3 aprile 2023

Seminario di Logica e Filosofia della Scienza - Luca San Mauro (TU, Wien)

3 aprile 2023


Lunedì 3 aprile 2023, ore 11:00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
sala "Altana"


Luca San Mauro (TU, Wien)

Learning mathematical structures


Abstract: Algorithmic Learning Theory (ALT), initiated by Gold and Putnam in the 1960s, comprehends several formal frameworks for the inductive inference. Broadly construed, ALT models the ways in which a learner may achieve systematic knowledge about a given environment, by accessing more and more data about it. In classical paradigms, the objects to be inferred are either formal languages or computable functions. In this talk, we present the following framework: An agent receives larger and larger pieces of an arbitrary copy of a countable structure and, at each stage, is required to output a conjecture about the isomorphism type of such a structure. The learning is successful if the conjectures eventually stabilize to a correct guess. We offer a complete model theoretic characterization of which families of structures are learnable. Finally, we describe how to apply our framework to develop an innovative response to a widely debated question in the philosophy of mathematics, i.e., how does one single out the standard model of the natural numbers from nonstandard ones?


→ Locandina




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