diff --git a/core/src/main/java/org/apache/calcite/rel/rules/CoreRules.java b/core/src/main/java/org/apache/calcite/rel/rules/CoreRules.java
index b88e1459b2e..0062c1f455c 100644
--- a/core/src/main/java/org/apache/calcite/rel/rules/CoreRules.java
+++ b/core/src/main/java/org/apache/calcite/rel/rules/CoreRules.java
@@ -16,6 +16,7 @@
  */
 package org.apache.calcite.rel.rules;
 
+import org.apache.calcite.plan.RelOptUtil.Exists;
 import org.apache.calcite.rel.RelNode;
 import org.apache.calcite.rel.core.Aggregate;
 import org.apache.calcite.rel.core.Calc;
@@ -348,6 +349,11 @@ private CoreRules() {}
   public static final IntersectToDistinctRule INTERSECT_TO_DISTINCT =
       IntersectToDistinctRule.Config.DEFAULT.toRule();
 
+  /** Rule that translates a {@link Intersect}
+   * into a {@link Exists} subquery. */
+  public static final IntersectToExistsRule INTERSECT_TO_EXISTS =
+      IntersectToExistsRule.Config.DEFAULT.toRule();
+
   /** Rule that translates a distinct
    * {@link Minus} into a group of operators
    * composed of {@link Union}, {@link Aggregate}, etc. */
diff --git a/core/src/main/java/org/apache/calcite/rel/rules/IntersectToExistsRule.java b/core/src/main/java/org/apache/calcite/rel/rules/IntersectToExistsRule.java
new file mode 100644
index 00000000000..a1c2be1eb93
--- /dev/null
+++ b/core/src/main/java/org/apache/calcite/rel/rules/IntersectToExistsRule.java
@@ -0,0 +1,161 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to you 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.
+ */
+package org.apache.calcite.rel.rules;
+
+import org.apache.calcite.plan.RelOptRuleCall;
+import org.apache.calcite.plan.RelOptUtil.Exists;
+import org.apache.calcite.plan.RelRule;
+import org.apache.calcite.rel.RelNode;
+import org.apache.calcite.rel.core.CorrelationId;
+import org.apache.calcite.rel.core.Intersect;
+import org.apache.calcite.rel.logical.LogicalIntersect;
+import org.apache.calcite.rel.type.RelDataType;
+import org.apache.calcite.rel.type.RelDataTypeField;
+import org.apache.calcite.rex.RexBuilder;
+import org.apache.calcite.rex.RexNode;
+import org.apache.calcite.rex.RexSubQuery;
+import org.apache.calcite.rex.RexUtil;
+import org.apache.calcite.sql.fun.SqlStdOperatorTable;
+import org.apache.calcite.tools.RelBuilder;
+import org.apache.calcite.tools.RelBuilderFactory;
+import org.apache.calcite.util.ImmutableBitSet;
+
+import com.google.common.collect.ImmutableSet;
+
+import org.immutables.value.Value;
+
+import java.util.ArrayList;
+import java.util.List;
+import java.util.stream.Collectors;
+
+/**
+ * Planner rule that translates a {@link Intersect}
+ * (<code>all</code> = <code>false</code>)
+ * into a {@link Exists}.
