diff --git a/compiler/src/dotty/tools/dotc/core/Definitions.scala b/compiler/src/dotty/tools/dotc/core/Definitions.scala
index f0d9582ef9fe..9e1a3d9a2baa 100644
--- a/compiler/src/dotty/tools/dotc/core/Definitions.scala
+++ b/compiler/src/dotty/tools/dotc/core/Definitions.scala
@@ -851,8 +851,8 @@ class Definitions {
     @tu lazy val TypeBox_CAP: TypeSymbol = TypeBoxClass.requiredType(tpnme.CAP)
 
   @tu lazy val MatchCaseClass: ClassSymbol = requiredClass("scala.runtime.MatchCase")
-  @tu lazy val NotClass: ClassSymbol = requiredClass("scala.util.Not")
-    @tu lazy val Not_value: Symbol = NotClass.companionModule.requiredMethod(nme.value)
+  @tu lazy val NotGivenClass: ClassSymbol = requiredClass("scala.util.NotGiven")
+    @tu lazy val NotGiven_value: Symbol = NotGivenClass.companionModule.requiredMethod(nme.value)
 
   @tu lazy val ValueOfClass: ClassSymbol = requiredClass("scala.ValueOf")
 
diff --git a/compiler/src/dotty/tools/dotc/typer/Implicits.scala b/compiler/src/dotty/tools/dotc/typer/Implicits.scala
index 03a81f42745b..61eb32bb11f5 100644
--- a/compiler/src/dotty/tools/dotc/typer/Implicits.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Implicits.scala
@@ -1072,7 +1072,7 @@ trait Implicits:
       else ViewProto(wildApprox(argument.tpe.widen), wildApprox(pt))
         // Not clear whether we need to drop the `.widen` here. All tests pass with it in place, though.
 
-    val isNot: Boolean = wildProto.classSymbol == defn.NotClass
+    val isNotGiven: Boolean = wildProto.classSymbol == defn.NotGivenClass
 
     /** Try to type-check implicit reference, after checking that this is not
       * a diverging search
@@ -1201,10 +1201,10 @@ trait Implicits:
         }
 
       def negateIfNot(result: SearchResult) =
-        if (isNot)
+        if (isNotGiven)
           result match {
             case _: SearchFailure =>
-              SearchSuccess(ref(defn.Not_value), defn.Not_value.termRef, 0)(
+              SearchSuccess(ref(defn.NotGiven_value), defn.NotGiven_value.termRef, 0)(
                 ctx.typerState.fresh().setCommittable(true),
                 ctx.gadt
               )
@@ -1220,7 +1220,7 @@ trait Implicits:
              |According to the new implicit resolution rules this is no longer possible;
              |the search will fail with a global ambiguity error instead.
              |
-             |Consider using the scala.util.Not class to implement similar functionality.""",
+             |Consider using the scala.util.NotGiven class to implement similar functionality.""",
              ctx.source.atSpan(span))
 
       /** A relation that influences the order in which implicits are tried.
diff --git a/docs/docs/reference/contextual/givens.md b/docs/docs/reference/contextual/givens.md
index b7670698ee68..b63607dfb68c 100644
--- a/docs/docs/reference/contextual/givens.md
+++ b/docs/docs/reference/contextual/givens.md
@@ -106,6 +106,29 @@ instance named `ctx` is established by matching against the first half of the `p
 
 In each case, a pattern-bound given instance consists of `given` and a type `T`. The pattern matches exactly the same selectors as the type ascription pattern `_: T`.
 
+## Negated Givens
+
+Scala 2's somewhat puzzling behavior with respect to ambiguity has been exploited to implement the analogue of a "negated" search in implicit resolution, where a query Q1 fails if some other query Q2 succeeds and Q1 succeeds if Q2 fails. With the new cleaned up behavior these techniques no longer work. But there is now a new special type `scala.util.NotGiven` which implements negation directly.
+
+For any query type `Q`, `NotGiven[Q]` succeeds if and only if the implicit
+search for `Q` fails, for example:
+
+```scala
+import scala.util.NotGiven
+
+trait Tagged[A]
+
+case class Foo[A](value: Boolean)
+object Foo:
+  given fooTagged[A](using Tagged[A]): Foo[A] = Foo(true)
+  given fooNotTagged[A](using NotGiven[Tagged[A]]): Foo[A] = Foo(false)
+
+@main def test() =
+  given Tagged[Int] with {}
+  assert(implicitly[Foo[Int]].value) // fooTagged is found
+  assert(!implicitly[Foo[String]].value) // fooNotTagged is found
+```
+
 ## Given Instance Initialization
 
