Limits of Schema Mappings
Schema mappings have been extensively studied in the context of data exchange and data integration, where they have turned out to be the right level of abstraction for formalizing data inter-operability tasks. Up to now and for the most part, schema mappings have been studied as static objects, in t...
| Main Authors: | , , , |
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| Format: | Conference item |
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Dagstuhl Publishing
2016
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| _version_ | 1826295156333084672 |
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| author | Kolaitis, P Pichler, R Sallinger, E Savenkov, V |
| author_facet | Kolaitis, P Pichler, R Sallinger, E Savenkov, V |
| author_sort | Kolaitis, P |
| collection | OXFORD |
| description | Schema mappings have been extensively studied in the context of data exchange and data integration, where they have turned out to be the right level of abstraction for formalizing data inter-operability tasks. Up to now and for the most part, schema mappings have been studied as static objects, in the sense that each time the focus has been on a single schema mapping of interest or, in the case of composition, on a pair of schema mappings of interest. In this paper, we adopt a dynamic viewpoint and embark on a study of sequences of schema mappings and of the limiting behavior of such sequences. To this effect, we first introduce a natural notion of distance on sets of finite target instances that expresses how “close” two sets of target instances are as regards the certain answers of conjunctive queries on these sets. Using this notion of distance, we investigate pointwise limits and uniform limits of sequences of schema mappings, as well as the companion notions of pointwise Cauchy and uniformly Cauchy sequences of schema mappings. We obtain a number of results about the limits of sequences of GAV schema mappings and the limits of sequences of LAV schema mappings that reveal striking differences between these two classes of schema mappings. We also consider the completion of the metric space of sets of target instances and obtain concrete representations of limits of sequences of schema mappings in terms of generalized schema mappings, i.e., schema mappings with infinite target instances as solutions to (finite) source instances. |
| first_indexed | 2024-03-07T03:56:43Z |
| format | Conference item |
| id | oxford-uuid:c31f586a-d60b-473b-a3e1-89dd489f98d6 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:56:43Z |
| publishDate | 2016 |
| publisher | Dagstuhl Publishing |
| record_format | dspace |
| spelling | oxford-uuid:c31f586a-d60b-473b-a3e1-89dd489f98d62022-03-27T06:14:13ZLimits of Schema MappingsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:c31f586a-d60b-473b-a3e1-89dd489f98d6Symplectic Elements at OxfordDagstuhl Publishing2016Kolaitis, PPichler, RSallinger, ESavenkov, VSchema mappings have been extensively studied in the context of data exchange and data integration, where they have turned out to be the right level of abstraction for formalizing data inter-operability tasks. Up to now and for the most part, schema mappings have been studied as static objects, in the sense that each time the focus has been on a single schema mapping of interest or, in the case of composition, on a pair of schema mappings of interest. In this paper, we adopt a dynamic viewpoint and embark on a study of sequences of schema mappings and of the limiting behavior of such sequences. To this effect, we first introduce a natural notion of distance on sets of finite target instances that expresses how “close” two sets of target instances are as regards the certain answers of conjunctive queries on these sets. Using this notion of distance, we investigate pointwise limits and uniform limits of sequences of schema mappings, as well as the companion notions of pointwise Cauchy and uniformly Cauchy sequences of schema mappings. We obtain a number of results about the limits of sequences of GAV schema mappings and the limits of sequences of LAV schema mappings that reveal striking differences between these two classes of schema mappings. We also consider the completion of the metric space of sets of target instances and obtain concrete representations of limits of sequences of schema mappings in terms of generalized schema mappings, i.e., schema mappings with infinite target instances as solutions to (finite) source instances. |
| spellingShingle | Kolaitis, P Pichler, R Sallinger, E Savenkov, V Limits of Schema Mappings |
| title | Limits of Schema Mappings |
| title_full | Limits of Schema Mappings |
| title_fullStr | Limits of Schema Mappings |
| title_full_unstemmed | Limits of Schema Mappings |
| title_short | Limits of Schema Mappings |
| title_sort | limits of schema mappings |
| work_keys_str_mv | AT kolaitisp limitsofschemamappings AT pichlerr limitsofschemamappings AT sallingere limitsofschemamappings AT savenkovv limitsofschemamappings |