Finite model theory for many valued logics

Project opportunity

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.

Scholarship value

As a scholarship recipient, you'll receive: 

  • living stipend of $28,854 per annum tax free (2022 rate), indexed annually
  • tuition fees covered
  • single Overseas Student Health Cover (OSHC)


Dr Guillermo Badia

School of Historical and Philosophical Inquiry


Preferred educational background

Your application will be assessed on a competitive basis.

We take into account your

  • previous academic record
  • publication record
  • honours and awards
  • employment history.

A working knowledge of mathematical logic would be of benefit to someone working on this project.

The applicant will demonstrate academic achievement in the field(s) of mathematics, philosophy or computer science and the potential for scholastic success.

A background or knowledge of mathematics is highly desirable.

Latest commencement date

If you are the successful candidate, you must commence by Research Quarter 3, 2023. You should apply at least 3 months prior to the research quarter commencement date.

If you are an international applicant, you may need to apply much earlier for visa requirements.

How to apply

You apply for this project as part of your PhD program application.

View application process