LIPIcs.CSL.2020.25.pdf
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On the Union Closed Fragment of Existential Second-Order Logic and Logics with Team Semantics
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28th EACSL Annual Conference on Computer Science Logic (CSL 2020)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Computer Science Logic (CSL) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2020-01-06
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Matthias Hoelzel and Richard Wilke. On the Union Closed Fragment of Existential Second-Order Logic and Logics with Team Semantics. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.CSL.2020.25
Abstract
We present syntactic characterisations for the union closed fragments of existential second-order logic and of logics with team semantics. Since union closure is a semantical and undecidable property, the normal form we introduce enables the handling and provides a better understanding of this fragment. We also introduce inclusion-exclusion games that turn out to be precisely the corresponding model-checking games. These games are not only interesting in their own right, but they also are a key factor towards building a bridge between the semantic and syntactic fragments. On the level of logics with team semantics we additionally present restrictions of inclusion-exclusion logic to capture the union closed fragment. Moreover, we define a team based atom that when adding it to first-order logic also precisely captures the union closed fragment of existential second-order logic which answers an open question by Galliani and Hella.
Subject Classification
ACM Subject Classification
- Theory of computation → Higher order logic
Keywords
- Higher order logic
- Existential second-order logic
- Team semantics
- Closure properties
- Union closure
- Model-checking games
- Syntactic charactisations of semantical fragments
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References
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