diff --git a/dbms/src/Functions/FunctionsLogical.h b/dbms/src/Functions/FunctionsLogical.h
index edb2f792ea2..9865efa5776 100644
--- a/dbms/src/Functions/FunctionsLogical.h
+++ b/dbms/src/Functions/FunctionsLogical.h
@@ -97,7 +97,14 @@ struct NotImpl
 {
     using ResultType = UInt8;
 
+<<<<<<< HEAD
     static inline UInt8 apply(A a) { return !a; }
+=======
+    static inline bool apply(A a)
+    {
+        return !a;
+    }
+>>>>>>> 1e0e3c8973 (fix inconsistent result before deleting some rows (#6133))
 };
 
 
@@ -134,7 +141,7 @@ struct AssociativeOperationImpl
     AssociativeOperationImpl(UInt8ColumnPtrs & in) : vec(in[in.size() - N]->getData()), continuation(in) {}
 
     /// Returns a combination of values in the i-th row of all columns stored in the constructor.
-    inline UInt8 apply(size_t i) const
+    inline bool apply(size_t i) const
     {
         if (Op::isSaturable())
         {
@@ -176,7 +183,14 @@ struct AssociativeOperationImpl<Op, 1>
 
     AssociativeOperationImpl(UInt8ColumnPtrs & in) : vec(in[in.size() - 1]->getData()) {}
 
+<<<<<<< HEAD
     inline UInt8 apply(size_t i) const { return vec[i]; }
+=======
+    inline bool apply(size_t i) const
+    {
+        return vec[i];
+    }
+>>>>>>> 1e0e3c8973 (fix inconsistent result before deleting some rows (#6133))
 };
 
