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#141
 
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Re: Foreign keys -
01-16-2008
, 06:22 PM
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On 15 jan, 08:24, Kira Yamato <kira... (AT) earthlink (DOT) net> wrote: On 2008-01-14 21:18:57 -0500, "Evan Keel" <evank... (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let * * * * R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation * * * * R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes . Then the foreign key B1 represents the functional dependency * * * * B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 -- B1, the foreign key also represents the inter-relational functional dependency * * * * K1 --> A2. Am I correct to say this? Not really. Your observation that sometimes the inference rules are the same for functional and inclusion dependencies is correct, but unfortunately this is not true in general. For example, the augmentation rule does not always hold for inclusion dependencies. In fact, axiomatizing the combination of functional and inclusion dependencies is a notoriously difficult problem and in the past there has been intensive research on that subject. |
functional dependencies can be defined across relations.
However, after reading the definition more carefully, functional
dependency is only defined within a single relation.
Foreign keys, on the other hand, represent inter-relational
constraints. It takes on a different definition.
Consequently, they take on different inference rules, as you stated.
I apologize for my confusion. Especially to Brian Selzer. And thanks
for both yours and his corrections.
--
-kira
#142
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On 15 jan, 08:24, Kira Yamato <kira... (AT) earthlink (DOT) net> wrote: On 2008-01-14 21:18:57 -0500, "Evan Keel" <evank... (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let * * * * R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation * * * * R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes . Then the foreign key B1 represents the functional dependency * * * * B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 -- B1, the foreign key also represents the inter-relational functional dependency * * * * K1 --> A2. Am I correct to say this? Not really. Your observation that sometimes the inference rules are the same for functional and inclusion dependencies is correct, but unfortunately this is not true in general. For example, the augmentation rule does not always hold for inclusion dependencies. In fact, axiomatizing the combination of functional and inclusion dependencies is a notoriously difficult problem and in the past there has been intensive research on that subject. |
functional dependencies can be defined across relations.
However, after reading the definition more carefully, functional
dependency is only defined within a single relation.
Foreign keys, on the other hand, represent inter-relational
constraints. It takes on a different definition.
Consequently, they take on different inference rules, as you stated.
I apologize for my confusion. Especially to Brian Selzer. And thanks
for both yours and his corrections.
--
-kira
#143
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On 15 jan, 08:24, Kira Yamato <kira... (AT) earthlink (DOT) net> wrote: On 2008-01-14 21:18:57 -0500, "Evan Keel" <evank... (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let * * * * R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation * * * * R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes . Then the foreign key B1 represents the functional dependency * * * * B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 -- B1, the foreign key also represents the inter-relational functional dependency * * * * K1 --> A2. Am I correct to say this? Not really. Your observation that sometimes the inference rules are the same for functional and inclusion dependencies is correct, but unfortunately this is not true in general. For example, the augmentation rule does not always hold for inclusion dependencies. In fact, axiomatizing the combination of functional and inclusion dependencies is a notoriously difficult problem and in the past there has been intensive research on that subject. |
functional dependencies can be defined across relations.
However, after reading the definition more carefully, functional
dependency is only defined within a single relation.
Foreign keys, on the other hand, represent inter-relational
constraints. It takes on a different definition.
Consequently, they take on different inference rules, as you stated.
I apologize for my confusion. Especially to Brian Selzer. And thanks
for both yours and his corrections.
--
-kira
#144
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On 15 jan, 08:24, Kira Yamato <kira... (AT) earthlink (DOT) net> wrote: On 2008-01-14 21:18:57 -0500, "Evan Keel" <evank... (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let * * * * R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation * * * * R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes . Then the foreign key B1 represents the functional dependency * * * * B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 -- B1, the foreign key also represents the inter-relational functional dependency * * * * K1 --> A2. Am I correct to say this? Not really. Your observation that sometimes the inference rules are the same for functional and inclusion dependencies is correct, but unfortunately this is not true in general. For example, the augmentation rule does not always hold for inclusion dependencies. In fact, axiomatizing the combination of functional and inclusion dependencies is a notoriously difficult problem and in the past there has been intensive research on that subject. |
functional dependencies can be defined across relations.
However, after reading the definition more carefully, functional
dependency is only defined within a single relation.
Foreign keys, on the other hand, represent inter-relational
constraints. It takes on a different definition.
Consequently, they take on different inference rules, as you stated.
I apologize for my confusion. Especially to Brian Selzer. And thanks
for both yours and his corrections.
--
-kira
#145
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On 15 jan, 08:24, Kira Yamato <kira... (AT) earthlink (DOT) net> wrote: On 2008-01-14 21:18:57 -0500, "Evan Keel" <evank... (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let * * * * R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation * * * * R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes . Then the foreign key B1 represents the functional dependency * * * * B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 -- B1, the foreign key also represents the inter-relational functional dependency * * * * K1 --> A2. Am I correct to say this? Not really. Your observation that sometimes the inference rules are the same for functional and inclusion dependencies is correct, but unfortunately this is not true in general. For example, the augmentation rule does not always hold for inclusion dependencies. In fact, axiomatizing the combination of functional and inclusion dependencies is a notoriously difficult problem and in the past there has been intensive research on that subject. |
functional dependencies can be defined across relations.
However, after reading the definition more carefully, functional
dependency is only defined within a single relation.
Foreign keys, on the other hand, represent inter-relational
constraints. It takes on a different definition.
Consequently, they take on different inference rules, as you stated.
I apologize for my confusion. Especially to Brian Selzer. And thanks
for both yours and his corrections.
--
-kira
#146
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On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 -- B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? -- -kira Not reading the whole thread (big mistake on my part), but how about the |
legit.
Evan
#147
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On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 -- B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? -- -kira Not reading the whole thread (big mistake on my part), but how about the |
legit.
Evan
#148
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On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 -- B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? -- -kira Not reading the whole thread (big mistake on my part), but how about the |
legit.
Evan
#149
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On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 -- B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? -- -kira Not reading the whole thread (big mistake on my part), but how about the |
legit.
Evan
#150
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On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel (AT) sbcglobal (DOT) net> said: Always a physical issue. Never a theory issue.Agree? Foreign keys are functional dependencies across two relations. More specifically, let R1(K1, A1, B1) be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary key and B1 is a foreign key to the relation R2(K2, A2) where K2 is R2's primary key and A2 is the set of its remaining attributes. Then the foreign key B1 represents the functional dependency B1 --> A2, which is the functional dependency across two relation I mentioned in the first sentence. Furthermore, through transitivity by the functional dependency K1 -- B1, the foreign key also represents the inter-relational functional dependency K1 --> A2. Am I correct to say this? -- -kira Not reading the whole thread (big mistake on my part), but how about the |
legit.
Evan
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