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Guarded Teams: The Horizontally Guarded Case

Authors Erich Grädel, Martin Otto

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Author Details

Erich Grädel
  • RWTH Aachen University, Germany
Martin Otto
  • Technische Universität Darmstadt, Germany

Acknowledgements

We gratefully acknowledge participation in the programme on Logical Structure in Computation at the Simons Institute in Berkeley in 2016, which provided interesting stimulation towards this work.

Cite As Get BibTex

Erich Grädel and Martin Otto. Guarded Teams: The Horizontally Guarded Case. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.CSL.2020.22

Abstract

Team semantics admits reasoning about large sets of data, modelled by sets of assignments (called teams), with first-order syntax. This leads to high expressive power and complexity, particularly in the presence of atomic dependency properties for such data sets. It is therefore interesting to explore fragments and variants of logic with team semantics that permit model-theoretic tools and algorithmic methods to control this explosion in expressive power and complexity. 
We combine here the study of team semantics with the notion of guarded logics, which are well-understood in the case of classical Tarski semantics, and known to strike a good balance between expressive power and algorithmic manageability. In fact there are two strains of guardedness for teams. Horizontal guardedness requires the individual assignments of the team to be guarded in the usual sense of guarded logics. Vertical guardedness, on the other hand, posits an additional (or definable) hypergraph structure on relational structures in order to interpret a constraint on the component-wise variability of assignments within teams.
In this paper we investigate the horizontally guarded case. We study horizontally guarded logics for teams and appropriate notions of guarded team bisimulation. In particular, we establish characterisation theorems that relate invariance under guarded team bisimulation with guarded team logics, but also with logics under classical Tarski semantics.

Subject Classification

ACM Subject Classification
  • Theory of computation → Finite Model Theory
Keywords
  • Team semantics
  • guarded logics
  • bisimulation
  • characterisation theorems

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