 
diff --git a/dbms/src/Functions/tests/gtest_logical.cpp b/dbms/src/Functions/tests/gtest_logical.cpp
new file mode 100644
index 00000000000..bdab91fda52
--- /dev/null
+++ b/dbms/src/Functions/tests/gtest_logical.cpp
@@ -0,0 +1,183 @@
+// Copyright 2022 PingCAP, Ltd.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <Interpreters/Context.h>
+#include <TestUtils/FunctionTestUtils.h>
+#include <TestUtils/TiFlashTestBasic.h>
+
+#include <string>
+#include <vector>
+
+namespace DB::tests
+{
+class Logical : public DB::tests::FunctionTest
+{
+};
+
+TEST_F(Logical, andTest)
+try
+{
+    const String & func_name = "and";
+
+    // column, column
+    ASSERT_COLUMN_EQ(
+        createColumn<Nullable<UInt8>>({0, 1, 0, 0, {}, 0}),
+        executeFunction(
+            func_name,
+            createColumn<Nullable<UInt8>>({0, 1, 0, 1, {}, 0}),
+            createColumn<Nullable<UInt8>>({0, 1, 1, 0, 1, {}})));
+    // column, const
+    ASSERT_COLUMN_EQ(
+        createColumn<Nullable<UInt8>>({1, 0}),
+        executeFunction(
+            func_name,
+            createConstColumn<Nullable<UInt8>>(2, 1),
+            createColumn<Nullable<UInt8>>({1, 0})));
+    // const, const
+    ASSERT_COLUMN_EQ(
+        createConstColumn<UInt8>(1, 1),
+        executeFunction(
+            func_name,
+            createConstColumn<Nullable<UInt8>>(1, 1),
+            createConstColumn<Nullable<UInt8>>(1, 1)));
+    // only null
+    ASSERT_COLUMN_EQ(
+        createColumn<Nullable<UInt8>>({{}, 0}),
+        executeFunction(
+            func_name,
+            createOnlyNullColumnConst(2),
+            createColumn<Nullable<UInt8>>({1, 0})));
+    // issue 6127
+    ASSERT_COLUMN_EQ(
+        createColumn<UInt8>({0, 1, 0, 0}),
+        executeFunction(
+            func_name,
+            createColumn<Int64>({0, 123, 0, 41}),
+            createColumn<UInt8>({0, 11, 221, 0})));
+    // issue 6127, position of UInt8 column may affect the result
+    ASSERT_COLUMN_EQ(
+        createColumn<UInt8>({0, 1, 0, 0}),
+        executeFunction(
+            func_name,
+            createColumn<UInt8>({0, 123, 0, 41}),
+            createColumn<Int64>({0, 11, 221, 0})));
+}
+CATCH
+
+TEST_F(Logical, orTest)
+try
+{
+    const String & func_name = "or";
+
+    // column, column
+    ASSERT_COLUMN_EQ(
+        createColumn<Nullable<UInt8>>({0, 1, 1, 1, 1, {}}),
+        executeFunction(
+            func_name,
+            createColumn<Nullable<UInt8>>({0, 1, 0, 1, {}, 0}),
+            createColumn<Nullable<UInt8>>({0, 1, 1, 0, 1, {}})));
+    // column, const
+    ASSERT_COLUMN_EQ(
+        createColumn<Nullable<UInt8>>({1, 1}),
+        executeFunction(
+            func_name,
+            createConstColumn<Nullable<UInt8>>(2, 1),
+            createColumn<Nullable<UInt8>>({1, 0})));
+    // const, const
+    ASSERT_COLUMN_EQ(
+        createConstColumn<UInt8>(1, 1),
+        executeFunction(
+            func_name,
+            createConstColumn<Nullable<UInt8>>(1, 1),
+            createConstColumn<Nullable<UInt8>>(1, 0)));
+    // only null
+    ASSERT_COLUMN_EQ(
+        createColumn<Nullable<UInt8>>({1, {}}),
+        executeFunction(
+            func_name,
+            createOnlyNullColumnConst(2),
+            createColumn<Nullable<UInt8>>({1, 0})));
+    // issue 5849
+    ASSERT_COLUMN_EQ(
+        createColumn<UInt8>({0, 1, 1, 1}),
+        executeFunction(
+            func_name,
+            createColumn<UInt8>({0, 123, 0, 41}),
+            createColumn<Int64>({0, 11, 221, 0})));
+}
+CATCH
+
+TEST_F(Logical, xorTest)
+try
+{
+    const String & func_name = "xor";
+
+    // column, column
+    ASSERT_COLUMN_EQ(
+        createColumn<Nullable<UInt8>>({0, 0, 1, 1, {}, {}}),
+        executeFunction(
+            func_name,
+            createColumn<Nullable<UInt8>>({0, 1, 0, 1, {}, 0}),
+            createColumn<Nullable<UInt8>>({0, 1, 1, 0, 1, {}})));
+    // column, const
+    ASSERT_COLUMN_EQ(
+        createColumn<Nullable<UInt8>>({0, 1}),
+        executeFunction(
+            func_name,
+            createConstColumn<Nullable<UInt8>>(2, 1),
+            createColumn<Nullable<UInt8>>({1, 0})));
+    // const, const
+    ASSERT_COLUMN_EQ(
+        createConstColumn<UInt8>(1, 0),
+        executeFunction(
+            func_name,
+            createConstColumn<Nullable<UInt8>>(1, 1),
+            createConstColumn<Nullable<UInt8>>(1, 1)));
+    // only null
+    ASSERT_COLUMN_EQ(
+        createOnlyNullColumnConst(2),
+        executeFunction(
+            func_name,
+            createOnlyNullColumnConst(2),
+            createColumn<Nullable<UInt8>>({1, 0})));
+}
+CATCH
+
+TEST_F(Logical, notTest)
+try
+{
+    const String & func_name = "not";
+
+    // column
+    ASSERT_COLUMN_EQ(
+        createColumn<Nullable<UInt8>>({1, 0, {}}),
+        executeFunction(
+            func_name,
+            createColumn<Nullable<UInt8>>({0, 1, {}})));
+    // const
+    ASSERT_COLUMN_EQ(
+        createConstColumn<UInt8>(1, 0),
+        executeFunction(
+            func_name,
+            createConstColumn<Nullable<UInt8>>(1, 1)));
+    // only null
+    ASSERT_COLUMN_EQ(
+        createOnlyNullColumnConst(1),
+        executeFunction(
+            func_name,
+            createOnlyNullColumnConst(1)));
+}
+CATCH
+
+} // namespace DB::tests
\ No newline at end of file