diff --git a/abducer/abducer_base.py b/abducer/abducer_base.py
index b1c661b..38cbf64 100644
--- a/abducer/abducer_base.py
+++ b/abducer/abducer_base.py
@@ -45,7 +45,10 @@ class AbducerBase(abc.ABC):
             dist_func = confidence_dist
         self.dist_func = dist_func
         if pred_res_parse is None:
-            pred_res_parse = lambda x : x["cls"]
+            if(dist_func == "hamming"):
+                pred_res_parse = lambda x : x["cls"]
+            elif dist_func == "confidence":
+                pred_res_parse = lambda x : x[" "]
         self.pred_res_parse = pred_res_parse
         
         self.cache = cache
@@ -75,20 +78,18 @@ class AbducerBase(abc.ABC):
             
         else:
             candidates, min_address_num, address_num = self.get_abduce_candidates(pred_res, ans, max_address_num, require_more_address)
+            cost_list = self.dist_func(pred_res, candidates)
         
         if(self.cache):
             self.cache_min_address_num[(tuple(pred_res), ans)] = min_address_num
             self.cache_candidates[(tuple(pred_res), ans, address_num)] = candidates
-
-        return candidates
-        
         
+        cost_list = self.dist_func(pred_res, candidates)
+        min_address_num = np.min(cost_list)
+        idxs = np.where(cost_list == min_address_num)[0]
+        candidates = [candidates[idx] for idx in idxs]
     
-    
-    
-        # if len(idxs) > 1:
-        #     return None
-        # return [candidates[idx] for idx in idxs]
+        return candidates[0]
     
     def address(self, address_num, pred_res, key):
         new_candidates = []
@@ -99,7 +100,7 @@ class AbducerBase(abc.ABC):
                 pred_res_array = np.array(pred_res)
                 if(np.count_nonzero(np.array(c) != pred_res_array[np.array(address_idx)]) == address_num):
                     pred_res_array[np.array(address_idx)] = c
-                    if(self.kb.logic_forward(pred_res_array) == key):
+                    if(abs(self.kb.logic_forward(pred_res_array) - key) <= 1e-3):
                         new_candidates.append(pred_res_array)
         return new_candidates, address_num
     
@@ -113,7 +114,7 @@ class AbducerBase(abc.ABC):
                 return None, None, None
             
             if(address_num == 0):
-                if(self.kb.logic_forward(pred_res) == key):
+                if(abs(self.kb.logic_forward(pred_res) - key) <= 1e-3):
                     candidates.append(pred_res)
             else:
                 new_candidates, address_num = self.address(address_num, pred_res, key)
@@ -148,7 +149,7 @@ if __name__ == "__main__":
     pseudo_label_list = list(range(10))
     kb = add_KB(pseudo_label_list)
     abd = AbducerBase(kb)
-    res = abd.abduce(([1, 1, 1], 4), max_address_num = 2, require_more_address = 1)
+    res = abd.abduce(([1, 1, 1], 4), max_address_num = 2, require_more_address = 0)
     print(res)
     print()
     res = abd.abduce(([1, 1, 1], 4), max_address_num = 2, require_more_address = 1)