Autumn school “Proof and Computation”

Fischbachau, Germany, 15th to 21st September 2024

http://www.mathematik.uni-muenchen.de/~schwicht/pc24.php

This year’s international autumn school “Proof and Computation” will be held from 15th to 21st September 2024 in Fischbachau near Munich. Its aim is to bring together young researchers in the field of Foundations of Mathematics, Computer Science and Philosophy.

- Predicative Foundations
- Constructive Mathematics and Type Theory
- Computation in Higher Types
- Extraction of Programs from Proofs

- Thierry Coquand (Gothenburg): Topos theory and constructive mathematics
- Klaus Mainzer (Munich): From Proof and Computation to AI - Logical, Mathematical, and Philosophical Foundations
- Gerhard Jäger (Bern): Foundations of explicit mathematics
- Sara Negri (Genoa): Enriched syntax for enhanced proof theory
- Monika Seisenberger (Swansea): Extraction of programs from proofs
- Holger Thies (Kyoto): Extracting efficient programs from proofs in analysis
- Freek Wiedijk (Nijmegen): The De Bruijn criterion versus the Poincare principle

There will be an opportunity to form ad-hoc groups working on specific projects, but also to discuss in more general terms the vision of constructing correct programs from proofs.

Graduate or PhD students and young postdoctoral researchers are invited to apply. Applications (e.g. a self-introduction including research interests and motivation) should be sent to

Chuangjie Xu xu@math.lmu.de.

Students are required to provide also a letter of recommendation, preferably from the thesis adviser.

Please specify in your application whether you are interested in applying for financial support (details provided below).

Deadline for applications: **7th June 2024**.

Applicants will be notified by 24th June 2024.

Successful applicants are eligible to apply for financial support that covers accommodation and meals for the duration of the autumn school. Information about funding application will be provided to the selected candidates.

The workshop is supported by the Udo Keller Stiftung (Hamburg) and the COST Action EuroProofNet https://europroofnet.github.io.

Klaus Mainzer

Peter Schuster

Helmut Schwichtenberg

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**Date**: Monday, 27 May 2024 at 16:00 CEST (UTC+2) on Zoom

**Speaker:** Ana María Mora-Márquez (Researcher and Wallenberg Academy Fellow,
University of Gothenburg)

**Title:** Medieval Aristotelian Logic is Scientific Method

**Abstract:**

This presentation aims to show that medieval Aristotelian logic can be generally
characterized as scientific method. To be sure, this method includes formal
logic as one of its parts, but formal logic is by no means the crucial part. In
fact, if, as I intend to show, the main aim of medieval Aristotelian logic is to
provide methods for knowledge production and distribution, so its crucial parts
are the methods for scientific proof provided in commentaries on Aristotle’s
Posterior Analytics and Topics.

In the first part of the presentation, I argue for the possibility of talking of medieval ‘science’, ‘scientific knowledge’, and ‘scientific method’ from a modern perspective, and discuss how the modern perspective relates to the Latin ‘scientia’ in its different senses. In the second part, I show the progression from Nicholas of Paris (1240s) and Albert the Great (1250s), who see Aristotelian logic as a systematic scientific method where syllogistic argument is fundamental, but who struggle to coherently organize it around syllogistic argument, to Radulphus Brito (1290s) who, still seeing Aristotelian logic as scientific method, uses the notion of ‘second intention’ in order to coherently structure it around syllogistic argument.

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**Date**: Monday, 3 June 2024 at 16:00 CEST (UTC+2) on Zoom

**Speaker:** Ivano Ciardelli (Associate Professor of Logic, University of Padua)

**Title:** Inquisitive modal logic—an overview

**Abstract:**

Inquisitive modal logic is a generalization of standard modal logic where the
language also contains questions, and modal operators that can be applied to
them. In this talk, I will provide an introductory overview of inquisitive modal
logic. I will review some motivations for the approach, present some prominent
examples of inquisitive modal logics, mention some results about them, and
outline directions for future work.

The intended audience for NLS is advanced master students, PhD-students, postdocs and experienced researchers wishing to learn the state of the art in a particular subject. As usual, this year we have an exciting lineup of five lecturers on a wide spectrum of topics.

Lecturers:

- Jandson Ribeiro (Philosophical logic)
- Sandra Kiefer (Learning and logic)
- Miika Hannula (Model theory)
- Greg Restall (Proof theory)
- Rineke Verbrugge (Logic, CS and AI)

For updated information about the summer school and to register, please follow the link:

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**Date**: Monday, 25 March 2024 at 16:00 CET (UTC+1) on Zoom

**Speaker:** Albert Visser, Professor of Logic at Utrecht University

**Title:** Restricted Sequential Theories

**Abstract:**

Sequential theories form a fundamental class of theories in logic. They have
full coding possibilities and allow us to build partial satisfaction predicates
for formulas of bounded depth-of-quantifier-alernations. In many respects, they
are the proper domain of Gödelian metamathematics. We explain the notion of
sequential theory.