 A given instance without type or context parameters is initialized on-demand, the first
diff --git a/library/src/scala/util/Not.scala b/library/src/scala/util/NotGiven.scala
similarity index 60%
rename from library/src/scala/util/Not.scala
rename to library/src/scala/util/NotGiven.scala
index 849bd32dad71..99cc903d4426 100644
--- a/library/src/scala/util/Not.scala
+++ b/library/src/scala/util/NotGiven.scala
@@ -8,38 +8,38 @@ package scala.util
  *  putting them in different traits we can instead define the following:
  *
  *     given i1: D(using ev: C) = ...
- *     given i2: D(using ev: Not[C]) = ...
+ *     given i2: D(using ev: NotGiven[C]) = ...
  *
- *  `Not` is treated specially in implicit search, similar to the way logical negation
- *  is treated in Prolog: The implicit search for `Not[C]` succeeds if and only if the implicit
+ *  `NotGiven` is treated specially in implicit search, similar to the way logical negation
+ *  is treated in Prolog: The implicit search for `NotGiven[C]` succeeds if and only if the implicit
  *  search for `C` fails.
  *
  *  In Scala 2 this form of negation can be simulated by setting up a conditional
  *  ambiguous implicit and an unconditional fallback, the way it is done with the
  *  `default`, `amb1` and `amb2` methods below. Due to the way these two methods are
- *  defined, `Not` is also usable from Scala 2.
+ *  defined, `NotGiven` is also usable from Scala 2.
  *
  *  In Dotty, ambiguity is a global error, and therefore cannot be used to implement negation.
- *  Instead, `Not` is treated natively in implicit search.
+ *  Instead, `NotGiven` is treated natively in implicit search.
  */
-final class Not[+T] private ()
+final class NotGiven[+T] private ()
 
-trait LowPriorityNot {
+trait LowPriorityNotGiven {
 
   /** A fallback method used to emulate negation in Scala 2 */
-  given default[T]: Not[T] = Not.value
+  given default[T]: NotGiven[T] = NotGiven.value
 }
-object Not extends LowPriorityNot {
+object NotGiven extends LowPriorityNotGiven {
 
-  /** A value of type `Not` to signal a successful search for `Not[C]` (i.e. a failing
+  /** A value of type `NotGiven` to signal a successful search for `NotGiven[C]` (i.e. a failing
    *  search for `C`). A reference to this value will be explicitly constructed by Dotty's
    *  implicit search algorithm
    */
-  def value: Not[Nothing] = new Not[Nothing]()
+  def value: NotGiven[Nothing] = new NotGiven[Nothing]()
 
   /** One of two ambiguous methods used to emulate negation in Scala 2 */
-  given amb1[T](using ev: T): Not[T] = ???
+  given amb1[T](using ev: T): NotGiven[T] = ???
 
   /** One of two ambiguous methods used to emulate negation in Scala 2 */
-  given amb2[T](using ev: T): Not[T] = ???
+  given amb2[T](using ev: T): NotGiven[T] = ???
 }
diff --git a/tests/neg-macros/i9972/Macro_1.scala b/tests/neg-macros/i9972/Macro_1.scala
index 65e69f8ccab3..8b7a82e3b841 100644
--- a/tests/neg-macros/i9972/Macro_1.scala
+++ b/tests/neg-macros/i9972/Macro_1.scala
@@ -1,7 +1,7 @@
 package notmacro
 
