PhD topics

If you would like to do a PhD under my supervision please contact me. The following are examples of PhD project that I’d be willing to supervise. See here for more information on funding and how to apply.

The Axiomatics of Rating and Ranking 
The general problem of how to rank or rate a number of different objects based only on a limited number of comparisons between the objects has become ubiquitous. It arises in sports (ranking of teams or players), in the search engines for the web (e.g., Google’s PageRank algorithm), in recommender systems (e.g., the Netflix challenge), to name just a few. Research on the problem has increased in recent years (owing, in part, to the increased availability of large datasets in a wide variety of fields), and a lot of different solutions have been proposed. Most of these diverse solutions rely on empirical evaluation for their justification. However what is often missing is a thorough analysis of the methods in terms of their theoretical properties. This foundational project will delve into a deep, theoretical investigation of the different ranking methods. It will look at identifying different axioms for ranking theory and try to characterise and classify the various methods according to the axioms they satisfy.  

New Operators for Horn Belief Change
The topic of belief change is important for Artificial Intelligence and Knowledge Representation. It is traditionally studied in a framework that assumes an agent’s knowledge base can be represented in a logical language containing full propositional logic. However there has been recent interest in studying the problem within the more restricted language of Horn logic. In this language formulas are restricted to a tractable rule-like form which makes them interesting for potential applications such as in build- ing ontologies. Indeed, Horn logic can be thought of as the propositional “backbone” to description logics such as EL which have been successfully used to express ontolog- ical knowledge. This project will fill two gaps that remain in the study of Horn belief change: (i) the study of Horn counterparts to several interesting new families of belief change operators that have recently been proposed for the full propositional case by S. O. Hansson, and (ii) the study of iterated Horn belief change.