Topics suggested for BA and MA theses

    Contact:

Heuristics for theory projection in analogical reasoning

Ulf Krumnack
Prof. Kai-Uwe Kühnberger
Dr. Helmar Gust

 

Heuristic-Driven Theory Projection (HDTP) is a framework for analogical reasoning currently under development at the IKW. It works in two stages by first identifying common structures in the modelling of two different domains and then transferring knowledge und proposing new conclusions.
Several steps in this process are based on heuristic knowledge. The thesis shall propose and implement different heuristics and examine their value in process of analogy making.

The semantics of theory projection

Ulf Krumnack
Prof. Kai-Uwe Kühnberger
Dr. Helmar Gust

 

Heuristic-Driven Theory Projection (HDTP) is based on an extended form of anti-unification of logical theories. It introduces certain second-order elements which seem to be well-founded on a syntactic level but whose semantics needs to be further investigated. A thesis should develop a model theoretic semantics and show its applicability in the description of analogies.

Design and implementation of the Structure Mapping Theory

Ulf Krumnack
Prof. Kai-Uwe Kühnberger
Dr. Helmar Gust

 

The structure mapping theory by D. Gentner is a well-known psychological theory for finding analogies and making analogical inferences. Although it is today's most prominent approach for analogies, the existing implementation of the structure mapping theory from the 1980s uses rather old technology.
This thesis shall examine the current state of the structure mapping theory and develop an algorithm to implement the analogical mapping process. The practical work -modelling and implementing the software- will play a significant part in the thesis.

A classification of analogies - types, fields of applications

Ulf Krumnack
Prof. Kai-Uwe Kühnberger
Dr. Helmar Gust

 

Humans use analogies in different situations and for different purposes. In science, new problems are understood and explained via analogies by well-known phenomena. Analogies are also used in education: e.g. mathematical operations on polynomials can be explained via analogies to operations on natural numbers. Analogies and metaphors are very important stylistic devices in linguistics, e.g. in poems, tales and fairy stories. We use analogies in our everyday life to solve new problems.
This thesis shall review literature to give an overview of analogy usage and analyze the different types of analogies. The student shall propose criteria for a classification of analogies.

Comparing analogy models

Ulf Krumnack
Prof. Kai-Uwe Kühnberger
Dr. Helmar Gust

 

Heuristic-Driven Theory Projection (HDTP) is a framework for analogical reasoning currently under development at the IKW. The representation is essentially logic-based. HDTP works in two stages by first identifying common structures in the modelling of two different domains and then transferring knowledge und proposing new conclusions.
Besides HDTP exist many other approaches to analogical mapping which use different representational formalisms and have different underlying assumptions how analogies occur. E.g., according to the Structure Mapping Theory (SMT) by Gentner, a domain is represented as a structure (a graph) with objects, attributes and relations. Analogies are identified via structural commonalities. The Analogical Constraint Mapping Engine (ACME) by Holyoack and Thagard uses neuronal networks to identify mappings. In turn, Indurkhya and Dastani use an algebraic framework for representation of domains.
The thesis shall select a number of approaches and compare them against HDTP with respect to their analogical mapping and inference mechanisms.

Analogical reasoning and learning

Ulf Krumnack
Prof. Kai-Uwe Kühnberger
Dr. Helmar Gust

 

Analogy making is the process by which humans extract operators used to solve one problem and map them onto a solution for another problem. The thesis shall investigate experimentally the human way of analogical reasoning and learning.
The findings can be compared to other learning strategies (e.g. inductive, abductive and deductive reasoning) or they can be tested against the analogical inference mechanisms in HDTP.

Learning first-order logical theories with neural networks in reasoning processes

Prof. Kai-Uwe Kühnberger
Dr. Helmar Gust

 

The well-known gap in Cognitive Science and Artificial Intelligence between symbolic and subsymbolic modelings seems to be a hard problem. An approach developed at the IKW to bridge this gap in one direction uses a translation of logical theories to a semisymbolic representation, namely to so-called Topos theory. This representation is homogeneous, variable-free, and uses only one inherent operation (concatenation of arrows). The semisymbolic level can be used to train a feedforward neural network that is not only learning the logical input theory, but rather the logical closure of this theory, i.e. a model of the underlying theory.
The thesis shall develop this approach further by applying it to complex logical input theories in reasoning and planning domains.

Comparing algebraic frameworks used in AI

Prof. Kai-Uwe Kühnberger
Dr. Helmar Gust

 

Rule-based and procedural approaches are dominating the field of reasoning in artificial intelligence. Examples are methods used for inductive, case-based, or qualitative reasoning. Alternatively, algebraic approaches can be used. Such approaches focus on structural representations and provide a powerful and formally sound foundation for inference algorithms. Examples are the usage of anti-unification in analogy and induction or relational algebras for qualitative reasoning.
The thesis shall compare different algebraic methods with respect to their expressive strength and other theoretic features.

Assessment of solutions for programming assignments in PROLOG and LISP

Dr. Helmar Gust

 

Assessing assignments and exams produces a big workload for lecturers and tutors.
Certain types of assignments like multiple choice exercises, can be easily corrected automatically.
Other types of exercises, e.g. programming exercises, can hardly be assessed completely automatically.
Nevertheless, it is possible to support the assessment of such exercises by methods comparing
the handed-in solutions with exemplary solutions on different levels: structurally and functionally.

Intensions as Algorithms

Prof. Kai-Uwe Kühnberger

 

Flexible Knowledge Basis for Heterogeneous Data

Dr. Helmar Gust

 

With the Problem of handling big heterogeneous (Web based) data new approaches of storing, retrieving,
and reasoning were developed. These methods differ from the classical relational data model.
Methods from the semantic web field allow data bases which directly use xml structures for data representation
or to use very flexible triple storages.