We are pleased to announce that the Set Theory, Logic and Topology department of the Alfréd Rényi Institute of Mathematics and the Department of Logic of Eötvös Loránd University organize an online workshop celebrating the 3rd World Logic Day at 14 January 2021.

The aim of World Logic Day is nicely summarized by the following quote:

"A dynamic and global annual celebration of World Logic Day aims at fostering international cooperation, promoting the development of logic, in both research and teaching, supporting the activities of associations, universities and other institutions involved with logic, and enhancing public understanding of logic and its implications for science, technology and innovation."

-- Proclamation of a World Logic Day UNESCO. General Conference, 40th, 2019.

**Organizers:**

Zalán Gyenis (Jagiellonian University)

Övge Öztürk (Eötvös Loránd University)

Máté Szabó (University of Oxford)

Gergely Székely (Rényi Institute)

**Scientific Program: **

Invited talks will be given online using Jitsi Meet at:

- https://8x8.vc/wld3/mainroom

The schedule is in Central European Time (CET).

- 14:55-15:00 CET, Opening
- 15:00-16:00 CET,

Mohamed Khaled (Bahçeşehir University):

*Algebras of concepts and their networks**Abstract*: Concept algebras, or cylindric algebras in another name, are algebras that `talk' about concepts that one can define on a given model (or in a given theory). These structures are confronted with a simple extension of the Boolean parallelism between logic and algebra. The theory of these algebras is directly related to the development of first-order logic. Concept algebras were invented by Alfred Tarski around 1947, and he named them cylindric algebras referring to the geometrical meaning of these algebras. The significance of concept algebras for providing new insights into logic has been proved over decades by Tarski and his followers.Recently, a new quantitative (and still qualitative) method for the comparison of theories, independent of their empirical adequacy, has been introduced. A conceptual distance was defined to measure the minimum number of concepts that distinguish two theories. The motivation for this study comes from logic, but the idea behind this distance is rooted in algebra. That opens new directions: What can be said about conceptual distance in terms of conceptual algebras? What can be said about the analogous distance defined for other classes of algebras, e.g., monounary algebras, or Boolean algebras.

- 16:00-17:00 CET,

Aleksandra Samonek (UCLouvain)

*Modeling inductive inference on linguistic content using dictionaries and vectors**Abstract*: A central idea behind the logic of vector space models (LVSM) proposed by Hannes Leitgeb in 2020 is to treat linguistic content as a vector, where a proposition or a concept, depending on a choice of content-carrier, exerts a "push" relative to other propositions or concepts. In this approach, inductive inference is defined as an "imperfect" push from the premisses towards a conclusion. In my talk I will show how LVSM may be applied to a new type of content carriers, called dictionaries, and how to define inductive inference on a network which emerges from applying LVSM in this context.

- 17:00-17:30, Break
- 17:30-18:30 CET,

István Juhász (Rényi Institute)

*Pinning Down Families of Open Sets**Abstract*: pdf

- 18:30-19:00 CET,

Giambattista Formica (Pontifical Urbaniana University) and Michèle Friend

*In the Footsteps of Hilbert: The Logical Foundations of Theories in Physics.**Abstract*: Giambattista Formica's reading of Hilbert combines formalism with pragmatism, especially when Hilbert is concerned with applying formal mathematical theories to science. That is, applied mathematical theories should be consistent, finitistic (formalism) but make some 'scientific sense' too (pragmatism). By 'scientific sense' we mean an intuitive sense that gives a sense of satisfaction or understanding.The Andéka-Németi group in Budapest have given us formal theories that are sufficient to model or capture the phenomena of special relativity, general relativity and Newtonian mechanics. Moreover, in keeping with formalist thinking, they give several formal theories that do similar work and investigate the formal relations between those theories. Nevertheless, the formal exercise is not just that. In the Andréka-Németi group, there is a concern to use the formal theories to

*explain*the phenomena of the respective physical theories, and the formal languages have to make some sort of 'physical sense'. In this way, the Andréka-Németi group follow in the footsteps of Hilbert, especially if we take the Formica reading of Hilbert.

**Online informal discussion after the talks (experimental):**

The informal discussions after the talks, in which the participants form smaller groups to discuss various topics, is an important part of events like this one. It is not at all clear how this can be simulated online (if it is possible to simulate it at all). Anyway, we will attempt to make an experimental attempt to have such informal discussion.

The idea is that we will try to use that in Jitsi Meet is easy to create and join chat rooms. Basically, there is a chatroom to every string, which is created by someone visiting the URL created by the concatenation of https://8x8.vc/ and the chosen string.

To avoid turning this informal disunion experiment into an infinite hide-and-seak among all the possible stings, we suggest participants to use the following chatroom-string patterns:

- https://8x8.vc/wld3/chatroom1
- https://8x8.vc/wld3/chatroom2
- https://8x8.vc/wld3/chatroom3

and to use the text chat of the main room (wld3mainroom) for coordination, e.g., introducing irregularly named chat rooms whose name may correspond to subjects to be discussed there.

Despite our best intention, this attempt can still fail in several ways. Nevertheless, we think that even the worst case scenario is much better than not even trying.

We kindly ask the participants to be open-minded and cooperative in this experiment.

**Previous events in Hungary:**

2nd Logic day: Rényi Institute/Eötvös Loránd University

1st Logic day: Eötvös Loránd University and University of Pécs.