# NLS 2024

Reykjavik Summer of Cool Logic 2024 (SCooL 2024), Reykjavik 10-21/6 2024

## Fifth Nordic Logic Summer School (NLS 2024)

### 10–13 June 2024, Reykjavík, Iceland

The fifth Nordic Logic Summer School is arranged under the auspices of the Scandinavian Logic Society. The four previous schools were organised in Bergen in Norway (2022), Stockholm in Sweden (2017), Helsinki in Finland (2015), and Nordfjordeid in Norway (2013). The intended audience is advanced master students, PhD-students, postdocs and experienced researchers wishing to learn the state of the art in a particular subject.

#### Programme Committee

**Co-chairs**

Nina Gierasimczuk (DTU Compute)

Lauri Hella (Tampere University)

**Members**

Torben Braüner (Roskilde University)

Fredrik Engström (University of Gothenburg)

Åsa Hirvonen (University of Helsinki)

Ana Ozaki (University of Bergen & University of Oslo)

### Organising Committee

Antonis Achilleos (Reykjavik University)

Aggeliki Chalki (Reykjavik University)

Vasiliki Kyriakou (Reykjavik University)

Jana Wagemaker (Reykjavik University)

Jasmine Xuereb (University of Malta and Reykjavik University)

#### Invited Speakers

**Speaker: Miika Hannula (University of Helsinki)**

*Title*: Model-theoretic perspectives on logics of dependence and independence

*Abstract*: Logics of dependence and independence (LDI) are formalisms for modelling and reasoning about notions of dependence and independence in diverse contexts. The semantics of LDI is not defined with respect to single variable assignments, but sets of assignments called teams. The rationale is the following: A single sample of two variables x and y cannot tell us anything about their mutual dependencies. It is only through multiple samples that their underlying dependencies can become manifest. The team semantics of LDI extends this idea to a compositional interpretation of logical connectives and quantifiers.

In the first half of this course we review the basic concepts and results of LDI, and consider some of its model-theoretic properties such as compactness. In the second half, we move on to discuss logics for quantitative notions of dependence and independence, such as conditional independence in probability theory. Here, every variable assignment in a team is associated with a weight. Similarly, the relations of a model are replaced with weighted relations. A useful abstraction is to assume that these weights come from a fixed semiring. We consider how the interpretation of logical formulae generalises to such weighted models and teams, and examine the impact this broadening has on properties of finite models and teams.

**Speaker: Sandra Kiefer (University of Oxford)**

*Title*: Learning Properties on Graphs and Other Relational Structures

*Abstract*: Graph Neural Networks (GNNs) are a machine learning architecture to learn functions on graphs. For example, since problem instances for combinatorial optimisation tasks are often modelled as graphs, GNNs have recently received attention as a natural framework for finding good heuristics in neural optimisation approaches.

The question which functions can actually be learnt by message-passing GNNs and which ones exceed their power links to the question of recognisability of (properties of) graphs, which has been studied extensively. In the main part of the course, we will consider this problem from the perspective of descriptive complexity. We will survey the expressivity of counting logics and use the expressivity limits to draw conclusions about the non-learnability of properties with GNNs.

In the remaining time, we will focus on the feasible part and provide a more fine-grained analysis of the actual learnability of properties that can be expressed in logics. We transition from GNNs and counting logics to extensions of first-order logic and discuss the computational complexity of learning logical formulas on relational structures from examples.

**Speaker: Greg Restall (University of St Andrews)**

*Title*: Proof Theory for Classical, Constructive, Substructural and Modal Logics

*Abstract*: In this course, I’ll introduce natural deduction and sequent calculus for classical, constructive and substructural logics, motivating and explaining how key results (normalisation for natural deduction proofs and cut elimination for sequent calculus derivations) may be proved, and how these interact with the presence or absence of the structural rules of weakening and contraction. We will also take a look at different proof systems designed to model modal and other intensional logics. Along the way we will see (1) the difference between multiplicative and additive rules for connectives (2) different ways to understand harmony between introduction and elimination rules (or left and right rules in the sequent calculus) (3) the ways in which rules for a connective may be understood as defining the concept introduced; (4) the connection between proof dynamics, dialogue and speech acts; (5) the relationship between proof search and model construction, and (6) connections between structural rules, paradoxes and fixed points.

**Speaker: Jandson Ribeiro (Cardiff University)**

*Title*: Belief Change: Foundations and Frontiers

*Abstract*: Belief Change, also dubbed Belief Revision and Belief Dynamics, studies how a corpus of beliefs should be rationally modified. This interdisciplinary field crosses philosophy, computer science and artificial intelligence. In this series of lectures, we will delve into the foundations of belief change and make our way through to recent research questions. We will start with the seminal paradigm of belief change, the AGM paradigm (named after its founders Alchourrón, Gärdenfors, and Makinson), within classical logics. In the second part of the lectures, we will discuss more recent works of belief change in non-classical logic, its implications, challenges and open research questions. The main goal is to provide a solid understanding of the field, from its origin to the more up-to-date research questions.

**Speaker: Rineke Verbrugge (University of Groningen)**

*Title*: From Epistemic Logic to Social Cognition

*Abstract*: Epistemic logic is the logic of knowledge: How do you reason about what you know and what others know? This logic appears to be crucial in describing negotiations in economics, parallel processors in computer science, and multi-agent systems in artificial intelligence. Epistemic logic is also philosophically and technically interesting: It has beautiful semantics. The lectures will deal with the following subjects from the area of epistemic logic: axiomatic systems and Kripke semantics for knowledge of multiple agents, beliefs, distributed knowledge, general knowledge and common knowledge, public announcement logic, and knowledge-based communication protocols.

One of the main questions of the course will be in which way epistemic logic is an idealization, and how people actually reason about their own and other people’s knowledge and beliefs, both in story situations where different participants have different perspectives as well as in competitive games and negotiations.

We will report on several experiments about ’theory of mind’, with animals, children and adult humans, and we will discuss how logic can be useful as a guide for empirical studies and computational cognitive modeling. Moreover, we will discuss the role of theory of mind in ‘Hybrid Intelligence’ — systems in which sofware agents, robots, and humans work together.

As a prerequisite for the course, knowledge of propositional logic and basic modal logic should suffice.

### Schedule

Monday | Tuesday | Wednesday | Thursday | |
---|---|---|---|---|

8:30-8:50 | Registration | |||

8:50-9:00 | Welcome - opening | |||

9:00-10:00 | Greg Restall | Greg Restall | Greg Restall | Greg Restall |

10:00-10:20 | Coffee break | Coffee break | Coffee break | Coffee break |

10:20-11:20 | Rineke Verbrugge | Rineke Verbrugge | Rineke Verbrugge | Rineke Verbrugge |

11:20-11:40 | Coffee break | Coffee break | Coffee break | Coffee break |

11:40-12:40 | Miika Hannula | Miika Hannula | Miika Hannula | Sandra Kiefer |

12:40-14:00 | Lunch | Lunch | Lunch | Lunch |

14:00-15:00 | Miika Hannula | Sandra Kiefer | Sandra Kiefer | Sandra Kiefer |

15:00-15:30 | Coffee break | Coffee break | Coffee break | Coffee break |

15:30-16:30 | Jandson Ribeiro | Jandson Ribeiro | Jandson Ribeiro | Jandson Ribeiro |

19:00-… | Joint NLS and SLSS dinner at La Primavera |

**Rooms**

M106 on Monday and Tuesday

M103 on Wednesday and Thursday

The rooms are on the ground floor (1st floor) of the building. Maps of the building can be found here.

#### Registration

Early registration deadline: May 24

You can register here.