## 项目介绍

The Institute of Philosophy at KU Leuven invites applications for a four-year PhD position in logical geometry and formal logic. The position is part of the ERC Starting Grant ‘STARTDIALOG: Towards a Systematic Theory of Aristotelian Diagrams in Logical Geometry’, led by prof. dr. Lorenz Demey. This project is embedded inside the Centre for Logic and Philosophy of Science (CLPS), which focuses on logic and philosophy of science, and also does research on (formal) epistemology, philosophy of mind and philosophy of language. Furthermore, the STARTDIALOG project also maintains close ties with the KU Leuven Institutes Leuven.AI and LECTIO, which do research on resp. artificial intelligence and intellectual history in Antiquity, the Middle Ages and the Renaissance. Website unit

##### Project

Aristotelian diagrams, such as the square of opposition, have been widely used throughout the history of philosophy and logic. Nowadays, they also have several applications in other disciplines that are concerned with logical reasoning, such as psychology, linguistics and computer science. The overarching goal of the STARTDIALOG project is to develop a unified theory of Aristotelian diagrams. In this PhD position, you will be responsible for carrying out an absolutely fundamental part of the project, viz., to study the behavior of Aristotelian diagrams in classical formal logic. A representative but non-exhaustive list of potential research topics looks like this:

- We currently have a well-defined notion of ‘Aristotelian isomorphism’, and some preliminary results on how to generalize this to a notion of ‘Aristotelian homomorphism’. Based on these results, can we define one or more categories of Aristotelian diagrams, in the category-theoretical sense of the word? Do these categories enjoy interesting properties? (Demey and his current PhD student Leander Vignero already have some promising results in this direction.)
- Given the notion of Aristotelian isomorphism, it should be straightforward to define a notion of ‘Aristotelian automorphism’, and thus also of the automorphism group Aut(D) associated with an Aristotelian diagram D. Does the automorphism group provide any interesting information about the Aristotelian diagram it is associated with? For the mathematically inclined: can we prove a representation theorem in this context, i.e. for every group G there exists an Aristotelian diagram D such that G is isomorphic to Aut(D)?
- There are already some results on the informational optimality of Aristotelian diagrams (in relation to their so-called ‘opposition’ and ‘implication’ counterparts). We would like to expand on these results and to further unify them into a streamlined framework.
- Logic-sensitivity is an important and well-known phenomenon in logical geometry. There are already some basic results about this, but we would like to expand on them, for example by investigating their interaction with the notion of Boolean complexity. Typical example: it is well-known that there exist fragments of formulas F and logical systems S1, S2 such that the Aristotelian diagram for F relative to S1 is a classical square of opposition, but that for F relative to S2 is a degenerate square of opposition. Do there also exist fragments F and logical systems S1, S2 such that the Aristotelian diagrams for F relative to S1 and to S2 are two Boolean subtypes of one and the same Aristotelian family (e.g. strong vs weak Jacoby-Sesmat-Blanché hexagons)? And most importantly, can we establish systematic relations between these different manifestations of logic-sensitivity?

In addition to conducting independent and collaborative research on these (and similar) topics, the successful applicant will also be expected to actively participate in the common activities of the STARTDIALOG project, including meetings, seminars, reading groups, workshops, etc.

##### Profile

- You have obtained (or will very soon obtain) an outstanding MA, MSc or Research MA degree in a relevant domain (e.g. philosophy, logic, mathematics, computer science, artificial intelligence).
- You have a thorough familiarity with the fundamentals of (classical) formal logic (e.g. syntax and semantics of propositional logic, first-order logic and modal logic, soundness and completeness, Lindenbaum-Tarski algebra, etc.). If your master’s thesis was focused on a topic in this area, that is a very strong plus. In other cases, you are willing to gain the required familiarity during the first few months of the position.
- You have outstanding formal and analytical skills.
- You have outstanding reading and writing skills in English.
- You are willing to work in an interdisciplinary and collaborative research environment, and to work and publish predominantly on the topic of STARTDIALOG project.

##### Offer

We offer a full-time PhD position for four years (subject to positive intermediate evaluations after one year and after two years), situated in the stimulating scientific environment of an ERC grant at one of Europe’s leading research universities. We offer an attractive wage and a budget for research expenses (including small equipment, travel and accommodation costs, the organization of events).

The successful candidate will be expected to spend 100% of their work time on research activities for the STARTDIALOG project.

The starting date is currently set at 1 October 2022, but this is negotiable.

##### Interested?

For more information please contact prof. dr. Lorenz Demey via e-mail: lorenz.demey@kuleuven.be. Upon request, he will send you a (much) more detailed description of the STARTDIALOG project.

Applications should include a cover letter, a detailed CV, a writing sample (e.g., an excerpt of the master’s thesis or a term paper, between 10 and 20 pages) and a one-page research statement, outlining your research priorities and emphases within the general context of the STARTDIALOG project.

You can apply for this job no later than August 23, 2022 via the online application toolKU Leuven seeks to foster an environment where all talents can flourish, regardless of gender, age, cultural background, nationality or impairments. If you have any questions relating to accessibility or support, please contact us at diversiteit.HR@kuleuven.be.

#### 联系方式

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