Forse devi definire la variabile in tutti i casi, perchè in tutti i casi la usi.
Codice PHP:
<FORM name="2", method="post">
<INPUT type="submit", name="submit", value="Accendi il forno"></input>
</FORM>
<?php
if(isset($_POST['submit'])){
$door_closed=true;
}else{
$door_closed=false;
}
if($door_closed==true){
echo "door_closed=true";
}else{
echo "door_closed=$door_closed";
}