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Predicate Logic Notation: What does a "dot" mean?
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whatmeanlogicpredicatedotnotationdoes
Problem
What does a dot (.) mean in predicates?
$\forall a \in A. \exists d \in D. H(a,d)$
Especially, how is the above different to
$ \exists d \in D. \forall a \in A. H(a,d)$
I've never seen this used in German lecture scripts.
$\forall a \in A. \exists d \in D. H(a,d)$
Especially, how is the above different to
$ \exists d \in D. \forall a \in A. H(a,d)$
I've never seen this used in German lecture scripts.
Solution
The dot just means "such that"; it's often omitted.
The difference between the two formulas is the difference between "everybody has a mother" and "there is somebody who is everybody's mother."
The difference between the two formulas is the difference between "everybody has a mother" and "there is somebody who is everybody's mother."
Context
StackExchange Computer Science Q#60072, answer score: 14
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