A theory is restricted if it can be axiomatised by axioms of bounded depth-of-quantifier-alernations. All finitely axiomatised theories are restriced, but, for example, also Primitive Recursive Arithmetic. We explain the small-is-very-small principle for restricted sequential theories which says that, whenever the given theory shows that a definable property has a small witness, i.e., a witness in a sufficiently small definable cut, then it shows that the property has a very small witness, i.e., a witness below a given standard number.

We sketch two proofs that restricted theories are incomplete (however complex the axiom set). One uses the small-is-very-small principle and the other a direct Rosser argument. (The second argument was developed in collaboration with Ali Enayat.)

]]>The Nordic Logic Summer School (NLS) and Scandinavian Logic Symposium (SLSS) are respectively the Summer School and the Symposium organized by the Scandinavial Logic Society. This year, both events will take place this June 2024 in Reykjavik, Iceland. NLS will take place from June 10 to 13, and SLSS from June 14 to 16.

The primary aim of the Symposium is to promote research in the field of logic (broadly conceived) carried out in research communities in Scandinavia. Moreover, it warmly invites the participation of logicians from all over the world. The meeting will include invited lectures and a forum for participants to present contributed talks.

The scope of SLSS is broad, ranging over the whole areas of Mathematical and Philosophical Logic, as well as Logical Methods in Computer Science, Artificial Intelligence, Linguistics, among others. Major topics include (but are not limited to):

- Proof Theory
- Constructivism
- Model Theory
- Set Theory
- Computability Theory
- Algebra and Logic
- Categorical Logic
- Modal and Temporal Logics
- Dynamic Logics
- Logic and Computer Science
- Logic in AI and Multi-Agent Systems
- Logic and Linguistics
- Philosophical Logic
- Philosophy of Logic, Mathematics and Computation

- Antonios Achilleos (Reykjavik University, co-chair)
- Dag Westerståhl (Stockholm University, Tsinghua University, co-chair)
- Gaia Belardinelli (University of Copenhagen)
- Jens Classen (Roskilde University)
- Salvatore Florio (University of Oslo)
- Juha Kontinen (University of Helsinki)
- Vera Koponen (Uppsala University)
- Maria Magdalena Ortiz de la Fuente (TU Wien)
- Mina Young Pedersen (University of Bergen)
- Esko Turunen (TU Wien)

- Fausto Barbero (University of Helsinki)
- Sara Negri (University of Genoa)
- Aybüke Özgün (ILLC, University of Amsterdam)

Abstracts of contributed talks, in PDF format, not exceeding two A4 (11pt)
pages, should be submitted through EasyChair:

https://easychair.org/conferences/?conf=slss2024
by April 7 2024 (AoE). Abstracts should be typeset following the format of a
LaTeX class file SLS2014.cls, or in a similar format if you prefer to not use
LaTeX.

NLS 2024 and SLSS 2024 are sponsored by the ASL. This means that any student who
wants to attend these events can apply for an ASL Student Travel Award, to
partially cover their expenses. Please not that to do so, the student must be an
ASL member and they must send their application to ASL by March 19 at the
latest. For more information and to apply for an ASL award, please follow this
link:

https://aslonline.org/student-travel-awards/

- Submission deadline: April 7
- Notification: April 30
- Final programme: TBA
- ASL travel award deadline: March 19
- Conference: 14-16 June, 2024

https://www.gu.se/en/flov/the-lindstrom-lectures

We are proud to announce that the 2024 Lindström Lectures will be delivered by
**Phokion G. Kolaitis**, Distinguished Research Professor at UC Santa Cruz and a
Principal Research Staff Member at the IBM Almaden Research Center, US.
Professor Kolaitis will deliver a **public lecture on Monday, 15 April 2024,
1800–2000** and a **research lecture on Wednesday, 17 April at 10–12**. Both
lectures will be held in the Faculty of Humanities, University of Gothenburg.
The public lecture will also be broadcast over Zoom. A Zoom link for the event
will be distributed on the
Nordic Online Logic Seminar
mailing list.

**Monday, 15 April 2024 at 18:00 (UTC+2)** at the Faculty of Humanities,
University of Gothenburg and over Zoom

**Phokion G. Kolaitis** (University of California Santa Cruz and IBM Research)

*Characterizing Rule-based Languages*

Abstract: There is a mature body of work in logic aiming to characterize logical
formalisms in terms of their structural or model-theoretic properties. The
origins of this work can be traced to Alfred Tarski’s program to characterize
metamathematical notions in “purely mathematical terms” and to Per Lindström’s
abstract characterizations of first-order logic. For the past forty years,
rule-based logical languages have been widely used in databases and in related
areas of computer science to express integrity constraints and to specify
transformations in data management tasks, such as data exchange and
ontology-based data access. The aim of this talk is to present an overview of
more recent results that characterize various classes of rule-based logical
languages in terms of their structural or model-theoretic properties.

