Logical data independence in the context of SQL and Java can be demonstrated in an application program connected to a database using the following example:

Let's say we have a hypothetical database with a "users" table containing the columns "id", "name", and "email".

SQL Code for Database Schema:

CREATE TABLE users (
    id INT PRIMARY KEY,
    name VARCHAR(50),
    email VARCHAR(100)
);

Now, let's consider a Java application program that interacts with this database.

Java Code for Data Retrieval:

import java.sql.Connection;
import java.sql.DriverManager;
import java.sql.ResultSet;
import java.sql.SQLException;
import java.sql.Statement;

public class UserDataRetrieval {
    public static void main(String[] args) {
        String url = "jdbc:mysql://localhost:3306/yourDatabaseName";
        String user = "username";
        String password = "password";

        try (Connection con = DriverManager.getConnection(url, user, password);
             Statement stmt = con.createStatement();
             ResultSet rs = stmt.executeQuery("SELECT id, name FROM users")) {

            while (rs.next()) {
                int userId = rs.getInt("id");
                String userName = rs.getString("name");
                System.out.println("User ID: " + userId + ", Name: " + userName);
            }
        } catch (SQLException ex) {
            ex();
        }
    }
}

In this scenario, logical data independence is achieved because the Java application is insulated from the underlying structure of the database. If the database schema changes (e.g., a new column "address" is added to the "users" table), the Java code can remain unchanged as long as the application's requirements for "id" and "name" columns in the "users" table remain consistent.

This demonstrates logical data independence, where changes to the logical structure or organization of the data in the database do not require changes to the application program's code as long as the application's data access requirements remain the same.

Let's say that you've decided to delete the "email" column from your "users" table.

SQL Code for Editing Database Schema:

ALTER TABLE users
DROP COLUMN email;

This action does not affect the Java application code provided previously because it retrieves only the "id" and "name" columns, and it doesn't care about the "email" column. Here is the Java code for reference:

Java Code for Data Retrieval:

import java.sql.Connection;
import java.sql.DriverManager;
import java.sql.ResultSet;
import java.sql.SQLException;
import java.sql.Statement;

public class UserDataRetrieval {
    public static void main(String[] args) {
        String url = "jdbc:mysql://localhost:3306/yourDatabaseName";
        String user = "username";
        String password = "password";

        try (Connection con = DriverManager.getConnection(url, user, password);
             Statement stmt = con.createStatement();
             ResultSet rs = stmt.executeQuery("SELECT id, name FROM users")) {

            while (rs.next()) {
                int userId = rs.getInt("id");
                String userName = rs.getString("name");
                System.out.println("User ID: " + userId + ", Name: " + userName);
            }
        } catch (SQLException ex) {
            ex();
        }
    }
}

Again, despite the modification in the logical schema of the database, the Java code remains untouched and can still function in the same manner as it did previously. Hence, this is an illustration of logical data independence. It shows that changes to the logical schema (like removing a column) need not affect application programs as long as the data they interact with is consistent.

If you are deleting the 'name' column from the 'users' table, it would certainly influence the Java application as it is directly using the 'name' column in its code.

SQL Code for Editing Database Schema:

ALTER TABLE users
DROP COLUMN name;

After this alteration, the previous Java code that was used to retrieve the 'name' field will no longer work, because the 'name' column doesn't exist in the 'users' table anymore.

To correct this, you need to modify your Java code as follows:

Java Code for Data Retrieval:

import java.sql.Connection;
import java.sql.DriverManager;
import java.sql.ResultSet;
import java.sql.SQLException;
import java.sql.Statement;

public class UserDataRetrieval {

    public static void main(String[] args) {
        String url = "jdbc:mysql://localhost:3306/yourDatabaseName";
        String user = "username";
        String password = "password";

        try (Connection con = DriverManager.getConnection(url, user, password);
            Statement stmt = con.createStatement();
            ResultSet rs = stmt.executeQuery("SELECT id FROM users")) {

            while (rs.next()) {
                int userId = rs.getInt("id");
                System.out.println("User ID: " + userId);
            }
        } catch (SQLException ex) {
            ex();
        }
    }
}

In this adjusted code, we are now just retrieving the 'id' column from the 'users' table, because the 'name' column has been removed from the table.

Please note that it in this case it was necessary to change the Java code due to the removal of the 'name' column, so the logical data independence was not preserved. The principle of logical data independence applies when a change in the logical level (like adding a new column) does not impact the application program that interacts with the data. If the application program depends on data that is deleted or changed, then changes will need to be made on the application level as well.