diff --git a/packaging/specifiers.py b/packaging/specifiers.py
index 6e5d4d59..a2d51b04 100644
--- a/packaging/specifiers.py
+++ b/packaging/specifiers.py
@@ -57,7 +57,8 @@ def __eq__(self, other: object) -> bool:
         objects are equal.
         """
 
-    @abc.abstractproperty
+    @property
+    @abc.abstractmethod
     def prereleases(self) -> Optional[bool]:
         """
         Returns whether or not pre-releases as a whole are allowed by this
@@ -724,7 +725,10 @@ def __contains__(self, item: UnparsedVersion) -> bool:
         return self.contains(item)
 
     def contains(
-        self, item: UnparsedVersion, prereleases: Optional[bool] = None
+        self,
+        item: UnparsedVersion,
+        prereleases: Optional[bool] = None,
+        installed: Optional[bool] = None,
     ) -> bool:
 
         # Ensure that our item is a Version or LegacyVersion instance.
@@ -746,6 +750,9 @@ def contains(
         if not prereleases and item.is_prerelease:
             return False
 
+        if installed and item.is_prerelease:
+            item = parse(item.base_version)
+
         # We simply dispatch to the underlying specs here to make sure that the
         # given version is contained within all of them.
         # Note: This use of all() here means that an empty set of specifiers
diff --git a/tests/test_specifiers.py b/tests/test_specifiers.py
index 41a3f829..5949ebf6 100644
--- a/tests/test_specifiers.py
+++ b/tests/test_specifiers.py
@@ -819,6 +819,15 @@ def test_specifier_contains_prereleases(self):
         assert spec.contains("1.0.dev1")
         assert not spec.contains("1.0.dev1", prereleases=False)
 
+    def test_specifier_contains_installed_prereleases(self):
+        spec = SpecifierSet("~=1.0")
+        assert not spec.contains("1.0.0.dev1", installed=True)
+        assert spec.contains("1.0.0.dev1", prereleases=True, installed=True)
+
+        spec = SpecifierSet("~=1.0", prereleases=True)
+        assert spec.contains("1.0.0.dev1", installed=True)
+        assert not spec.contains("1.0.0.dev1", prereleases=False, installed=False)
+
     @pytest.mark.parametrize(
         ("specifier", "specifier_prereleases", "prereleases", "input", "expected"),
         [