diff --git a/README.md b/README.md
index c83ebb9..0749b0b 100644
--- a/README.md
+++ b/README.md
@@ -192,6 +192,7 @@ We provide several examples in `examples/`. Each example is stored in a separate
 + [Handwritten Formula (HWF)](https://github.com/AbductiveLearning/ABLkit/tree/main/examples/hwf)
 + [Handwritten Equation Decipherment](https://github.com/AbductiveLearning/ABLkit/tree/main/examples/hed)
 + [Zoo](https://github.com/AbductiveLearning/ABLkit/tree/main/examples/zoo)
++ [BDD-OIA](https://github.com/AbductiveLearning/ABLkit/tree/main/examples/bdd_oia)
 
 ## References
 
diff --git a/ablkit/reasoning/reasoner.py b/ablkit/reasoning/reasoner.py
index 2905007..5626468 100644
--- a/ablkit/reasoning/reasoner.py
+++ b/ablkit/reasoning/reasoner.py
@@ -180,8 +180,8 @@ class Reasoner:
             candidates_idxs = [[self.label_to_idx[x] for x in c] for c in candidates]
             return avg_confidence_dist(data_example.pred_prob, candidates_idxs)
         else:
-            candidate_idxs = [[self.label_to_idx[x] for x in c] for c in candidates]
-            cost_list = self.dist_func(data_example, candidates, candidate_idxs, reasoning_results)
+            candidates_idxs = [[self.label_to_idx[x] for x in c] for c in candidates]
+            cost_list = self.dist_func(data_example, candidates, candidates_idxs, reasoning_results)
             if len(cost_list) != len(candidates):
                 raise ValueError(
                     "The length of the array returned by dist_func must be equal to the number "
diff --git a/examples/bdd_oia/README.md b/examples/bdd_oia/README.md
new file mode 100644
index 0000000..0900a4f
--- /dev/null
+++ b/examples/bdd_oia/README.md
@@ -0,0 +1,50 @@
+# BDD-OIA
+
+This example shows an implementation of [BDD-OIA](https://twizwei.github.io/bddoia_project/) task. The BDD-OIA dataset comprises frames extracted from driving scene videos, which are utilized for autonomous driving predictions. Each frame is annotated with 4 binary labels, indicating the possible actions, namely $\textsf{move forward}$, $\textsf{stop}$, $\textsf{turn left}$, $\textsf{turn right}$. Each frame is also annotated with 21 intermediate binary concepts such as $\textsf{red light}$, $\textsf{road clear}$, etc., underlying the reasons for the possible actions.
+
+The objective is to predict possible actions for each frame. During training, we only make use of the label supervision, along with a knowledge base, which comprises information about the relations between concepts and actions, e.g., $\textsf{red light} \lor \textsf{traffic sign} \lor \textsf{obstacle} \implies \textsf{stop}$. The training set consists of 16,000 frames, while the test set contains 4,500 annotated data points.
+
+Before usage, the dataset was pre-processed by [Marconato et al. (2023)](https://proceedings.neurips.cc/paper_files/paper/2023/file/e560202b6e779a82478edb46c6f8f4dd-Paper-Conference.pdf) using a pretrained Faster-RCNN model on BDD-100k, in conjunction with the first module in CBM-AUC [(Sawada & Nakamura, 2022)](https://arxiv.org/abs/2202.01459), resulting in embeddings of dimension 2048.
+
+## Run
+
+```bash
+pip install -r requirements.txt
+cd dataset
+unzip dataset.zip
+cd ..
