Upwards Closed Dependencies in Team Semantics
We prove that adding upwards closed first-order dependency atoms to first-order logic with team semantics does not increase its expressive power (with respect to sentences), and that the same remains true if we also add constancy atoms. As a consequence, the negations of functional dependence, condi...
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2013-07-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1305.4288v2 |
| Summary: | We prove that adding upwards closed first-order dependency atoms to first-order logic with team semantics does not increase its expressive power (with respect to sentences), and that the same remains true if we also add constancy atoms. As a consequence, the negations of functional dependence, conditional independence, inclusion and exclusion atoms can all be added to first-order logic without increasing its expressive power. Furthermore, we define a class of bounded upwards closed dependencies and we prove that unbounded dependencies cannot be defined in terms of bounded ones. |
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| ISSN: | 2075-2180 |