+ *
+ * @see CoreRules#INTERSECT_TO_EXISTS
+ */
+@Value.Enclosing
+public class IntersectToExistsRule
+    extends RelRule<IntersectToExistsRule.Config>
+    implements TransformationRule {
+
+  /** Creates an IntersectToExistRule. */
+  protected IntersectToExistsRule(Config config) {
+    super(config);
+  }
+
+  @Deprecated // to be removed before 2.0
+  public IntersectToExistsRule(Class<? extends Intersect> intersectClass,
+      RelBuilderFactory relBuilderFactory) {
+    this(Config.DEFAULT.withRelBuilderFactory(relBuilderFactory)
+        .as(Config.class)
+        .withOperandFor(intersectClass));
+  }
+
+  //~ Methods ----------------------------------------------------------------
+
+  @Override public void onMatch(RelOptRuleCall call) {
+    final Intersect intersect = call.rel(0);
+    if (intersect.all) {
+      return; // nothing we can do
+    }
+
+    final RelBuilder builder = call.builder();
+    final RexBuilder rexBuilder = builder.getRexBuilder();
+
+    RelDataType rowType = intersect.getRowType();
+    List<RelNode> inputs = intersect.getInputs();
+    RelNode current = inputs.get(0);
+
+    // get all column indices of intersect
+    ImmutableBitSet fieldIndices = ImmutableBitSet.of(rowType.getFieldList()
+        .stream().map(RelDataTypeField::getIndex)
+        .collect(Collectors.toList()));
+
+    // iterate over the inputs and apply exists subquery
+    for (int i = 1; i < inputs.size(); i++) {
+      RelNode nextInput = inputs.get(i).stripped();
+
+      // create correlation
+      CorrelationId correlationId = intersect.getCluster().createCorrel();
+      RexNode correl =
+          rexBuilder.makeCorrel(rowType, correlationId);
+
+      // create condition in exists filter, and use correlation
+      List<RexNode> conditions = new ArrayList<>();
+      for (int fieldIndex : fieldIndices) {
+        RexNode outerField = rexBuilder.makeInputRef(rowType, fieldIndex);
+        RexNode innerField = rexBuilder.makeFieldAccess(correl, fieldIndex);
+        conditions.add(
+            rexBuilder.makeCall(SqlStdOperatorTable.IS_NOT_DISTINCT_FROM,
+                outerField, innerField));
+      }
+      RexNode condition = RexUtil.composeConjunction(rexBuilder, conditions);
+
+      // build exists subquery
+      RelNode existsSubQuery = builder.push(nextInput)
+          .filter(condition)
+          .project(builder.fields(fieldIndices))
+          .build();
+
+      // apply exists subquery to the current relation
+      current = builder.push(current)
+          .filter(ImmutableSet.of(correlationId),
+              RexSubQuery.exists(existsSubQuery))
+          .build();
+    }
+
+    builder.push(current);
+    List<RexNode> projects = new ArrayList<>();
+    for (int fieldIndex : fieldIndices) {
+      RexNode rexNode = builder.fields().get(fieldIndex);
+      RelDataType originalType =
+          rowType.getFieldList().get(projects.size()).getType();
+      RexNode expr;
+      if (!originalType.equals(rexNode.getType())) {
+        expr = rexBuilder.makeCast(originalType, rexNode, true, false);
+      } else {
+        expr = rexNode;
+      }
+      projects.add(expr);
+    }
+
+    RelNode result = builder.project(projects)
+        .distinct()
+        .build();
+
+    call.transformTo(result);
+  }
+
+  /** Rule configuration. */
+  @Value.Immutable
+  public interface Config extends RelRule.Config {
