code problem

hi guys i have a problem to understand with my project in the picture .++

is a PIR sensor connected with is out strictly to the pin 3 , this one send his statement to 13 . it is connected to the relais board of 5 v a light saber of 36 led 12v is linked in ! then the problem is when the pir sensor detect a movement it turns off the lamp in stead of turn on ! no movement must to means no light !

the code is below i try to change at the end high to low but doesnt work

THX IN ADVANCE

int calibrationTime = 5;

//the time when the sensor outputs a low impulse
long unsigned int lowIn;

//the amount of milliseconds the sensor has to be low
//before we assume all motion has stopped
long unsigned int pause = 5000;

boolean lockLow = true;
boolean takeLowTime;

int pirPin = 3; //the digital pin connected to the PIR sensor's output
int ledPin = 13;


/////////////////////////////
//SETUP
void setup(){
Serial.begin(9600);
pinMode(pirPin, INPUT);
pinMode(ledPin, OUTPUT);
digitalWrite(pirPin, LOW);

//give the sensor some time to calibrate
Serial.print("CALIBRAZIONE SENSORE ");
for(int i = 0; i < calibrationTime; i++){
Serial.print(".");
delay(1000);
}
Serial.println(" fatto");
Serial.println("SENSORE ATTIVO");
delay(50);
}

////////////////////////////
//LOOP
void loop(){

if(digitalRead(pirPin) == HIGH){
digitalWrite(ledPin, HIGH); //the led visualizes the sensors output pin state
if(lockLow){
//makes sure we wait for a transition to LOW before any further output is made:
lockLow = false;
Serial.println("DIO CANE");
Serial.print("movimento rilevato in ");
Serial.print(millis()/1000);
Serial.println(" sec");
delay(50);
}
takeLowTime = true;
}

if(digitalRead(pirPin) == LOW){
digitalWrite(ledPin, LOW); //the led visualizes the sensors output pin state

if(takeLowTime){
lowIn = millis(); //save the time of the transition from high to LOW
takeLowTime = false; //make sure this is only done at the start of a LOW phase
}
//if the sensor is low for more than the given pause,
//we assume that no more motion is going to happen
if(!lockLow && millis() - lowIn > pause){
//makes sure this block of code is only executed again after
//a new motion sequence has been detected
lockLow = true;
Serial.print("MOVIMENTO FINITO IN: "); //output
Serial.print((millis() - pause)/1000);
Serial.println(" sec");
delay(50);
}
}
}

I would use this

if (__>__)
 ____
else ()
____

see if that format works

I would add some more ( ) in this line to ensure it compiles as intended:

if(!lockLow && millis() - lowIn > pause){

change to:

if(!lockLow && ((millis() - lowIn) > pause)){