentation to their colleagues. The presentations will follow a fixed structure suggested by the lecturer, address concrete questions, and do not require the preparation of slides.

** NEWS **
Due to sick leave of the lecturer, the initial session of the course is postponed to Tuesday, March 9th, 14:00 (Zoom link via TUWEL).

ECTS breakdown:

42 h - Basic units 

6 units of 7 h each including: 

• 1,5 video lectures 
• 1 h online exercise session
• 4,5 h exercises  (incl. before and after the the exercise session, est. 1h/3,5h resp.)

18 h Special  topics 

3 topics of 6 hours each, including: 

• 4,5 h of reseach and preparation of own theme
• 1,5 h attending presentations and discussion

15 h - General 

• 1,5 hours - Introductory session 
• 13,5 hours - 3 quizzes of 4,5 h each(4h preparation, 0,5h quiz)

 ----  Total: 75 hours

  The  students can prove their achievement of the learning outcomes with:

• submitted solutions to the exercise sheets, 
• online quizzes at the end of the blocks, 
• short presentation of the reading assignments. 

Both exercise sheets and quiz results can be improved and retaken throughout the semester, and the grade will then be based on the mastery that is eventually achieved (independently of the number of attempts and resubmissions).     Alternatively, the students can choose to take a final exam (with two parts: a written practical part, and online theory quiz) at the end of the semester, but the exam can only be taken if at least two reading assignments have been presented in the lecture.

Registration is open.

Due to sick leave of the lecturer, the initial session of the course is postponed to Tuesday, March 9th.

Basic knowledge in these areas  is an advantage, but not a requirement: logic, theory of databases, complexity theory, foundations of semantic web, knowledge representation and reasoning.

By having a broad selection of exercises and reading topics, the course is tailored to accomodate for both people with a more theory-oriented interestinterested in DLs as computational logics, and people with interest in the practical use of ontologies, who want to properly understand the foundations of modeling and reasoning with them.