+    Config DEFAULT = ImmutableIntersectToExistsRule.Config.of()
+        .withOperandFor(LogicalIntersect.class);
+
+    @Override default IntersectToExistsRule toRule() {
+      return new IntersectToExistsRule(this);
+    }
+
+    /** Defines an operand tree for the given classes. */
+    default Config withOperandFor(Class<? extends Intersect> intersectClass) {
+      return withOperandSupplier(b -> b.operand(intersectClass).anyInputs())
+          .as(Config.class);
+    }
+  }
+}
diff --git a/core/src/test/java/org/apache/calcite/rel/rel2sql/RelToSqlConverterTest.java b/core/src/test/java/org/apache/calcite/rel/rel2sql/RelToSqlConverterTest.java
index 6d59536d231..d9ca61ef87b 100644
--- a/core/src/test/java/org/apache/calcite/rel/rel2sql/RelToSqlConverterTest.java
+++ b/core/src/test/java/org/apache/calcite/rel/rel2sql/RelToSqlConverterTest.java
@@ -37,6 +37,7 @@
 import org.apache.calcite.rel.rules.AggregateProjectMergeRule;
 import org.apache.calcite.rel.rules.CoreRules;
 import org.apache.calcite.rel.rules.FilterJoinRule;
+import org.apache.calcite.rel.rules.IntersectToExistsRule;
 import org.apache.calcite.rel.rules.ProjectOverSumToSum0Rule;
 import org.apache.calcite.rel.rules.ProjectToWindowRule;
 import org.apache.calcite.rel.rules.PruneEmptyRules;
@@ -244,6 +245,33 @@ private static String toSql(RelNode root, SqlDialect dialect,
     sql(query).withMysql().ok(expected);
   }
 
+  /**
+   * Test case of
+   * <a href="https://issues.apache.org/jira/browse/CALCITE-6836">[CALCITE-6836]
+   * Add Rule to convert INTERSECT to EXISTS</a>. */
+  @Test void testIntersectToExistsRule() {
+    String query = "SELECT \"product_name\"\n"
+            + "FROM \"foodmart\".\"product\"\n"
+            + "INTERSECT\n"
+            + "SELECT \"product_name\"\n"
+            + "FROM \"foodmart\".\"product\"";
+    String expected = "SELECT `product_name`\n"
+            + "FROM (SELECT `product_name`\n"
+            + "FROM `foodmart`.`product`) AS `t`\n"
+            + "WHERE EXISTS (SELECT *\n"
+            + "FROM (SELECT `product_name`\n"
+            + "FROM `foodmart`.`product`) AS `t0`\n"
+            + "WHERE `product_name` IS NOT DISTINCT FROM `t`.`product_name`)\n"
+            + "GROUP BY `product_name`";
+    HepProgramBuilder builder = new HepProgramBuilder();
+    builder.addRuleClass(IntersectToExistsRule.class);
+    HepPlanner hepPlanner = new HepPlanner(builder.build());
+    RuleSet rules =
+            RuleSets.ofList(CoreRules.INTERSECT_TO_EXISTS);
+
+    sql(query).withMysql().optimize(rules, hepPlanner).ok(expected);
+  }
+
   @Test void testGroupByBooleanLiteral() {
     String query = "select avg(\"salary\") from \"employee\" group by true";
     String expectedRedshift = "SELECT AVG(\"employee\".\"salary\")\n"
diff --git a/core/src/test/java/org/apache/calcite/test/RelOptRulesTest.java b/core/src/test/java/org/apache/calcite/test/RelOptRulesTest.java
index cd15f88ac87..3da590970d4 100644
--- a/core/src/test/java/org/apache/calcite/test/RelOptRulesTest.java
+++ b/core/src/test/java/org/apache/calcite/test/RelOptRulesTest.java
@@ -9716,4 +9716,50 @@ private void checkJoinAssociateRuleWithTopAlwaysTrueCondition(boolean allowAlway
     fixture().withRelBuilderConfig(a -> a.withBloat(-1))
         .relFn(relFn).withPlanner(planner).check();
   }
+
+  /**
+   * Test case of