-import scala.util.Not
+import scala.util.NotGiven
 
 object Main extends App {
-  summon[Not[T[Int]]] // error
+  summon[NotGiven[T[Int]]] // error
 }
diff --git a/tests/neg-macros/i9972b/Macro_1.scala b/tests/neg-macros/i9972b/Macro_1.scala
index ecb22a0b3755..38be5cf05153 100644
--- a/tests/neg-macros/i9972b/Macro_1.scala
+++ b/tests/neg-macros/i9972b/Macro_1.scala
@@ -1,3 +1,3 @@
 
 def test: Unit =
-  summon[scala.util.Not[T[Int]]] // error
+  summon[scala.util.NotGiven[T[Int]]] // error
diff --git a/tests/neg/i5234a.scala b/tests/neg/i5234a.scala
index 389b215fe45b..88e20846400a 100644
--- a/tests/neg/i5234a.scala
+++ b/tests/neg/i5234a.scala
@@ -1,10 +1,10 @@
 object Test {
-  import scala.util.Not
+  import scala.util.NotGiven
 
   class Foo
   class Bar
   implicit def foo: Foo = ???
   implicitly[Foo]
-  implicitly[Not[Foo]] // error
-  implicitly[Not[Bar]]
+  implicitly[NotGiven[Foo]] // error
+  implicitly[NotGiven[Bar]]
 }
diff --git a/tests/neg/i5234b.scala b/tests/neg/i5234b.scala
index 2dd1d679336f..cae4cc6f16ff 100644
--- a/tests/neg/i5234b.scala
+++ b/tests/neg/i5234b.scala
@@ -1,23 +1,23 @@
-final class Not2[T] private ()
+final class NotGiven2[T] private ()
 
-trait LowPriorityNot2 {
+trait LowPriorityNotGiven2 {
 
   /** A fallback method used to emulate negation in Scala 2 */
-  implicit def default[T]: Not2[T] = Not2.value.asInstanceOf[Not2[T]]
+  implicit def default[T]: NotGiven2[T] = NotGiven2.value.asInstanceOf[NotGiven2[T]]
 }
-object Not2 extends LowPriorityNot2 {
+object NotGiven2 extends LowPriorityNotGiven2 {
 
-  /** A value of type `Not` to signal a successful search for `Not[C]` (i.e. a failing
+  /** A value of type `NotGiven` to signal a successful search for `NotGiven[C]` (i.e. a failing
    *  search for `C`). A reference to this value will be explicitly constructed by
    *  Dotty's implicit search algorithm
    */
-  def value: Not2[Nothing] = new Not2[Nothing]()
+  def value: NotGiven2[Nothing] = new NotGiven2[Nothing]()
 
   /** One of two ambiguous methods used to emulate negation in Scala 2 */
-  implicit def amb1[T](implicit ev: T): Not2[T] = ???
+  implicit def amb1[T](implicit ev: T): NotGiven2[T] = ???
 
   /** One of two ambiguous methods used to emulate negation in Scala 2 */
-  implicit def amb2[T](implicit ev: T): Not2[T] = ???
+  implicit def amb2[T](implicit ev: T): NotGiven2[T] = ???
 }
 
 object Test {
@@ -25,6 +25,6 @@ object Test {
   class Bar
   implicit def foo: Foo = ???
   implicitly[Foo]
-  implicitly[Not2[Foo]] // error
-  implicitly[Not2[Bar]]
+  implicitly[NotGiven2[Foo]] // error
+  implicitly[NotGiven2[Bar]]
 }
diff --git a/tests/neg/i5234c.scala b/tests/neg/i5234c.scala
index 59a7c605c65e..0d9754f85788 100644
--- a/tests/neg/i5234c.scala
+++ b/tests/neg/i5234c.scala
@@ -1,9 +1,9 @@
 object Test {
-  import scala.util.Not
+  import scala.util.NotGiven
 
   class Foo
   implicit def foo: Foo = ???
 
-  def foo[T](implicit ev: Not[T]) = ???
+  def foo[T](implicit ev: NotGiven[T]) = ???
   foo[Foo] // error
 }
diff --git a/tests/run/i3396.scala b/tests/run/i3396.scala
index eea4371e0636..8f10e7bcfcbd 100644
--- a/tests/run/i3396.scala
+++ b/tests/run/i3396.scala
@@ -1,4 +1,4 @@
-import scala.util.Not
+import scala.util.NotGiven
 
 object Test {
 
@@ -9,7 +9,7 @@ object Test {
     implicit def fooDefault[A]: Foo[A] = Foo(true)
   }
   object Foo extends FooLowPrio {
-    implicit def fooNotTagged[A](implicit ev: Not[Tagged[A]]): Foo[A] = Foo(false)
+    implicit def fooNotTagged[A](implicit ev: NotGiven[Tagged[A]]): Foo[A] = Foo(false)
   }