How can I solve "laravel/horizon v1.1.0 requires ext-pcntl * -> the requested PHP extension pcntl is missing from your system"?

Run composer with the --ignore-platform-reqs option and specify pcntl and posix

composer install --ignore-platform-reqs

As per the accepted answer, but you can add this to your composer.json so that you don't have to run --ignore-platform-reqs all the time

"config": {
  "platform": {
    "ext-pcntl": "7.3",
    "ext-posix": "7.3"
  }
}

install horizon this way :

composer require laravel/horizon --ignore-platform-reqs

then run

php artisan horizon:install