The post Logic Seminar talk announcement: Intuitionistic propositional logic first appeared on Institute for Logic and Data Science.

]]>**Title**: Intuitionistic propositional logic

**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.

The talk will take place physically at FMI (Academiei 14), Hall 214 “Google”.

The post Logic Seminar talk announcement: Intuitionistic propositional logic first appeared on Institute for Logic and Data Science.

]]>The post Logic Seminar talk announcement: Arithmetic Terms III first appeared on Institute for Logic and Data Science.

]]>**Title**: 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.

The talk will take place physically at FMI (Academiei 14), Hall 214 “Google”.

The post Logic Seminar talk announcement: Arithmetic Terms III first appeared on Institute for Logic and Data Science.

]]>The post Logic Seminar talk: Proof mining and applications to optimization and nonlinear analysis first appeared on Institute for Logic and Data Science.

]]>**Title**: 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.

The talk will take place physically at FMI (Academiei 14), Hall 214 “Google”.

The post Logic Seminar talk: Proof mining and applications to optimization and nonlinear analysis first appeared on Institute for Logic and Data Science.

]]>The post This week’s LLMs for Romanian Workshop announcement first appeared on Institute for Logic and Data Science.

]]>The workshop aims to build and strengthen the community of researchers and practitioners interested in open Romanian language models (cf. OpenLLM-Ro), with a focus on public and open corpora, as well as open-source training and evaluation code.

The workshop is affiliated with Romanian AI Days; it is jointly organized by the Institute for Logic and Data Science (ILDS), University of Bucharest, and University Politehnica of Bucharest.

The event will be held physically and broadcast online on YouTube. Participation is free, but we have a limited number of places available, so please register here.

For more information, check out the workshop page.

The post This week’s LLMs for Romanian Workshop announcement first appeared on Institute for Logic and Data Science.

]]>The post Proof Mining Seminar talk: Proof mining and probability first appeared on Institute for Logic and Data Science.

]]>**Title**: Proof mining and probability

**Abstract**:

Due to previous ad hoc case studies, the insight was made that a significant proportion of results in probability theory (and finite measure theory, in general) made use of infinite unions and sigma additivity in a very sparing way, allowing for a formalisation amenable to bound extraction, in the style of the classical proof mining metatheorems. This talk will discuss aspects of recently developed formal systems stemming from this perspective. While these systems entail many subtle details and features, we shall focus on those that allow us to discuss their key achievements. This includes a novel extension of Bezem’s majorizability that explains the uniformities in the extracted bounds of previous case studies and the formalisation of a strategy that transfers quantitative deterministic results to their corresponding probabilistic analogues. This is joint work with Nicholas Pischke.

**Google Meet link**: https://meet.google.com/jpw-hrwe-evu

The post Proof Mining Seminar talk: Proof mining and probability first appeared on Institute for Logic and Data Science.

]]>The post The Age of Algorithms Workshop announcement first appeared on Institute for Logic and Data Science.

]]>This multidisciplinary workshop aims to address and explore various dimensions of what we may now call “the age of algorithms”. From large language models already proven to be able to complete tasks of human-level complexity, to smart devices capable of making expert decisions in specialized fields like medicine or healthcare, and social media algorithms that filter every bit of information and shape our preferences online, algorithms have become an indispensable part of our world – with the good, but also with the bad, the risks, the uncertainty.

The event will be held physically (and broadcast online, details to come). Participation is free, but we have a limited number of places available, so please register no later than 15 June 2024 (see webpage for details).

For more information, check out the workshop page.

The post The Age of Algorithms Workshop announcement first appeared on Institute for Logic and Data Science.

]]>The post Logic Seminar talk: On recurrent sequences of integers first appeared on Institute for Logic and Data Science.

]]>**Title**: On recurrent sequences of integers

**Abstract**:

There is a method to ultimately express recurrent sequences of integers by arithmetic terms. This is joint work with Lorenzo Sauras-Altuzarra.

**References**:

[1] M. Prunescu, L. Sauras-Altuzarra, On the representation of C-recursive integer sequences by arithmetic terms. arXiv:2405.04083 [math.LO], 2024.

The talk will take place physically at FMI (Academiei 14), Hall 214 “Google”.

The post Logic Seminar talk: On recurrent sequences of integers first appeared on Institute for Logic and Data Science.

]]>The post Deep Blockchain Fundamentals Workshop announcement first appeared on Institute for Logic and Data Science.

]]>The event will be held physically (and broadcast online, details to come). Participation is free, but we have a limited number of places available, so please register here.

For more information, check out the workshop page.

The post Deep Blockchain Fundamentals Workshop announcement first appeared on Institute for Logic and Data Science.

]]>The post Logic Seminar talk: On representability by arithmetic terms first appeared on Institute for Logic and Data Science.

]]>**Title**: On representability by arithmetic terms

**Abstract**:

Consider number-theoretic functions like \(\tau\), which represents the number of divisors of a natural number, \(\sigma\), which yields the sum of its divisors, or Euler’s totient function \(\varphi\), which computes, for any \(n\), the number of residues modulo \(n\), which are relatively prime to \(n\). There are methods to compute these functions for a given argument \(n\) from the prime number decomposition of \(n\), but it is difficult to imagine arithmetic closed terms in \(n\) alone, computing them. Yet, those functions are Kalmár-elementary and by the results of Mazzanti and Marchenkov, such terms do exist. As well, closed arithmetic terms represent the \(n\)th prime and various other number-theoretical functions. I will show how such terms can be effectively constructed. Work in progress.

The talk will take place physically at FMI (Academiei 14), Hall 214 “Google”.

The post Logic Seminar talk: On representability by arithmetic terms first appeared on Institute for Logic and Data Science.

]]>The post Logic Seminar talk: Partial (co)recursive functions in Coq and Lean first appeared on Institute for Logic and Data Science.

]]>**Title**: Partial (co)recursive functions in Coq and Lean

**Abstract**:

We present a novel method, based on domain theory, for defining partial recursive functions in interactive theorem provers like Coq and Lean, which would normally reject such definitions, as they require the termination of all functions. Our approach further extends to a representation of coinductive types and partial corecursive functions on them, which enhances the expressiveness of both systems. While Coq does contain built-in corecursion, it does not accept functions like *mirror *on infinitely deep trees, due to it violating the so-called guardedness condition, or *filter *on streams, as it is not total. Both of these can be defined in the presented encoding. Furthermore, Lean lacks entirely a native notion of coinductives, therefore the domain-theoretical representation can be used to build them from scratch in it. This is joint work with David Nowak and Vlad Rusu.

The talk will take place physically at FMI (Academiei 14), Hall 214 “Google”.

The post Logic Seminar talk: Partial (co)recursive functions in Coq and Lean first appeared on Institute for Logic and Data Science.

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