https://www.dagstuhl.de/15261

### June 21 – 26 , 2015, Dagstuhl Seminar 15261

# Logics for Dependence and Independence

## Organizers

Erich Grädel (RWTH Aachen, DE)

Juha Kontinen (University of Helsinki, FI)

Jouko Väänänen (University of Helsinki, FI)

Heribert Vollmer (Leibniz Universität Hannover, DE)

## For support, please contact

## Documents

Dagstuhl Report, Volume 5, Issue 6

Aims & Scope

List of Participants

Shared Documents

Dagstuhl Seminar Schedule [pdf]

## Summary

### Brief Introduction to the Topic

Dependence and independence are interdisciplinary notions that are pervasive in many areas of science. They appear in domains such as mathematics, computer science, statistics, quantum physics, and game theory. The development of logical and semantical structures for these notions provides an opportunity for a systematic approach, which can expose surprising connections between different areas, and may lead to useful general results.

Dependence Logic is a new tool for modeling dependencies and interaction in dynamical scenarios. Reflecting this, it has higher expressive power and complexity than classical logics used for these purposes previously. Algorithmically, first-order dependence logic corresponds exactly to the complexity class NP and to the so-called existential fragment of second-order logic. Since the introduction of dependence logic in 2007, the framework has been generalized, e.,g., to the contexts of modal, intuitionistic, and probabilistic logic. Moreover, interesting connections have been found to complexity theory, database theory, statistics, and dependence logic has been applied in areas such as linguistics, social choice theory, and physics. Although significant progress has been made in understanding the computational side of these formalisms, still many central questions remain unsolved so far.

The Dagstuhl seminar 'Dependence Logic: Theory and Applications' had a major impact to the field of dependence logic opening up connections to new application areas. The aim of this follow-up seminar was to gather together the people working in dependence logic and in the application areas, especially those researchers who have recently started working in this quickly developing area to communicate state-of-the-art advances and embark on a systematic interaction.

### Organization of the Seminar and Activities

The seminar brought together 38 researchers from mathematics, statistics, database theory, natural language semantics, and theoretical computer science. The participants consisted of both senior and junior researchers, including a number of postdocs and advanced graduate students.

Participants were invited to present their work and to communicate state-of-the-art advances. Over the five days of the seminar, 27 talks of various lengths took place. Introductory and tutorial talks of 90-60 minutes were scheduled prior to seminar. Most of the remaining slots were filled, mostly with shorter talks, as the seminar commenced. The organizers considered it important to leave ample free time for discussion.

The tutorial talks were scheduled during the beginning of the week in order to establish a common background for the different communities that came together for the seminar. The presenters and topics were:

- Jouko Väänänen and Juha Kontinen, Dependence Logic
- Bernhard Thalheim, Database Constraints -- A Survey
- Ilya Shpitser, Causal inference
- Lauri Hella, Modal dependence logic
- Ivanio Ciardelli, Dependency as Question Entailment
- Antti Hyttinen, Statistical Independence, Causality and Constraint Satisfaction

There were additionally two introductory talks with a more focused and technical topic:

- Alex Simpson, Sheaf semantics for independence logics
- Phokion Kolaitis, The Query Containment Problem: Set Semantics vs. Bag Semantics

Additionally, the following shorter presentations were given during the seminar:

- Asa Hirvonen, Model theoretic independence
- Kerkko Luosto, Dimensions for Modal Dependence Logic
- Gianluca Paolini, Measure teams
- Olaf Beyersdorff, Proof Complexity of Quantified Boolean Formulas
- Antti Kuusisto, Propositional dependence logic via Kripke semantics
- Johanna Stumpf, Characterisation of the expressive power of modal logic with inclusion atoms
- Sebastian Link, Dependence-driven, non-invasive cleaning of uncertain data
- Jonni Virtema, Complexity of Propositional Inclusion and Independence Logic
- Katsuhiko Sano, Characterizing Frame Definability in Team Semantics via The Universal Modality
- Raine Rönnholm, Expressing properties of teams in k-ary inclusion-exclusion logic
- Julian Bradfield, On the structure of events in Boolean games
- Fan Yang, Some proof theoretical results on propositional logics of dependence and independence
- Erich Grädel, Counting in Team Semantics
- Fredrik Engström, Generalized quantifiers and Dependence Logic
- Miika Hannula, Axiomatizing dependencies in team semantics
- Dietmar Berwanger, An NL-fragment of inclusion logic
- Nicolas de Rugy-Altherre, Tractability Frontier of Data Complexity in Team Semantics

For some of these, an abstract can be found below.

The seminar achieved its aim of bringing together researchers from various related communities to share state-of-the-art research. The organizers left ample time outside of this schedule of talks and many fruitful discussions between participants took place throughout the afternoons and evenings.

### Concluding Remarks and Future Plans

The organizers regard the seminar as a great success. Bringing together researchers from different areas fostered valuable interactions and led to fruitful discussions. Feedback from the participants was very positive as well.

Finally, the organizers wish to express their gratitude toward the Scientific Directorate of the Center for its support of this seminar.

**Summary text license**

Creative Commons BY 3.0 Unported license

Erich Grädel, Juha Kontinen, Jouko Väänänen, and Heribert Vollmer

## Dagstuhl Seminar Series

- 19031: "Logics for Dependence and Independence" (2019)
- 13071: "Dependence Logic: Theory and Applications" (2013)

## Classification

- Data Structures / Algorithms / Complexity
- Verification / Logic

## Keywords

- Dependence logic
- Mathematical logic
- Computational complexity
- Finite model theory
- Game theory