Research Areas

We investigate questions concerning the foundations of mathematics, especially following the Hilbert school and the scientific work of Paul Bernays. Proof-theoretic research, rooted in the traditions of Alfred Tarski, Saul Kripke and Dag Prawitz, concerns both mathematical theories and structural questions. Key research areas are proof-theoretic semantics, constructive semantics and type theory.

Former Collaborators: Paulo G. Santos; Roberta Bonacina; René Gazzari; Wilfried Keller

Relevant Publications:

• Santos, P. and Kahle, R.: k-Provability in PA. Logica Universalis, 2021. (DOI 10.1007/s11787-021-00278-1)
• Kahle, R. & Rathjen, M. (eds.): The Legacy of Kurt Schütte. Springer, 2020.
• Kahle, R.: "Sehr geehrter Herr Professor!'' Proof Theory in 1949 in a Letter from Schütte to Bernays. In R. Kahle and M. Rathjen (editors): The Legacy of Kurt Schütte, pages 3-19. Springer, 2020.

The new AI, based on stastic analysis of big data, has a whole series of promising successes to show (e.g. on image recognition; medicine; self-driving cars; etc.). However, AI is not a "panacea" either. It will not be expected to solve the stopping problem, for example, and if efficient factorization algorithms were within its reach, Internet banking would probably have to be stopped as well. We discuss computational issues for which modern AI cannot (yet?) be seen to provide solutions. In particular, we are interested in the question how it could be formally shown that these problems cannot be solved by AI methods.

Two workshops on this topic have already been organized at the annual conference of the Gesellschaft der Informatik: Conceptual Challenges for AI.

Relevant Publications:

• Kahle, R. and Mainzer, K. Grenzen der KI - theoretisch, praktisch, ethisch. Springer Verlag, 2022.
• Kahle, R.: Wozu (ver)führt uns die neue KI? In Anna Strasser, Wolfgang Sohst, Ralf Stapelfeldt, and Katja Stepec (Herausgeber): Künstliche Intelligenz: Die große Verheißung. Philosophische Kontexte, vol. 8, Xenomoi, 2021.
• Kahle, R.: Primzahlen als Herausforderung. In R. Reussner, A. Koziolek, and R. Heinrich (editors): INFORMATIK 2020. Lecture Notes in Informatics, Gesellschaft für Informatik, S. 719-727, 2021.
• Mainzer, K.: Wie sicher ist KI? In R. Reussner, A. Koziolek, and R. Heinrich (editors): INFORMATIK 2020. Lecture Notes in Informatics, Gesellschaft für Informatik, S. 695-718, 2021.
• Kahle, R. and Mainzer, K.: Konzeptionelle Herausforderungen für die KI. In R. Reussner, A. Koziolek, and R. Heinrich (editors): INFORMATIK 2020. Lecture Notes in Informatics, Gesellschaft für Informatik, S. 693-694, 2021.
• Mainzer, K.: Künstliche Intelligenz: „Post Corona“. 2020.
• Mainzer, K.: Grundlagen, Forschung und Philosophie: „Post Corona“. 2020.

Intensional phenomena are still a challenge for logical analysis. Here we try to provide more adequate tools with new approaches, among others from proof theory. The topic is also treated from the specifically linguistic perspective.

Relevant Publications:

• Kahle, R.: The Intensional Structure of Epistemic Convictions. In Loek Cleophas and Mieke Massink (editors): Software Engineering and Formal Methods. SEFM 2020, Collocated Workshops. Lecture Notes in Computer Science, vol. 12524, Springer, 2021.