+python main.py
+```
+
+## Usage
+
+```bash
+usage: main.py [-h] [--no-cuda] [--epochs EPOCHS] [--lr LR]
+               [--batch-size BATCH_SIZE] [--loops LOOPS]
+               [--segment_size SEGMENT_SIZE]
+               [--save_interval SAVE_INTERVAL]
+               [--max-revision MAX_REVISION]
+               [--require-more-revision REQUIRE_MORE_REVISION]
+
+BDD_OIA example
+
+optional arguments:
+  -h, --help            show this help message and exit
+  --no-cuda             disables CUDA training
+  --epochs EPOCHS       number of epochs in each learning loop iteration
+                        (default : 1)
+  --lr LR               base model learning rate (default : 0.002)
+  --batch-size BATCH_SIZE
+                        base model batch size (default : 32)
+  --loops LOOPS
+                        number of loop iterations (default : 2)
+  --segment_size SEGMENT_SIZE
+                        segment size (default : 0.01)
+  --save_interval SAVE_INTERVAL
+                        save interval (default : 1)
+  --max-revision MAX_REVISION
+                        maximum revision in reasoner (default : 3)
+  -require-more-revision REQUIRE_MORE_REVISION
+                        require more revision in reasoner (default : 3)
+
+```
diff --git a/examples/bdd_oia/bridge.py b/examples/bdd_oia/bridge.py
new file mode 100644
index 0000000..0139277
--- /dev/null
+++ b/examples/bdd_oia/bridge.py
@@ -0,0 +1,23 @@
+import numpy as np
+from typing import List, Any
+from ablkit.data import ListData
+from ablkit.bridge import SimpleBridge
+
+class BDDBridge(SimpleBridge):
+    def idx_to_pseudo_label(self, data_examples: ListData) -> List[List[Any]]:
+        pred_idx = data_examples.pred_idx  # [ ndarray(1,nc),... ]
+        pred_pseudo_label = []
+        for sub_list in pred_idx:
+            sub_list = sub_list.squeeze()  # 1 x nc -> nc
+            pred_pseudo_label.append([self.reasoner.idx_to_label[_idx] for _idx in sub_list])
+        data_examples.pred_pseudo_label = pred_pseudo_label
+        return data_examples.pred_pseudo_label
+
+    def pseudo_label_to_idx(self, data_examples: ListData) -> List[List[Any]]:
+        abduced_pseudo_label = data_examples.abduced_pseudo_label
+        abduced_idx = []
+        for sub_list in abduced_pseudo_label:
+            sub_list = np.array([self.reasoner.label_to_idx[_lab] for _lab in sub_list])
+            abduced_idx.append(sub_list)
+        data_examples.abduced_idx = abduced_idx
+        return data_examples.abduced_idx
\ No newline at end of file
diff --git a/examples/bdd_oia/dataset/data_util.py b/examples/bdd_oia/dataset/data_util.py
new file mode 100644
index 0000000..23bb9a8
--- /dev/null
+++ b/examples/bdd_oia/dataset/data_util.py
@@ -0,0 +1,18 @@
+import os
+import numpy as np
+
+CURRENT_DIR = os.path.abspath(os.path.dirname(__file__))
+
+
+def get_dataset(fname, get_pseudo_label=True):
+    fname = os.path.join(CURRENT_DIR, fname)
+    data = np.load(fname)
+    X = data["X"]
+    X = [[emb.astype(np.float32)] for emb in X]
+    pseudo_label = data["pseudo_label"].astype(int).tolist() if get_pseudo_label else None
+    Y = data["Y"][:, :4].astype(int).tolist()
+    Y = [tuple(y) for y in Y]
+    return X, pseudo_label, Y
+
+if __name__ == '__main__':
+    dataset = get_dataset("val.npz")
\ No newline at end of file
diff --git a/examples/bdd_oia/dataset/dataset.zip b/examples/bdd_oia/dataset/dataset.zip
new file mode 100644
index 0000000..82f6914
Binary files /dev/null and b/examples/bdd_oia/dataset/dataset.zip differ
diff --git a/examples/bdd_oia/main.py b/examples/bdd_oia/main.py
new file mode 100644
index 0000000..219f76e
--- /dev/null
+++ b/examples/bdd_oia/main.py
@@ -0,0 +1,147 @@
+import argparse
+import os.path as osp
+import numpy as np
+import torch
+from torch import optim
+
+from ablkit.data.evaluation import SymbolAccuracy
+from ablkit.reasoning import Reasoner
+from ablkit.utils import ABLLogger, print_log
+
+from models.nn import *
+from models.bdd_nn import BDDNN
+from models.bdd_model import BDDABLModel
+from reasoning.bddkb import BDDKB
