PhD student position in finite model theory for many valued logics, St Lucia (Australia)

This Earmarked Scholarship project is aligned with a recently awarded Category 1 research grant. It offers you the opportunity to work with leading researchers and contribute to large projects of national significance.

Data available for collection in the real world is very often not a matter of yes or no, not a matter of all or nothing, but actually a matter of degrees. There is a growing need to represent this information in graded databases. Moreover, real-world data usually involves only finitely-many objects. Mathematical logic offers precise syntactic tools via logical languages that allow for expressing and querying information, which has already proved its power in the case of finite databases with binary yes-or-no properties with the deep development of classical finite model theory. On another research stream, mathematical fuzzy logic has developed a wealth of results about logical tools for general (possibly infinite) graded structures. However, graded finite structures pose specific difficulties that do not allow a straightforward application of general results. In this project, we want to fill this obvious theoretical gap by putting forward a mathematically ambitious study of graded finite structures, which may turn out to be crucial for a wider applicability of mathematical logic.