SOPhiA 2021

Salzburgiense Concilium Omnibus Philosophis Analyticis

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Programme - Talk

How do we understand proof(texts) a frame-semantic approach?
(Logic, )

How do we understand proof(texts) a frame-semantic approach?



Frames have already been studied in detail in artificial intelligence (AI), cognitive science and linguistics. They were first introduced in AI by Minsky (1974) and model situations in which one can offer (or request) additional information on demand by connecting a situation with background knowledge. Hence frames explain how the receiver completes the information conveyed by the sender.

We want to make use of the concept to model how an individual can understand a mathematical text elaborating f.i. a proof. The general argument is that a student is internalizing these frames during the university studies, which makes it possible to fill gaps in proofs as they are presented in a text.

We follow Petersen (2015), who develops a model using feature structures closely related to Carpenter (1992).

In this talk we develop a global organization of mathematical knowledge, which a student might learn parts of. We offer a suggestion for a typology of different kinds of frames that come into play when we develop a theory of mathematical knowledge.

This work is foundational in its spirit but strongly connected to several applications. Such include design of knowledge management systems, automated and interactive theorem proving and mathematics education.



This talk is based on Anonymised (2019), (2021)



Literature

Anonymised (2019), (2021)

Carpenter, B. (1992). The logic of typed feature structures (Cambridge tracts in theoretical computer science). Cambridge: Cambridge University Press.

Minsky, M. (1974). A framework for representing knowledge. Technical report. Cambridge, MA: MIT

Petersen, W. (2015). Representation of concepts as frames. In: T. Gamerschlag, D. Gerland, R. Osswald, and W. Petersen (Eds.), Meaning, Frames, and Conceptual Representation, Studies in Language and Cognition. Düsseldorf: Düsseldorf University Press.


Chair: Yannick Kohl
Time: 11:20-11:50, 11 September 2021 (Saturday)
Location: SR 1.006

Deniz Sarikaya 
(Universität Hamburg, Germany)

I am Deniz Sarikaya and currently doing a PhD in Philosophy at the University of Hamburg (UHH) funded by the Studienstiftung des deutschen Volkes (German Academic Scholarship Foundation) with additional ideal support by the Claussen-Simon-Stiftung. This project is augmented through a stay at the ETH Zurich.

Testability and Meaning deco