+from dataset.data_util import get_dataset
+from bridge import BDDBridge
+from metric import BDDReasoningMetric
+
+
+def multi_label_confidence_dist(data_example, candidates, candidates_idxs, reasoning_results):
+    pred_prob = data_example.pred_prob.T  # nc x 1
+    pred_prob = np.concatenate([1-pred_prob, pred_prob], axis=1)  # nc x 2
+    cols = np.arange(len(candidates_idxs[0]))[None, :]
+    corr_prob = pred_prob[cols, candidates_idxs]
+    costs = - np.sum(np.log(corr_prob + 1e-6), axis=1)
+    return costs
+
+def get_args():
+    parser = argparse.ArgumentParser(description="BDD-OIA example")
+    parser.add_argument(
+        "--no-cuda", action="store_true", default=False, help="disables CUDA training"
+    )
+    parser.add_argument(
+        "--epochs",
+        type=int,
+        default=1,
+        help="number of epochs in each learning loop iteration (default : 1)",
+    )
+    parser.add_argument(
+        "--lr", type=float, default=2e-3, help="base model learning rate (default : 0.002)"
+    )
+    parser.add_argument(
+        "--batch-size", type=int, default=32, help="base model batch size (default : 32)"
+    )
+    parser.add_argument(
+        "--loops", type=int, default=2, help="number of loop iterations (default : 2)"
+    )
+    parser.add_argument(
+        "--segment_size", type=int, default=0.01, help="segment size (default : 0.01)"
+    )
+    parser.add_argument("--save_interval", type=int, default=1, help="save interval (default : 1)")
+    parser.add_argument(
+        "--max-revision", type=int, default=3, help="maximum revision in reasoner (default : 3)"
+    )
+    parser.add_argument(
+        "--require-more-revision",
+        type=int,
+        default=3,
+        help="require more revision in reasoner (default : 3)",
+    )
+
+    args = parser.parse_args()
+    return args
+
+def main():
+    args = get_args()
+
+    # Build logger
+    print_log("Abductive Learning on the BDD-OIA example.", logger="current")
+
+    # -- Working with Data ------------------------------
+    print_log("Working with Data.", logger="current")
+    train_data = get_dataset(fname="train.npz", get_pseudo_label=True)
+    val_data = get_dataset(fname="val.npz", get_pseudo_label=True)
+    test_data = get_dataset(fname="test.npz", get_pseudo_label=True)
+
+    # -- Building the Learning Part ---------------------
+    print_log("Building the Learning Part.", logger="current")
+
+    # Build necessary components for BDDNN
+    cls = ConceptNet()
+    loss_fn = nn.BCEWithLogitsLoss()
+    optimizer = optim.Adam(cls.parameters(), lr=args.lr)
+    use_cuda = not args.no_cuda and torch.cuda.is_available()
+    device = torch.device("cuda" if use_cuda else "cpu")
+    scheduler = optim.lr_scheduler.OneCycleLR(
+        optimizer,
+        max_lr=args.lr,
+        pct_start=0.15,
+        epochs=args.loops,
+        steps_per_epoch=int(1 / args.segment_size) + 1,
+    )
+
+    # Build BDDNN
+    base_model = BDDNN(
+        cls,
+        loss_fn,
+        optimizer,
+        scheduler=scheduler,
+        device=device,
+        batch_size=args.batch_size,
+        num_epochs=args.epochs,
+    )
+
+    # Build ABLModel
+    model = BDDABLModel(base_model)
+
+    # -- Building the Reasoning Part --------------------
+    print_log("Building the Reasoning Part.", logger="current")
+
+    # Build knowledge base
+    kb = BDDKB()
+
+    # Create reasoner
+    reasoner = Reasoner(
+        kb,
+        dist_func=multi_label_confidence_dist,
+        max_revision=args.max_revision,
+        require_more_revision=args.require_more_revision
+    )
+
+    # -- Building Evaluation Metrics --------------------
+    print_log("Building Evaluation Metrics.", logger="current")
+    metric_list = [SymbolAccuracy(prefix="bdd_oia"), BDDReasoningMetric(kb=kb, prefix="bdd_oia")]
+
+    # -- Bridging Learning and Reasoning ----------------
+    print_log("Bridge Learning and Reasoning.", logger="current")
+    bridge = BDDBridge(model, reasoner, metric_list)
+
+    # Retrieve the directory of the Log file and define the directory for saving the model weights.
