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Kant's view was incorporated into the standard predicate logic by Frege and Russell, who treat existence not as a property of objects (predicate), but as a property of properties (quantifier). It applies to a list of properties ("conception") and returns true or false depending on whether there is an object in the domain of discourse which instantiates that list. Of course, existence can still be treated as a "characteristic" of objects with the help of identity, ∃x(x=a) expresses that a exists. But on a closer look what is being asserted is not that a exists but rather that the predicate is-a ("=a") is instantiated. There is no way to say that some a does not exist, ¬∃x(x=a) rather says that being-a is not a property of anything. One can object to such logicization of Kant's view (against his express words, apparently), but this is the prevailing interpretation of what he meant even among opponents of his view. Kant's notion of "conception" was developed into the descriptivist semantics by Russell, which came under heavy criticism, especially by Kripke in 1970s, see Kripke’s Attack on Descriptivism by Speaks, who offered an alternative theory of reference. Arguing with Kripke over Existence on Maverick Philosopher quotes him on existence specifically:

Kant's view was incorporated into the standard predicate logic by Frege and Russell, who treat existence not as a property of objects (predicate), but as a property of properties (quantifier). It applies to a list of properties ("conception") and returns true or false depending on whether there is an object in the domain of discourse which instantiates that list. Of course, existence can still be treated as a "characteristic" of objects with the help of identity, ∃x(x=a) expresses that a exists. But on a closer look what is being asserted is not that a exists but rather that the predicate is-a ("=a") is instantiated. There is no way to say that some a does not exist, ¬∃x(x=a) rather says that being-a is not a property of anything. One can object to such logicization of Kant's view (against his express words, apparently), but this is the prevailing interpretation of what he meant even among opponents of his view. Kant's notion of "conception" was developed into the descriptivist semantics by Russell, which came under heavy criticism, especially by Kripke in 1970s, see Kripke’s Attack on Descriptivism by Speaks, who offered an alternative theory of reference. Arguing with Kripke over Existence on Maverick Philosopher quotes him on existence specifically:

Kant's view was incorporated into the standard predicate logic by Frege and Russell, who treat existence not as a property of objects (predicate), but as a property of properties (quantifier). It applies to a list of properties ("conception") and returns true or false depending on whether there is an object in the domain of discourse which instantiates that list. Of course, existence can still be treated as a "characteristic" of objects with the help of identity, ∃x(x=a) expresses that a exists. But on a closer look what is being asserted is not that a exists but rather that the predicate is-a ("=a") is instantiated. There is no way to say that some a does not exist, ¬∃x(x=a) rather says that being-a is not a property of anything. One can object to such logicization of Kant's view (against his express words, apparently), but this is the prevailing interpretation of what he meant even among opponents of his view. Kant's notion of "conception" was developed into the descriptivist semantics by Russell, which came under heavy criticism, especially by Kripke in 1970s, see Kripke’s Attack on Descriptivism by Speaks, who offered an alternative theory of reference. Arguing with Kripke over Existence on Maverick Philosopher quotes him on existence specifically:

Kant's view was incorporated into the standard predicate logic by Frege and Russell, who treat existence not as a property of objects (predicate), but as a property of properties (quantifier). It applies to a list of properties ("conception") and returns true or false depending on whether there is an object in the domain of discourse which instantiates that list. Of course, existence can still be treated as a "characteristic" of objects with the help of identity, ∃x(x=a) expresses that a exists. But on a closer look what is being asserted is not that a exists but rather that the predicate is-a ("=a") is instantiated. There is no way to say that some a does not exist, ¬∃x(x=a) rather says that being-a is not a property of anything. One can object to such logicization of Kant's view (against his express words, apparently), but this is the prevailing interpretation of what he meant even among opponents of his view. Kant's notion of "conception" was developed into the descriptivist semantics by Russell, which came under heavy criticism, especially by Kripke in 1970s, see Kripke’s Attack on Descriptivism by Speaks, who offered an alternative theory of reference. Arguing with Kripke over Existence on Maverick Philosopher quotes him on existence specifically:

"What the standard Platonic-Aristotelian interpretation puts in Parmenides’ mouth may be phrased by claiming that, for him, any concept including or entailing nonbeing in any form applies to nothing... much contemporary philosophy is dominated by what one may call the Parmenidean Thesis: everything exists... The philosophers we are about to meet have reinforced the Parmenidean position in two moves: (1) they have expanded the slogan “Existence is not a predicate” into the thesis that existence is (nothing but) property-instantiation; (2) they have also explained existence in terms of the logical notion of quantification. Both moves were made mainly by Frege and, derivatively, by Russell.

 

[...] Here comes a non-Parmenidean approach. To begin with, “exists” is a predicate of individuals just like the others – a predicate for real, not only from the point of view of our ordinary language’s surface grammar. It is a predicate in the same sense that “eats”, “flies”, and “is a man” are... The motto is Alexander’s famous one: “To be is to have causal powers”... The Parmenidean conception, once forced to admit that even from its viewpoint existence can be a property of individuals, still explains it away, defining it via the existential quantifier and identity, that is, via logical notions. But existence is not taken as a logical notion from now on: if to exist has to do with the enjoying of causal powers, whatever these actually are, they are not logical features."

"What the standard Platonic-Aristotelian interpretation puts in Parmenides’ mouth may be phrased by claiming that, for him, any concept including or entailing nonbeing in any form applies to nothing... much contemporary philosophy is dominated by what one may call the Parmenidean Thesis: everything exists... The philosophers we are about to meet have reinforced the Parmenidean position in two moves: (1) they have expanded the slogan “Existence is not a predicate” into the thesis that existence is (nothing but) property-instantiation; (2) they have also explained existence in terms of the logical notion of quantification. Both moves were made mainly by Frege and, derivatively, by Russell.

[...] Here comes a non-Parmenidean approach. To begin with, “exists” is a predicate of individuals just like the others – a predicate for real, not only from the point of view of our ordinary language’s surface grammar. It is a predicate in the same sense that “eats”, “flies”, and “is a man” are... The motto is Alexander’s famous one: “To be is to have causal powers”... The Parmenidean conception, once forced to admit that even from its viewpoint existence can be a property of individuals, still explains it away, defining it via the existential quantifier and identity, that is, via logical notions. But existence is not taken as a logical notion from now on: if to exist has to do with the enjoying of causal powers, whatever these actually are, they are not logical features."