Motivation

Progression is a form of projection reasoning that updates an initial state to a future one according to the effects of actions, and determines what holds in the updated state. In single-agent systems, progression has been extensively studied, mainly via the logical formalism of the Situation Calculus and its epistemic variants[¹,²].

In multi-agent scenarios, however, precisely characterizing each agent’s mental state requires reasoning about higher-order knowledge and beliefs, such as statements of the form: “I know that he knows …, and I do not know whether she knows …”. A multi-agent progression framework would provide a solid foundation for research in areas including multi-agent epistemic planning, games, strategy synthesis, and protocol synthesis[³,⁴,⁵].

Despite its potential, progression in multi-agent systems has not been sufficiently explored. The main obstacle lies in the lack of suitable symbolic representations for an agent’s (higher-order) mental state and the absence of a framework for characterizing changes in higher-order beliefs.

Goals

The goal of this thesis is to investigate existing methods for progression reasoning and to propose a multi-agent extension. More specifically, the work will involve the following steps:

1. Review the existing logical foundations and propose necessary revisions.
2. Develop a progression approach for multi-agent systems and prove its validity.
3. Demonstrate the proposed approach through concrete, illustrative examples.

The thesis is expected to result in a research paper for submission to a relevant conference.

What we expect

We are looking for candidates who:

1. Have a strong interest in topics related to reasoning and cognition, including both theoretical and interdisciplinary perspectives.
2. Have a solid understanding of logic, ideally with background knowledge in temporal logic or modal logic.
3. Have passed at least one of the following courses with a good grade:
   • Mathematical logic (MaLo)
   • Computability and Complexity (BuK)
   • Knowledge Representation (KR)
   • The Logic of Knowledge Bases (LKB)

Interested?

If you are interested or have further questions, please contact Qihui Feng(feng@kbsg.rwth-aachen.de). It is highly recommended to enclose your CV & transcript in the contact email.

Reference