+    log_dir = ABLLogger.get_current_instance().log_dir
+    weights_dir = osp.join(log_dir, "weights")
+
+    #  Train and Test
+    bridge.train(
+        train_data=train_data,
+        val_data=val_data,
+        loops=args.loops,
+        segment_size=args.segment_size,
+        save_interval=args.save_interval,
+        save_dir=weights_dir,
+    )
+    bridge.test(test_data)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/bdd_oia/metric.py b/examples/bdd_oia/metric.py
new file mode 100644
index 0000000..c73c2f9
--- /dev/null
+++ b/examples/bdd_oia/metric.py
@@ -0,0 +1,24 @@
+from typing import Optional
+
+from ablkit.reasoning import KBBase
+from ablkit.data import BaseMetric, ListData
+
+class BDDReasoningMetric(BaseMetric):
+    def __init__(self, kb: KBBase, prefix: Optional[str] = None) -> None:
+        super().__init__(prefix)
+        self.kb = kb
+
+    def process(self, data_examples: ListData) -> None:
+        pred_pseudo_label_list = data_examples.pred_pseudo_label
+        y_list = data_examples.Y
+        x_list = data_examples.X
+        for pred_pseudo_label, y, x in zip(pred_pseudo_label_list, y_list, x_list):
+            pred_y = self.kb.logic_forward(pred_pseudo_label, *(x,) if self.kb._num_args == 2 else ())
+            for py, yy in zip(pred_y, y):
+                self.results.append(int(py == yy))
+
+    def compute_metrics(self) -> dict:
+        results = self.results
+        metrics = dict()
+        metrics["reasoning_accuracy"] = sum(results) / len(results)
+        return metrics
\ No newline at end of file
diff --git a/examples/bdd_oia/models/bdd_model.py b/examples/bdd_oia/models/bdd_model.py
new file mode 100644
index 0000000..bdddb7e
--- /dev/null
+++ b/examples/bdd_oia/models/bdd_model.py
@@ -0,0 +1,24 @@
+from typing import Dict
+
+import numpy as np
+from ablkit.data import ListData
+from ablkit.learning import ABLModel
+from ablkit.utils import reform_list
+
+class BDDABLModel(ABLModel):
+    def predict(self, data_examples: ListData) -> Dict:
+        model = self.base_model
+        data_X = data_examples.flatten("X")
+        if hasattr(model, "predict_proba"):
+            prob = model.predict_proba(X=data_X)
+            label = np.where(prob > 0.5, 1, 0).astype(int)
+            prob = reform_list(prob, data_examples.X)
+        else:
+            prob = None
+            label = model.predict(X=data_X)
+        label = reform_list(label, data_examples.X)
+
+        data_examples.pred_idx = label
+        data_examples.pred_prob = prob
+
+        return {"label": label, "prob": prob}
\ No newline at end of file
diff --git a/examples/bdd_oia/models/bdd_nn.py b/examples/bdd_oia/models/bdd_nn.py
new file mode 100644
index 0000000..5fdd378
--- /dev/null
+++ b/examples/bdd_oia/models/bdd_nn.py
@@ -0,0 +1,94 @@
+import logging
+import os
+from typing import Any, Callable, List, Optional, Tuple, Union
+
+import numpy
+import torch
+from torch.utils.data import DataLoader, Dataset
+
+from ablkit.learning import BasicNN, PredictionDataset, ClassificationDataset
+from ablkit.utils.logger import print_log
+
+
+class MultiLabelClassificationDataset(ClassificationDataset):
+    def __init__(self, X: List[Any], Y: List[int], transform: Optional[Callable[..., Any]] = None):
+        if (not isinstance(X, list)) or (not isinstance(Y, list)):
+            raise ValueError("X and Y should be of type list.")
+        self.X = X
+        self.Y = torch.FloatTensor(numpy.stack(Y, axis=0)) # float32 for BCELoss
+        self.transform = transform
+
+class BDDNN(BasicNN):
+
+    def predict(
+        self,
+        data_loader: Optional[DataLoader] = None,
+        X: Optional[List[Any]] = None,
+    ) -> numpy.ndarray:
+        if data_loader is not None and X is not None:
+            print_log(
+                "Predict the class of input data in data_loader instead of X.",
+                logger="current",
+                level=logging.WARNING,
+            )
+
+        if data_loader is None:
+            dataset = PredictionDataset(X, self.test_transform)
+            data_loader = DataLoader(
+                dataset,
+                batch_size=self.batch_size,
+                num_workers=self.num_workers,
+                collate_fn=self.collate_fn,
+                pin_memory=torch.cuda.is_available(),
+            )
+        pred_probs = self._predict(data_loader).sigmoid()
+        pred = torch.where(pred_probs > 0.5, 1, 0).int()
+        return pred.cpu().numpy()
+
+    def predict_proba(
+        self,
+        data_loader: Optional[DataLoader] = None,
+        X: Optional[List[Any]] = None,
+    ) -> numpy.ndarray:
+        if data_loader is not None and X is not None:
+            print_log(
+                "Predict the class probability of input data in data_loader instead of X.",
+                logger="current",
+                level=logging.WARNING,
+            )
+
+        if data_loader is None:
+            dataset = PredictionDataset(X, self.test_transform)
+            data_loader = DataLoader(
+                dataset,
+                batch_size=self.batch_size,
+                num_workers=self.num_workers,
+                collate_fn=self.collate_fn,
+                pin_memory=torch.cuda.is_available(),
+            )
+        pred_probs = self._predict(data_loader).sigmoid()  # B x NC
+        return pred_probs.cpu().numpy()
+
+    def _data_loader(
+        self,
+        X: Optional[List[Any]],
+        y: Optional[List[int]] = None,
+        shuffle: Optional[bool] = True,
+    ) -> DataLoader:
+        if X is None:
+            raise ValueError("X should not be None.")
