Reminder: A Logic Day in Bogotá (@UNAL, 15 January)
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Andrés Villaveces
Jan 14, 2024, 8:06:39 PMJan 14
to logbog, Nicolas Martinez Bejarano, José Nicolás Nájar Salinas, Nicolas Martinez Alba, Edwin Celis, Gustavo Cipagauta, Xavier Caicedo, mauro.a...@urosario.edu.co, Juan Sebastian Algecira Flautero, Jose Miguel Contreras Mantilla, Susana Faciolince Santoyo, Samuel Felipe Roldan Moros
Feliz Año 2024, Happy New Year to all!
Empezamos este año con un evento muy especial, relacionado parcialmente con el Día Mundial de la Lógica, este próximo lunes en la Universidad Nacional (Salón 404-212).
9:00 – Jouko Väänänen (Univ. Helsinki, Univ. Amsterdam)
Applications of set theory to infinitary model theory
Abstract: The basic question that I will be talking about is, whether the Scott-analysis of countable models can be extended to uncountable models? I will talk about the history and partial successes involved in trying to solve this problem. I will start with a review of what I call the Scott-analysis. Eventually I am led to the realm of Generalized Baire Spaces and to set theoretical problems arising from it.
10:15 – Juliette Kennedy (University of Helsinki)
Extracting syntax from semantics
Abstract: If a model class is a class of structures of the same similarity type closed under isomorphism, under what conditions can the class be said to have a natural syntax, or a natural logic? How to think about model classes that have no syntax, no notion of formula? More generally, does syntax always supervene on semantics? In this talk we present some old and new results dealing with these questions.
11:30 – Michael Harris (Columbia University, Université de Paris)
Understanding proofs (human and artificial)
Abstract: The drive to incorporate methods of artificial intelligence in mathematics raises the possibility of the separation of proofs from understanding. One can easily imagine a formal proof that can be formally validated but not understood by anyone: not by humans, either because the proof is written in impenetrable code or simply because it is too complex; not by machines, unless the term “understanding” is radically redefined . It may be objected that many existing proofs are too long and intricate for any one person to understand. Nevertheless, it is a common practice to invite the authors to explain such a proof in seminar talks, or for study groups to break down a proof into comprehensible chunks, so that one may speak of a collective (human) understanding. My talk will try to imagine machine-made proofs that cannot be understood even in this way. In the process, I will examine strategies by which mathematicians seek to make proofs understandable; how one might determine whether or not these strategies have been successful with a human audience; and what it would mean to test a machine’s understanding of a proof.
Applications of set theory to infinitary model theory
Abstract: The basic question that I will be talking about is, whether the Scott-analysis of countable models can be extended to uncountable models? I will talk about the history and partial successes involved in trying to solve this problem. I will start with a review of what I call the Scott-analysis. Eventually I am led to the realm of Generalized Baire Spaces and to set theoretical problems arising from it.
10:15 – Juliette Kennedy (University of Helsinki)
Extracting syntax from semantics
Abstract: If a model class is a class of structures of the same similarity type closed under isomorphism, under what conditions can the class be said to have a natural syntax, or a natural logic? How to think about model classes that have no syntax, no notion of formula? More generally, does syntax always supervene on semantics? In this talk we present some old and new results dealing with these questions.
11:30 – Michael Harris (Columbia University, Université de Paris)
Understanding proofs (human and artificial)
Abstract: The drive to incorporate methods of artificial intelligence in mathematics raises the possibility of the separation of proofs from understanding. One can easily imagine a formal proof that can be formally validated but not understood by anyone: not by humans, either because the proof is written in impenetrable code or simply because it is too complex; not by machines, unless the term “understanding” is radically redefined . It may be objected that many existing proofs are too long and intricate for any one person to understand. Nevertheless, it is a common practice to invite the authors to explain such a proof in seminar talks, or for study groups to break down a proof into comprehensible chunks, so that one may speak of a collective (human) understanding. My talk will try to imagine machine-made proofs that cannot be understood even in this way. In the process, I will examine strategies by which mathematicians seek to make proofs understandable; how one might determine whether or not these strategies have been successful with a human audience; and what it would mean to test a machine’s understanding of a proof.
Ver detalles aquí: https://avillavecesn.net/a-logic-day-in-bogota-15-january-2024/
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avillavecesn.net
Departamento de Matemáticas - Edificio 404
Universidad Nacional de Colombia
AK 30 # 45-03
111321 - Bogotá - Colombia
Tel: +57 601 3165000 ext 13209
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