Creating a complete text correction AI with HTML, JavaScript, and PHP would involve several steps and would require a deep understanding of natural language processing.
In this example, the user can input text into the textarea and click the "Correct Text" button to send the text to a server-side PHP script. The PHP script uses the LanguageTool API to correct the text and sends the corrected text back to the client, where it is displayed in a div element.
Note that this is a very basic example and a real-world text correction AI would involve much more complex natural language processing techniques. Additionally, this example uses a third-party API, which may not be suitable for all use cases. You would also need to replace 'YOUR_API_KEY' with your actual LanguageTool API key.