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PhD Project logic for AI

Logic for AI

Principal supervisor: Prof Michael Zakharyaschev

Machine learning based AI (sometimes called sub-symbolic AI) is good at recognising faces, diseases, dangerous behaviour, weak positions in games, maybe even driving cars. Yet, it is not 100% reliable when dealing with bank accounts, deciding credit ratings, marking exam papers, let alone checking software correctness or proving theorems. An alternative, logic-based AI (sometimes called symbolic AI) is 100% precise but often not efficient from the computational complexity point of view. For example, logical calculi such as first- or higher-order predicate logics or their temporal, spatial, etc. extensions are algorithmically undecidable. The aim of this project is two-fold:

- on the one hand, we are looking for logic-based knowledge representation and reasoning formalisms in various practical domains that balance sufficient expressive power with acceptable computational complexity and practical algorithms; we are especially interested in reasoning about multi-dimensional domains such as timestamped sensor data;

- on the other hand, we would like to combine, where possible, the machine learning and logic-based approaches to AI using, for example, the former to build knowledge graphs and the latter to query them.

Candidate Requirements:

This PhD is aimed at graduates with a strong mathematical (in particular, mathematical logic and computational complexity) background. The research may be purely theoretical, but it may also include a substantial practical component with coding and experiments.

Key References:

[1] D. Gabbay, A. Kurucz, F. Wolter, M. Zakharyaschev, Many-Dimensional Modal Logics: Theory and Applications, volume 148 of Studies in Logic, Elsevier, 2003

[2] S. Demri, V. Goranko, M. Lange: Temporal Logics in Computer Science: Finite-State Systems. Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, 2016

[3] S. Arora and B. Barak: Computational Complexity: a modern approach. Cambridge University Press, 2009

[4] F. Baader, I. Horrocks, C. Lutz, U. Sattler: An Introduction to Description Logic. Cambridge University Press, 2017

Further details about the project may be obtained from:

Principal supervisor: Prof Michael Zakharyaschev

Further information about PhDs at CSIS is available via this link.