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#171
 
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Re: Towards a definition of atomic -
02-05-2008
, 04:54 AM
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On Feb 4, 11:29 pm, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote: On 4 feb, 03:09, David BL <davi... (AT) iinet (DOT) net.au> wrote: What do you think of the idea to use existence of a bijection as a definition of information equivalence between databases (expressed with alternative DB schema)? It depends a bit on what intuitive concept of equivalence you want to formalize. Under this definition, for example, all schemas that have countably infinite many instances are equivalent. That is probably too crude. Way too crude! * Yes, I can see the bijection needs to be constrained somehow. Presumably the bijection exists if and only if the set of instances for each schema have the same cardinality. * I gather that is in fact the definition of equal cardinality. |
genericity as defined in the context of database query and
transformation language research. It is probably the single most
important concept for understanding that theory, but something that
people often have difficulty getting their head around.
-- Jan Hidders
#172
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On Feb 4, 11:29 pm, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote: On 4 feb, 03:09, David BL <davi... (AT) iinet (DOT) net.au> wrote: What do you think of the idea to use existence of a bijection as a definition of information equivalence between databases (expressed with alternative DB schema)? It depends a bit on what intuitive concept of equivalence you want to formalize. Under this definition, for example, all schemas that have countably infinite many instances are equivalent. That is probably too crude. Way too crude! * Yes, I can see the bijection needs to be constrained somehow. Presumably the bijection exists if and only if the set of instances for each schema have the same cardinality. * I gather that is in fact the definition of equal cardinality. |
genericity as defined in the context of database query and
transformation language research. It is probably the single most
important concept for understanding that theory, but something that
people often have difficulty getting their head around.
-- Jan Hidders
#173
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On Feb 4, 11:29 pm, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote: On 4 feb, 03:09, David BL <davi... (AT) iinet (DOT) net.au> wrote: What do you think of the idea to use existence of a bijection as a definition of information equivalence between databases (expressed with alternative DB schema)? It depends a bit on what intuitive concept of equivalence you want to formalize. Under this definition, for example, all schemas that have countably infinite many instances are equivalent. That is probably too crude. Way too crude! * Yes, I can see the bijection needs to be constrained somehow. Presumably the bijection exists if and only if the set of instances for each schema have the same cardinality. * I gather that is in fact the definition of equal cardinality. |
genericity as defined in the context of database query and
transformation language research. It is probably the single most
important concept for understanding that theory, but something that
people often have difficulty getting their head around.
-- Jan Hidders
#174
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On Feb 4, 11:29 pm, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote: On 4 feb, 03:09, David BL <davi... (AT) iinet (DOT) net.au> wrote: What do you think of the idea to use existence of a bijection as a definition of information equivalence between databases (expressed with alternative DB schema)? It depends a bit on what intuitive concept of equivalence you want to formalize. Under this definition, for example, all schemas that have countably infinite many instances are equivalent. That is probably too crude. Way too crude! * Yes, I can see the bijection needs to be constrained somehow. Presumably the bijection exists if and only if the set of instances for each schema have the same cardinality. * I gather that is in fact the definition of equal cardinality. |
genericity as defined in the context of database query and
transformation language research. It is probably the single most
important concept for understanding that theory, but something that
people often have difficulty getting their head around.
-- Jan Hidders
#175
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On Feb 4, 11:29 pm, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote: On 4 feb, 03:09, David BL <davi... (AT) iinet (DOT) net.au> wrote: What do you think of the idea to use existence of a bijection as a definition of information equivalence between databases (expressed with alternative DB schema)? It depends a bit on what intuitive concept of equivalence you want to formalize. Under this definition, for example, all schemas that have countably infinite many instances are equivalent. That is probably too crude. Way too crude! * Yes, I can see the bijection needs to be constrained somehow. Presumably the bijection exists if and only if the set of instances for each schema have the same cardinality. * I gather that is in fact the definition of equal cardinality. |
genericity as defined in the context of database query and
transformation language research. It is probably the single most
important concept for understanding that theory, but something that
people often have difficulty getting their head around.
-- Jan Hidders
#176
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On Feb 4, 11:29 pm, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote: On 4 feb, 03:09, David BL <davi... (AT) iinet (DOT) net.au> wrote: What do you think of the idea to use existence of a bijection as a definition of information equivalence between databases (expressed with alternative DB schema)? It depends a bit on what intuitive concept of equivalence you want to formalize. Under this definition, for example, all schemas that have countably infinite many instances are equivalent. That is probably too crude. Way too crude! * Yes, I can see the bijection needs to be constrained somehow. Presumably the bijection exists if and only if the set of instances for each schema have the same cardinality. * I gather that is in fact the definition of equal cardinality. |
genericity as defined in the context of database query and
transformation language research. It is probably the single most
important concept for understanding that theory, but something that
people often have difficulty getting their head around.
-- Jan Hidders
#177
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On Feb 4, 11:29 pm, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote: On 4 feb, 03:09, David BL <davi... (AT) iinet (DOT) net.au> wrote: What do you think of the idea to use existence of a bijection as a definition of information equivalence between databases (expressed with alternative DB schema)? It depends a bit on what intuitive concept of equivalence you want to formalize. Under this definition, for example, all schemas that have countably infinite many instances are equivalent. That is probably too crude. Way too crude! * Yes, I can see the bijection needs to be constrained somehow. Presumably the bijection exists if and only if the set of instances for each schema have the same cardinality. * I gather that is in fact the definition of equal cardinality. |
genericity as defined in the context of database query and
transformation language research. It is probably the single most
important concept for understanding that theory, but something that
people often have difficulty getting their head around.
-- Jan Hidders
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