Listing products with multiple categories in Prest

I'm communicating with Prestashop 1.5 Web Services for listing products and its filters are simple enough for basic cases, but what about multiple categories:

Can I get a list of products that belong to category 1 AND 2?
Can I get a list of products that belong to category 1 OR 2?

For your information here is Prestashop 1.5 Filter management process in classes/webservice/WebserviceRequest:

/**
 * get SQL retrieve Filter
 *
 * @param string $sqlId
 * @param string $filterValue
 * @param string $tableAlias = 'main.'
 * @return string
 */
protected function getSQLRetrieveFilter($sqlId, $filterValue, $tableAlias = 'main.')
{
    $ret = '';
    preg_match('/^(.*)\[(.*)\](.*)$/', $filterValue, $matches);
    if (count($matches) > 1)
    {
        if ($matches[1] == '%' || $matches[3] == '%')
            $ret .= ' AND '.bqSQL($tableAlias).'`'.bqSQL($sqlId).'` LIKE "'.pSQL($matches[1].$matches[2].$matches[3])."\"\n";
        elseif ($matches[1] == '' && $matches[3] == '')
        {
            if (strpos($matches[2], '|') > 0)
            {
                $values = explode('|', $matches[2]);
                $ret .= ' AND (';
                $temp = '';
                foreach ($values as $value)
                    $temp .= bqSQL($tableAlias).'`'.bqSQL($sqlId).'` = "'.bqSQL($value).'" OR ';
                $ret .= rtrim($temp, 'OR ').')'."\n";
            }
            elseif (preg_match('/^([\d\.:-\s]+),([\d\.:-\s]+)$/', $matches[2], $matches3))
            {
                unset($matches3[0]);
                if (count($matches3) > 0)
                {
                    sort($matches3);
                    $ret .= ' AND '.$tableAlias.'`'.bqSQL($sqlId).'` BETWEEN "'.pSQL($matches3[0]).'" AND "'.pSQL($matches3[1])."\"\n";
                }
            }
            else
                $ret .= ' AND '.$tableAlias.'`'.bqSQL($sqlId).'`="'.pSQL($matches[2]).'"'."\n";
        }
        elseif ($matches[1] == '>')
            $ret .= ' AND '.$tableAlias.'`'.bqSQL($sqlId).'` > "'.pSQL($matches[2])."\"\n";
        elseif ($matches[1] == '<')
            $ret .= ' AND '.$tableAlias.'`'.bqSQL($sqlId).'` < "'.pSQL($matches[2])."\"\n";
        elseif ($matches[1] == '!')
            $ret .= ' AND '.$tableAlias.'`'.bqSQL($sqlId).'` != "'.pSQL($matches[2])."\"\n";
    }
    else
        $ret .= ' AND '.$tableAlias.'`'.bqSQL($sqlId).'` '.(Validate::isFloat(pSQL($filterValue)) ? 'LIKE' : '=').' "'.pSQL($filterValue)."\"\n";
    return $ret;
}

From this we can notice that, unlike what the official documention says:

We can simulate a OR condition with a pipe | between values.
We can simulate a BETWEEN condition with a coma , between values.
We can simulate a LIKE %% condition with a leading or/and a following percent % of our value.
We can simulate a > condition with a > in front of the value.
We can simulate a < condition with a < in front of the value.
We can simulate a != condition with a ! in front of the value.

But I can't find a solution to simulate a AND condition. If you find one feel free to update this answer.

You can easily override this method to add your own AND filter.

For Prestashop 1.6 there's a little difference with the ! condition:

} elseif ($matches[1] == '!') {
     $multiple_values = explode('|', $matches[2]);
     foreach ($multiple_values as $value) {
         $ret .= ' AND '.$tableAlias.'`'.bqSQL($sqlId).'` != "'.pSQL($value)."\"\n";
     }
}