My research

A central topic of my research is the foundations of artificial intelligence and machine learning. Artificial intelligence has made impressive progress, but it also brings with it new problems. In order to better understand both the progress and the problems, we need a reliable theory for the underlying neural networks, which we, however, still lack. Developing such a theory is an important challenge at the intersection of computer science, math, philosophy, cognitive science, and other subjects. For classical computer programs, this largely has been solved: we understand their possibilities, limitations, complexity, semantics, logic, verification, safety, etc. My approach is to develop an analogous understanding for the sub-symbolic computation of neural networks. I view this kind of computation as dynamical systems; and in my PhD thesis, I developed a domain-theoretic semantics for them.

Beyond this topic, my research interests include, e.g., the philosophy of language (hyperintensionality, synonymy, vagueness) and philosophical logic (relevance logic, counterfactuals, non-monotonic logics, logical constants). I enjoy using the tools of dynamical systems theory, domain theory, category theory, duality theory, universal algebra, modal logic, and formal epistemology - and especially learning new ones.

IAS Fellowship

We want to identify the most promising interactions between logic and artificial intelligence (AI). In concrete cases, we ask how exactly the analytic strength of logic can help with the notorious problems of modern AI concerning explainability, interpretability, and verifiability. Conversely, we also ask which new questions, insights, and methodology in logic are spurred by AI. We see a quickly rising interest in these interfaces, and we think the time is ripe for systematizing and catalyzing these efforts.

To put this into context, the history of AI is often conceptualized as a pendulum: swinging back and forth between symbolic approaches based on logic and sub-symbolic approaches based on neural networks. Modern AI is far on the sub-symbolic side, but its problems call again for the advantages of symbolic approaches. In fact, the General Data Protection Regulation (GDPR) of the European Union assigns a central role to logic in AI: users have a right to an explanation, i.e., to “meaningful information about the logic involved” (Art. 15 GDPR). However, what this logic might look like is underspecified. Our project helps to remedy this.