Terrell said:∃x¬R(x,a) --> ¬∃R(a,x)
thank you stephen!Stephen Tashi said:As fresh_42 pointed out, the usual notation would be something like ##\lnot( \exists x ( R(a,x) )##
Your general approach is correct.
yes i missed an "x" there. how was "a" not quantified?fresh_42 said:I have trouble to understand your notation. ##\lnot R(x,a)## suggests, that it is a statement, whereas ##\exists R(a,x)## looks like an element somewhere. Furthermore ##a## isn't quantified.
Well, is ##a## fixed? Then it could be taken as part of ##R##, if ##R## is symmetric, which I don't know. Or does it mean for all ##a##, or there is an ##a##? Since it is in all occurrences of ##R## I tend to put it into the definition of ##R## to get rid of it, as it seems to be unnecessary. But then there are ##R(a,x)## and ##R(x,a)## and I don't know. what is the difference between them.Terrell said:yes i missed an "x" there. how was "a" not quantified?
Existential generalization is a logical inference rule that allows us to conclude that something exists based on the existence of a specific instance or example.
Existential generalization works by taking a specific instance or example of something that exists and generalizing it to say that there exists at least one thing that has that property or characteristic.
An example of using existential generalization would be if we observe a black cat and conclude that there exists at least one black animal, without having observed any other black animals.
The limitations of using existential generalization include the fact that it only allows us to conclude the existence of something, but not its uniqueness or quantity.
Existential generalization and universal generalization are similar in that they both involve generalizing from specific instances to a more general statement. However, existential generalization deals with the existence of something, while universal generalization deals with the properties or characteristics of something.