Instructors

• Bernhard Fisseni (Duisburg-Essen)
• Bernhard Schröder (Duisburg-Essen)

Abstract

The frame concept, developed in Artificial Intelligence, cognitive science and linguistics, has recently regained interest in philosophy and philosophy of science. There have also been attempts at modelling mathematical proofs using frames, starting from a distinction between structural frames, which capture expectations about proof methods as well as constituents of proofs and their relations, and ontological frames, which capture the mathematical structures and typical referring linguistic and formulaic expressions.

In the course, we will first discuss cognitive aspects of the frame concept with respect to acquiring proof techniques on the one hand and to linguistic aspects of producing and reading proof texts on the other. In the second, practical part, you will apply the concept in the analysing textbook proofs. Finally, we will reflect on the practical part, discussing difficulties and new ideas.

Schedule

Reading

Please read the German or the English package. The German notation is closer to the notation we will use.

German package

• Busemann, Stephan. 1993. „5. Sprachverarbeitung“. In Einführung in die künstliche Intelligenz, edited by Günter Görz. Bonn: Addison-Wesley. Kapitel 5.2.6 to 5.2.7.
• Fisseni, Bernhard, and Bernhard Schröder. 2006. Grammatiken mit Merkmalstrukturen. Foliensatz.
• Fisseni, Bernhard, Deniz Sarikaya, Martin Schmitt, and Bernhard Schröder. 2019. „How to Frame a Mathematician: Modelling the Cognitive Background of Proofs“. In Reflections on the Foundations of Mathematics, edited by Stefania Centrone, Deborah Kant, and Deniz Sarikaya, 407:417–36. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-15655-8_19.

English package

• Petersen, Wiebke. 2021. „Representation of Concepts as Frames“. In Meaning, Frames, and Conceptual Representation, edited by Thomas Gamerschlag, Doris Gerland, Rainer Osswald, and Wiebke Petersen, 43–68. De Gruyter. https://doi.org/10.1515/9783110720129-003. (author’s version with a less confusing layout: https://user.phil.hhu.de/~petersen/paper/Petersen_dup_2015.pdf)
• Fisseni, Bernhard, Deniz Sarikaya, Martin Schmitt, and Bernhard Schröder. 2019. „How to Frame a Mathematician: Modelling the Cognitive Background of Proofs“. In Reflections on the Foundations of Mathematics, edited by Stefania Centrone, Deborah Kant, and Deniz Sarikaya, 407:417–36. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-15655-8_19.