+   * <a href="https://issues.apache.org/jira/browse/CALCITE-6836">[CALCITE-6836]
+   * Add Rule to convert INTERSECT to EXISTS</a>. */
+  @Test void testIntersectToExistsRuleOneField() {
+    String sql = "SELECT a.ename FROM emp AS a\n"
+        + "INTERSECT\n"
+        + "SELECT b.name FROM dept AS b";
+    sql(sql).withRule(CoreRules.INTERSECT_TO_EXISTS)
+        .check();
+  }
+
+  @Test void testIntersectToExistsRulePrimaryKey() {
+    String sql = "SELECT a.empno FROM emp AS a\n"
+        + "INTERSECT\n"
+        + "SELECT b.empno FROM emp AS b";
+    sql(sql).withRule(CoreRules.INTERSECT_TO_EXISTS)
+        .check();
+  }
+
+  @Test void testIntersectToExistsRuleMultiFields() {
+    String sql = "SELECT a.ename, a.job FROM emp AS a\n"
+        + "INTERSECT\n"
+        + "SELECT b.ename, b.job FROM emp AS b";
+    sql(sql).withRule(CoreRules.INTERSECT_TO_EXISTS)
+        .check();
+  }
+
+  @Test void testIntersectToExistsRuleMultiIntersect() {
+    String sql = "SELECT a.ename FROM emp AS a\n"
+        + "INTERSECT\n"
+        + "SELECT b.name FROM dept AS b\n"
+        + "INTERSECT\n"
+        + "SELECT c.ename FROM emp AS c";
+    sql(sql).withRule(CoreRules.INTERSECT_TO_EXISTS)
+        .check();
+  }
+
+  @Test void testIntersectToExistsRuleWithAll() {
+    String sql = "SELECT a.ename FROM emp AS a\n"
+        + "INTERSECT ALL\n"
+        + "SELECT b.name FROM dept AS b";
+    sql(sql).withRule(CoreRules.INTERSECT_TO_EXISTS)
+        .checkUnchanged();
+  }
 }
diff --git a/core/src/test/resources/org/apache/calcite/test/RelOptRulesTest.xml b/core/src/test/resources/org/apache/calcite/test/RelOptRulesTest.xml
index 1cb6c346791..da6d4c300c1 100644
--- a/core/src/test/resources/org/apache/calcite/test/RelOptRulesTest.xml
+++ b/core/src/test/resources/org/apache/calcite/test/RelOptRulesTest.xml
@@ -5840,6 +5840,143 @@ LogicalIntersect(all=[true])
   LogicalProject(EMPNO=[$0], ENAME=[$1], JOB=[$2], MGR=[$3], HIREDATE=[$4], SAL=[$5], COMM=[$6], DEPTNO=[$7], SLACKER=[$8])
     LogicalFilter(condition=[=($7, 30)])
       LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+]]>
+    </Resource>
+  </TestCase>
+  <TestCase name="testIntersectToExistsRuleMultiFields">
+    <Resource name="sql">
+      <![CDATA[SELECT a.ename, a.job FROM emp AS a
+INTERSECT
+SELECT b.ename, b.job FROM emp AS b]]>
+    </Resource>
+    <Resource name="planBefore">
+      <![CDATA[
+LogicalIntersect(all=[false])
+  LogicalProject(ENAME=[$1], JOB=[$2])
+    LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+  LogicalProject(ENAME=[$1], JOB=[$2])
+    LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+]]>
+    </Resource>
+    <Resource name="planAfter">
+      <![CDATA[
+LogicalAggregate(group=[{0, 1}])
+  LogicalFilter(condition=[EXISTS({
+LogicalFilter(condition=[AND(IS NOT DISTINCT FROM($0, $cor0.ENAME), IS NOT DISTINCT FROM($1, $cor0.JOB))])
+  LogicalProject(ENAME=[$1], JOB=[$2])
+    LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+})], variablesSet=[[$cor0]])
+    LogicalProject(ENAME=[$1], JOB=[$2])
+      LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+]]>
+    </Resource>
+  </TestCase>
+  <TestCase name="testIntersectToExistsRuleMultiIntersect">
+    <Resource name="sql">
+      <![CDATA[SELECT a.ename FROM emp AS a
+INTERSECT
+SELECT b.name FROM dept AS b
+INTERSECT
+SELECT c.ename FROM emp AS c]]>
+    </Resource>
+    <Resource name="planBefore">
