Below you can see a list of past talks at the Logic Seminar in this season. For forthcoming talks, see the main page.
Thursday, December 12, 2024
Adriana Bălan (National University of Science and Technology Politehnica Bucharest)
Regularity and complete distributivity in fuzzy metric spaces and formal contexts
Abstract:
Invertibility is an ubiquitous concept in Mathematics. In this talk, I will discuss the relationship between two seemingly unrelated notions of invertibility: regularity of multi-valued relations and complete distributivity of (complete) fuzzy metric spaces.
References:
[1] A. Bălan, On the tensor product of quantale-enriched completely distributive categories. Accepted for publication in Fundamental Structures in Computational and Pure Mathematics, Trends in Mathematics, Springer (2025).
Thursday, December 5, 2024
Andrei Sipoș (University of Bucharest and IMAR)
Around Herbrand’s Theorem II
Abstract:
We present our extension [2] to first-order arithmetic of Gerhardy and Kohlenbach’s proof [1] of Herbrand’s Theorem.
References:
[1] P. Gerhardy, U. Kohlenbach, Extracting Herbrand disjunctions by functional interpretation. Arch. Math. Logic 44, 633–644, 2005.
[2] A. Sipoș, On extracting variable Herbrand disjunctions. Studia Logica 110, 1115–1134, 2022.
Thursday, November 28, 2024
Andrei Sipoș (University of Bucharest and IMAR)
Around Herbrand’s Theorem I
Abstract:
We present Gerhardy and Kohlenbach’s proof [1] of Herbrand’s Theorem for first-order logic, which uses the Dialectica interpretation.
References:
[1] P. Gerhardy, U. Kohlenbach, Extracting Herbrand disjunctions by functional interpretation. Arch. Math. Logic 44, 633–644, 2005.
Thursday, November 21, 2024
Dafina Trufaș (University of Bucharest and ILDS)
Intuitionistic propositional logic II
Abstract:
We present two proofs of the completeness theorem for Intuitionistic Propositional Logic, corresponding to Kripke and to Heyting algebras semantics, respectively. Furthermore, the equivalence between the two validity notions is established.
Thursday, November 14, 2024
Dafina Trufaș (University of Bucharest and ILDS)
Intuitionistic propositional logic I
Abstract:
We present two proofs of the completeness theorem for Intuitionistic Propositional Logic, corresponding to Kripke and to Heyting algebras semantics, respectively. Furthermore, the equivalence between the two validity notions is established.
Thursday, October 31, 2024
Mihai Prunescu (University of Bucharest and IMAR and ILDS)
Arithmetic Terms III
Abstract:
We present other two representations of the C-recursive sequences by the speaker and new approaches to the prime numbers. The latter is joint work in progress with Lorenzo Sauras-Altuzarra and Joseph Shunia.
Thursday, October 17, 2024
Horațiu Cheval (University of Bucharest and ILDS)
Proof mining and applications to optimization and nonlinear analysis
Abstract:
We present the main results from [1], obtained as part of the program of proof mining, consisting of quantitative information on the asymptotic behavior of iterations from optimization and nonlinear analysis. We begin with a brief introduction to proof mining, after which we present results concerning the Tikhonov-Mann and modified Halpern iterations for finding fixed points of nonexpansive mappings in a very general nonlinear setting, where the main quantitative content we get takes the form of uniform rates of asymptotic regularity. This then generalizes to iterations for approximating common fixed points of families of nonexpansive mappings, for which we again compute rates of asymptotic regularity, as well as rates of metastability. Finally, we obtain linear rates of asymptotic regularity for a variety of iterations encountered in the optimization literature.
References:
[1] H. Cheval. Proof mining and applications to optimization and nonlinear analysis. PhD Thesis, submitted, 2024.