diff --git a/horse/prob/kfl.kk b/horse/prob/kfl.kk
index 992eff4..8f60f42 100644
--- a/horse/prob/kfl.kk
+++ b/horse/prob/kfl.kk
@@ -101,8 +101,8 @@ pub fun (+)(a: kfl, b: kfl): e kfl
     // Cases with _ on the left simplify later cases that all absorb to the right.
     (Guaranteed, _) -> Guaranteed
     (_, Guaranteed) -> Guaranteed
-    (Cry-If-Not, _) -> Cry-If-Not
-    (Most-Likely, Cry-If-Not) -> Guaranteed
+    (Cry-If-Not, _) -> Guaranteed
+    (Most-Likely, Cry-If-Not) -> Cry-If-Not
     (Most-Likely, _) -> Cry-If-Not
     (_, Cry-If-Not) -> Cry-If-Not
     (Probably, Most-Likely) -> Cry-If-Not
@@ -124,3 +124,35 @@ pub fun (+)(a: kfl, b: kfl): e kfl
     (_, Doubtful) -> Doubtful
     (_, Probably-Not) -> Probably-Not
     (_, Impossible) -> Impossible
+
+// KFL union, or the probability of occurrence of exactly one of two independent events.
+pub fun either(a: kfl, b: kfl): e kfl
+  val (l, h) = match a.cmp(b) // this operation is commutative
+    Gt -> (b, a)
+    _ -> (a, b)
+  match (l, h)
+    (Impossible, r) -> r
+    (Probably-Not, Guaranteed) -> Cry-If-Not
+    (Probably-Not, r) -> r
+    (Doubtful, Guaranteed) -> Most-Likely
+    (Doubtful, Cry-If-Not) -> Most-Likely
+    (Doubtful, Most-Likely) -> Probably
+    (Doubtful, Probably) -> Mayhapsibly
+    (Doubtful, Mayhapsibly) -> Mayhapsibly
+    (Doubtful, Unlikely) -> Mayhapsibly
+    (Doubtful, _) -> Unlikely
+    (Unlikely, Guaranteed) -> Probably
+    (Unlikely, Cry-If-Not) -> Mayhapsibly
+    (Unlikely, Most-Likely) -> Mayhapsibly
+    (Unlikely, _) -> Probably
+    (Mayhapsibly, Guaranteed) -> Mayhapsibly
+    (Mayhapsibly, Cry-If-Not) -> Mayhapsibly
+    (Mayhapsibly, Most-Likely) -> Mayhapsibly
+    (Mayhapsibly, _) -> Probably
+    (Probably, Guaranteed) -> Unlikely
+    (Probably, Cry-If-Not) -> Unlikely
+    (Probably, Most-Likely) -> Unlikely
+    (Probably, _) -> Mayhapsibly
+    (Most-Likely, _) -> Doubtful
+    (Cry-If-Not, _) -> Probably-Not
+    (Guaranteed, _) -> Impossible