+      <![CDATA[
+LogicalIntersect(all=[false])
+  LogicalIntersect(all=[false])
+    LogicalProject(ENAME=[$1])
+      LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+    LogicalProject(NAME=[CAST($1):VARCHAR(20) NOT NULL])
+      LogicalTableScan(table=[[CATALOG, SALES, DEPT]])
+  LogicalProject(ENAME=[$1])
+    LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+]]>
+    </Resource>
+    <Resource name="planAfter">
+      <![CDATA[
+LogicalFilter(condition=[EXISTS({
+LogicalFilter(condition=[IS NOT DISTINCT FROM($0, $cor0.ENAME)])
+  LogicalProject(ENAME=[$1])
+    LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+})], variablesSet=[[$cor0]])
+  LogicalAggregate(group=[{0}])
+    LogicalFilter(condition=[EXISTS({
+LogicalFilter(condition=[IS NOT DISTINCT FROM($0, $cor1.ENAME)])
+  LogicalProject(NAME=[CAST($1):VARCHAR(20) NOT NULL])
+    LogicalTableScan(table=[[CATALOG, SALES, DEPT]])
+})], variablesSet=[[$cor1]])
+      LogicalProject(ENAME=[$1])
+        LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+]]>
+    </Resource>
+  </TestCase>
+  <TestCase name="testIntersectToExistsRuleOneField">
+    <Resource name="sql">
+      <![CDATA[SELECT a.ename FROM emp AS a
+INTERSECT
+SELECT b.name FROM dept AS b]]>
+    </Resource>
+    <Resource name="planBefore">
+      <![CDATA[
+LogicalIntersect(all=[false])
+  LogicalProject(ENAME=[$1])
+    LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+  LogicalProject(NAME=[CAST($1):VARCHAR(20) NOT NULL])
+    LogicalTableScan(table=[[CATALOG, SALES, DEPT]])
+]]>
+    </Resource>
+    <Resource name="planAfter">
+      <![CDATA[
+LogicalAggregate(group=[{0}])
+  LogicalFilter(condition=[EXISTS({
+LogicalFilter(condition=[IS NOT DISTINCT FROM($0, $cor0.ENAME)])
+  LogicalProject(NAME=[CAST($1):VARCHAR(20) NOT NULL])
+    LogicalTableScan(table=[[CATALOG, SALES, DEPT]])
+})], variablesSet=[[$cor0]])
+    LogicalProject(ENAME=[$1])
+      LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+]]>
+    </Resource>
+  </TestCase>
+  <TestCase name="testIntersectToExistsRulePrimaryKey">
+    <Resource name="sql">
+      <![CDATA[SELECT a.empno FROM emp AS a
+INTERSECT
+SELECT b.empno FROM emp AS b]]>
+    </Resource>
+    <Resource name="planBefore">
+      <![CDATA[
+LogicalIntersect(all=[false])
+  LogicalProject(EMPNO=[$0])
+    LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+  LogicalProject(EMPNO=[$0])
+    LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+]]>
+    </Resource>
+    <Resource name="planAfter">
+      <![CDATA[
+LogicalFilter(condition=[EXISTS({
+LogicalFilter(condition=[IS NOT DISTINCT FROM($0, $cor0.EMPNO)])
+  LogicalProject(EMPNO=[$0])
+    LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+})], variablesSet=[[$cor0]])
+  LogicalProject(EMPNO=[$0])
+    LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+]]>
+    </Resource>
+  </TestCase>
+  <TestCase name="testIntersectToExistsRuleWithAll">
+    <Resource name="sql">
+      <![CDATA[SELECT a.ename FROM emp AS a
+INTERSECT ALL
+SELECT b.name FROM dept AS b]]>
+    </Resource>
+    <Resource name="planBefore">
+      <![CDATA[
+LogicalIntersect(all=[true])
+  LogicalProject(ENAME=[$1])
+    LogicalTableScan(table=[[CATALOG, SALES, EMP]])
+  LogicalProject(NAME=[CAST($1):VARCHAR(20) NOT NULL])
+    LogicalTableScan(table=[[CATALOG, SALES, DEPT]])
 ]]>
     </Resource>
   </TestCase>