**Wednesday, 17 April 2024 at 10:00 (UTC+2)**

**Phokion G. Kolaitis** (University of California Santa Cruz and IBM Research)

*Homomorphism Counts: Expressive Power and Query Algorithms*

Abstract: A classical result by Lovász asserts that two graphs G and H are
isomorphic if and only if they have the same left profile, that is, for every
graph F, the number of homomorphisms from F to G coincides with the number of
homomorphisms from F to H. A similar result is also known to hold for right
profiles, that is, two graphs G and H are isomorphic if and only if for every
graph F, the number of homomorphisms from G to F coincides with the number of
homomorphisms from H to F. During the past several years, there has been a study
of equivalence relations that are relaxations of isomorphism obtained by
restricting the left profile or the right profile to suitably restricted classes
of graphs, instead of the class of all graphs. Furthermore, a notion of a query
algorithm based on homomorphism counts was recently introduced and investigated.
The aim of this talk is to present an overview of some of the main results in
this area with emphasis on the differences between left homomorphism counts and
right homomorphism counts.

The Nordic Online Logic Seminar
is organised monthly over Zoom, with expository talks on topics of interest for
the broader logic community. The seminar is open for professional or aspiring
logicians and logic aficionados worldwide. If you wish to receive the Zoom ID
and password for it, as well as further announcements, please subscribe here:

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**Date**: Monday, ~~26 February~~ 4 March 2024 at 16:00 CET (UTC+1) on Zoom

**Speaker:** Lauri Hella, Professor at the Faculty of Information Technology and
Communication Sciences, Tampere University

**Title:** Game characterizations for the number of quantifiers

**Abstract**

A game that characterizes definability of classes of structures by first-order
sentences containing a given number of quantifiers was introduced by Immerman
in 1981. In this talk I describe two other games that are equivalent with the
Immerman game in the sense that they characterize definability by a given number
of quantifiers.

In the Immerman game, Duplicator has a canonical optimal strategy, and hence Duplicator can be completely removed from the game by replacing her moves with default moves given by this optimal strategy. On the other hand, in the other two games there is no such optimal strategy for Duplicator. Thus, the Immerman game can be regarded as a one-player game, but the other two games are genuine two-player games.

The talk is based on joint work with Kerkko Luosto.

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**Date**: Monday, 29 January 2024 at 16:00 CET (UTC+1) on Zoom

**Speaker**: Peter Pagin, Professor Emeritus at the Department of Philosophy at
Stockholm University

**Title**: Switcher Semantics and quantification

**Abstract**:

Switcher Semantics is a semantic framework that is basically characterised by
allowing *switching*: when recursively applying a semantic function *μ* to a
complex term *t*, the semantic function applying to an immediate subterm *t’* of
*t* may be a function *μ’*, distinct from *μ*. An operator-argument-position
pair is called a *switcher* if it induces such a switch. Switcher semantic
systems do not satisfy the standard form of compositionality, but a generalized
form, which allows greater flexibility. In earlier work (mostly published), some
together with Kathrin Glüer, some with Dag Westerståhl, it has been applied to
natural language constructions like proper names in modal contexts, general
terms in modal contexts, indexicals in temporal contexts, quotation, and belief
contexts. This talk will focus on quantifiers and quantification. First-order
quantifiers can be regarded as switchers, switching from truth conditions to
satisfaction conditions. The larger topic is quantification into switched
contexts. I shall begin by giving an introduction to the framework.

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**Date**: Monday, 18 December 2023 at 16:00 CET (UTC+1) on Zoom

**Speaker:** Göran Sundholm (Professor of Logic (em.), Leiden University

**Title:** Curry-Howard—a meaning explanation or just another realizability interpretation?

**Abstract**

Around 1930 a major paradigm shift occurred in the foundations of mathematics;
we may call it the METAMATHEMATICAL TURN. Until then the task of a logician had
been to design and explain a full-scale formal language that was adequate for
the practice of mathematical analysis in such a way that the axioms and rules of
inference of the theory were rendered evident by the explanations.

The metamathematical turn changed the status of the formal languages: now they became (meta)mathematical objects of study. We no longer communicate with the aid of the formal systems – we communicate about them. Kleene’s realizability (JSL 1945) gave a metamathematical (re-)interpretation of arithmetic inside arithmetic. Heyting and Kolmogorov (1931-2), on the other hand, had used “proofs” of propositions, respectively “solutions” to problems, in order to explain the meaning of the mathematical language, rather than reinterpret it internally.

We now have the choice to view the Curry-Howard isomorphism, say, as a variant of realizability, when it will be an internal mathematical re-interpretation, or to adopt an atavistic, Frege-like, viewpoint and look at the language as being rendered meaningful. This perspective will be used to discuss another paradigm shift, namely that of distinguishing constructivism and intuitionism. The hesitant attitude of Gödel, Kreisel, and Michael Dummett, will be spelled out, and, at the hand of unpublished source material, a likely reason given.

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