Biannual Report - Fachbereich Mathematik - Technische Universität ...

are available through a process of unfolding (e.g., of transition systems or game graphs
into trees). Fully acyclic unfoldings are, however, typically unavailable in settings where
only finite structures are admissible. For such applications, especially in the realm of finite
model theory, the focus must therefore be on
• suitable relaxations of full acyclicity that can be realised in finitary coverings (partial
unfoldings), and
• methods that make available in these relaxed scenarios the good algorithmic and
model-theoretic properties that are familiar from fully acyclic unfoldings.
The new project puts the development of constructions and methods at the center with
a view to a more systematic understanding and to extending the reach of corresponding
model-theoretic techniques to further application domains.
At the level of basic research the project is geared to draw on logical and model-theoretic
methods as well as on new connections with techniques from discrete mathematics (e.g.,
permutation groups, the combinatorics of graphs and hypergraphs, discrete geometry,
combinatorial and algebraic methods). First major results have been reported in [3].
Support: DFG
Contact: M. Otto
References
[1] V. Barany, G. Gottlob, and M. Otto. Querying the guarded fragment. Preprint of journal version
of LICS’10 paper, available online, 2012.
[2] M. Otto. Highly acyclic groups, hypergraph covers and the guarded fragment. Journal of the
ACM, 59, 2012.
[3] M. Otto. On groupoids and hypergraphs. Technical report, 37 pages, available online
arXiv:1211.5656, 2012.
[4] M. Otto. Expressive completeness through logically tractable models. Annals of Pure and
Applied Logic, 2013. to appear.
Project: Classical Realizability
In the last decade J.-L. Krivine introduced his realizability interpretation for various classical
systems including Zermelo Fraenkel set theory [1]. Whereas most of the models so far
were based on term models for λ-calculus with control I have recently studied a domaintheoretic
model obtained by solving the domain equation D ∼ = Σ Dω in the category of
coherence spaces. In the ensuing classical realizability model the type ∇(2) is infinite. I
am trying to show that it is not Dedekind infinite because this would entail that the Axiom
of Dependent Choice fails in this model which is a difficult open problem in the area.
Partner: A. Miquel (ENS Lyon)
Contact: T. Streicher
References
[1] J.-L. Krivine. Realizability in classical logic. Panoramas et synthèses, 27, 2009.
Project: Homotopy Type Theory inside Realizability Models
1.2 Research Groups 55