Non-Monotonic Uncertainty Handling and Learning

Mentored by Sebastian Rudolph, Markus Krötzsch, Carsten Lutz
at TU Dresden

Approximation Fixpoint Theory (AFT) is a unifying framework for defining and analysing semantics of logic-based formalisms for non-monotonic reasoning. Traditional AFT is situated within classical, crisp logic where propositions are either true or false.

The goal of this project is to fundamentally generalise AFT so as to be able to cover formalisms that handle uncertainty. Technically, the main task will be generalising the set of employed truth values to more fine-grained representations, e.g. the unit interval as used in fuzzy logics, weights as in weighted logics, or abstractions thereof. The resulting generalised AFT framework will present a novel unifying foundation for handling uncertainty orthogonally alongside existing methods for handling incomplete information and thus advance the state of the art of composite AI. In particular, this generalisation establishes a connection with the recently proposed logical neural networks, a comprehensive neuro-symbolic framework for unifying reasoning from symbols with learning from data.

Work environment

You will join a diverse team of highly motivated individuals conducting foundational research in computational logic at an internationally visible level. For potential computational experiments, you will have access to high performance computing systems via the Center for Information Services and High Performance Computing at TU Dresden.

SECAI offers a first-class environment for advancing your career. You can work with internationally renowned researchers and benefit from the school’s strong networks in industry and research. The graduation of highly qualified researchers is a central project goal in SECAI and doctoral students receive strong support for their professional and personal development.

Prerequisites

• Master's degree (or equivalent) in Computer Science, Mathematics, Formal Logic, or a related field
• Profound understanding of mathematical logic and computational aspects of logical reasoning; a technical background in lattice theory and fixpoint theory is an advantage
• Experience with developing prototypical implementations and conducting computational experiments
• Excellent communication skills in English, both spoken and in writing