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.

]]>The post Nitro NLP: AI Workshops & NLP Hackathon for students first appeared on Institute for Logic and Data Science.

]]>Nitro NLP starts on March 23 with workshops that train students to solve AI tasks and ends on March 28 with an NLP Hackathon. The competition will be centered around a Romanian corpus, offering students a unique opportunity to delve into and tackle challenges in machine learning and natural language processing.

The event is open to both university and high school students.

The post Nitro NLP: AI Workshops & NLP Hackathon for students first appeared on Institute for Logic and Data Science.

]]>The post Logic Seminar talk: Equilibria in multiagent online problems with predictions first appeared on Institute for Logic and Data Science.

]]>**Title**: Equilibria in multiagent online problems with predictions

**Abstract**:

We study the power of (competitive) algorithms with predictions in a multiagent setting. To this extent we introduce a multiagent version of the ski-rental problem. In this problem agents can collaborate by pooling resources to get a group licence for some asset. If the licence price is not met agents have to rent the asset individually for the day at a unit price. Otherwise the licence becomes available for everyone in perpetuity at no extra cost. Our main contribution is a best-response analysis of a single-agent competitive algorithm that assumes perfect knowledge of other agents’ actions (but no knowledge of its own renting time). We then give an analysis of the setting when agents have a predictor for their own active time, yielding a tradeoff between robustness and consistency. We investigate the effect of using such a predictor in an equilibrium, as well as the new equilibria formed in this way. This is joint work with Cosmin Bonchiș and Victor Bogdan (West University of Timișoara).

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

The post Logic Seminar talk: Equilibria in multiagent online problems with predictions first appeared on Institute for Logic and Data Science.

]]>The post Logic Seminar talk: Modal logic for program specification first appeared on Institute for Logic and Data Science.

]]>**Title**: Modal logic for program specification

**Abstract**:

We developed a many-sorted hybrid polyadic modal logic, which allows us to define both the syntax of a programming language and its evaluation context. Consequently, in the syntactic layer of our system, we represent a programming language and its operational semantics such that a program execution is represented as a deductive sequence of formulas having appropriate sorts. Our goals were to define an expressive and flexible system based on a classically developed many-sorted modal logic, such that one can perform both program execution and verification. We started with a generalization of the already existing approaches on many-sorted modal logic, and we continued with various forms of hybridization. At each stage we proved completeness theorems, we analyzed the theoretical properties of our logics, and we provided relevant examples.

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

The post Logic Seminar talk: Modal logic for program specification first appeared on Institute for Logic and Data Science.

]]>The post Proof Mining Seminar talk: Duality, Fréchet Differentiability and Bregman Distances in Hyperbolic Space first appeared on Institute for Logic and Data Science.

]]>**Title**: Duality, Fréchet Differentiability and Bregman Distances in Hyperbolic Space

**Abstract**:

I discuss recent results which provide quantitative and abstract strong convergence results for sequences from a cIn the context of general hyperbolic metric spaces, I discuss a new notion of a dual system (akin to the influential notion from the context of topological vector spaces) that allows for a uniform study of different notions of duality for these nonlinear spaces. Over this abstract notion of duality, we lift various notions from convex analysis into this nonlinear setting, including Fréchet differentiability and Bregman distances. Further, we introduce a notion of a monotone operator relative to a given dual system and, using the new Fréchet derivatives, we study corresponding resolvents relative to a given gradient, generalizing the seminal notion of Eckstein from the linear setting. These resolvents are then related to corresponding notions of Bregman quasi-nonexpansive mappings which are introduced relative to this generalization of the classical Bregman distance and we prove a convergence result of an analogue of the proximal point algorithm (together with quantitative results on its convergence in form of a rate of metastability) using the abstract convergence results for generalized Fejér monotone sequences in metric spaces introduced in the preceding talk.

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

The post Proof Mining Seminar talk: Duality, Fréchet Differentiability and Bregman Distances in Hyperbolic Space first appeared on Institute for Logic and Data Science.

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