+        if y is None:
+            y = [0] * len(X)
+        if not len(y) == len(X):
+            raise ValueError("X and y should have equal length.")
+
+        dataset = MultiLabelClassificationDataset(X, y, transform=self.train_transform)
+        data_loader = DataLoader(
+            dataset,
+            batch_size=self.batch_size,
+            shuffle=shuffle,
+            num_workers=self.num_workers,
+            collate_fn=self.collate_fn,
+            pin_memory=torch.cuda.is_available(),
+        )
+        return data_loader
diff --git a/examples/bdd_oia/models/nn.py b/examples/bdd_oia/models/nn.py
new file mode 100644
index 0000000..216be0e
--- /dev/null
+++ b/examples/bdd_oia/models/nn.py
@@ -0,0 +1,22 @@
+from torch import nn
+
+class SimpleNet(nn.Module):
+    def __init__(self, num_features=2048, num_concepts=21):
+        super(SimpleNet, self).__init__()
+        self.fc = nn.Linear(num_features, num_concepts)
+
+    def forward(self, x):
+        return self.fc(x)
+
+class ConceptNet(nn.Module):
+    def __init__(self, num_features=2048, num_concepts=21):
+        super(ConceptNet, self).__init__()
+        intermidate_dim = 256
+        self.fc = nn.Sequential(
+            nn.Linear(num_features, intermidate_dim),
+            nn.SiLU(),
+            nn.Linear(intermidate_dim, num_concepts)
+        )
+
+    def forward(self, x):
+        return self.fc(x)
diff --git a/examples/bdd_oia/reasoning/bddkb.py b/examples/bdd_oia/reasoning/bddkb.py
new file mode 100644
index 0000000..3548c69
--- /dev/null
+++ b/examples/bdd_oia/reasoning/bddkb.py
@@ -0,0 +1,46 @@
+# -*- coding: utf-8 -*-
+from ablkit.reasoning import KBBase
+
+class BDDKB(KBBase):
+    def __init__(self, pseudo_label_list=None):
+        if pseudo_label_list is None:
+            pseudo_label_list = [0, 1]
+        super().__init__(pseudo_label_list)
+
+    def logic_forward(self, attrs):
+        """
+        Abduction space
+        (0, 1, 0, 0) 610812
+        (0, 1, 0, 1) 75012
+        (0, 1, 1, 0) 75012
+        (0, 1, 1, 1) 9212
+        (1, 0, 0, 0) 12996
+        (1, 0, 0, 1) 1596
+        (1, 0, 1, 0) 1596
+        (1, 0, 1, 1) 196
+        """
+        assert len(attrs) == 21
+        green_light, follow, road_clear, red_light, traffic_sign, car, person, rider, other_obstacle, \
+        left_lane, left_green_light, left_follow, no_left_lane, left_obstacle, left_solid_line, \
+        right_lane, right_green_light, right_follow, no_right_lane, right_obstacle, right_solid_line = attrs
+
+        illegal_return = (0, 0, 0, 0)
+        if red_light == green_light == 1:
+            return illegal_return
+        obstacle = car or person or rider or other_obstacle
+        if road_clear == obstacle:
+            return illegal_return
+        move_forward = (green_light or follow or road_clear)
+        stop = (red_light or traffic_sign or obstacle)
+        if stop:
+            move_forward = 0
+
+        can_turn_left = left_lane or left_green_light or left_follow
+        cannot_turn_left = no_left_lane or left_obstacle or left_solid_line
+        turn_left = can_turn_left and int(not cannot_turn_left)
+
+        can_turn_right = right_lane or right_green_light or right_follow
+        cannot_turn_right = no_right_lane or right_obstacle or right_solid_line
+        turn_right = can_turn_right and int(not cannot_turn_right)
+
+        return move_forward, stop, turn_left, turn_right
\ No newline at end of file
diff --git a/examples/bdd_oia/requirements.txt b/examples/bdd_oia/requirements.txt
new file mode 100644
index 0000000..c238889
--- /dev/null
+++ b/examples/bdd_oia/requirements.txt
@@ -0,0 +1,2 @@
+torch
+ablkit