Determine font color based on background color

(StartA <= EndB) and (EndA >= StartB)

Proof:
Let ConditionA Mean that DateRange A Completely After DateRange B

_                        |---- DateRange A ------|
|---Date Range B -----|                          _

(True if StartA > EndB)

Let ConditionB Mean that DateRange A is Completely Before DateRange B

|---- DateRange A -----|                        _ 
_                          |---Date Range B ----|

(True if EndA < StartB)

Then Overlap exists if Neither A Nor B is true -
(If one range is neither completely after the other,
nor completely before the other, then they must overlap.)

Now one of De Morgan's laws says that:

Not (A Or B) <=> Not A And Not B

Which translates to: (StartA <= EndB) and (EndA >= StartB)

NOTE: This includes conditions where the edges overlap exactly. If you wish to exclude that,
change the >= operators to >, and <= to <

NOTE2. Thanks to @Baodad, see this blog, the actual overlap is least of:
{ endA-startA, endA - startB, endB-startA, endB - startB }

(StartA <= EndB) and (EndA >= StartB) (StartA <= EndB) and (StartB <= EndA)

NOTE3. Thanks to @tomosius, a shorter version reads:
DateRangesOverlap = max(start1, start2) < min(end1, end2)
This is actually a syntactical shortcut for what is a longer implementation, which includes extra checks to verify that the start dates are on or before the endDates. Deriving this from above:

If start and end dates can be out of order, i.e., if it is possible that startA > endA or startB > endB, then you also have to check that they are in order, so that means you have to add two additional validity rules:
(StartA <= EndB) and (StartB <= EndA) and (StartA <= EndA) and (StartB <= EndB) or:
(StartA <= EndB) and (StartA <= EndA) and (StartB <= EndA) and (StartB <= EndB) or,
(StartA <= Min(EndA, EndB) and (StartB <= Min(EndA, EndB)) or:
(Max(StartA, StartB) <= Min(EndA, EndB)

But to implement Min() and Max(), you have to code, (using C ternary for terseness),:
(StartA > StartB? Start A: StartB) <= (EndA < EndB? EndA: EndB)

I already knew about the color escapes, I used them in my bash prompt a while ago. Thanks anyway.
What I wanted was to integrate it with the logging module, which I eventually did after a couple of tries and errors.
Here is what I end up with:

BLACK, RED, GREEN, YELLOW, BLUE, MAGENTA, CYAN, WHITE = range(8)

#The background is set with 40 plus the number of the color, and the foreground with 30

#These are the sequences need to get colored ouput
RESET_SEQ = "\033[0m"
COLOR_SEQ = "\033[1;%dm"
BOLD_SEQ = "\033[1m"

def formatter_message(message, use_color = True):
    if use_color:
        message = message.replace("$RESET", RESET_SEQ).replace("$BOLD", BOLD_SEQ)
    else:
        message = message.replace("$RESET", "").replace("$BOLD", "")
    return message

COLORS = {
    'WARNING': YELLOW,
    'INFO': WHITE,
    'DEBUG': BLUE,
    'CRITICAL': YELLOW,
    'ERROR': RED
}

class ColoredFormatter(logging.Formatter):
    def __init__(self, msg, use_color = True):
        logging.Formatter.__init__(self, msg)
        self.use_color = use_color

    def format(self, record):
        levelname = record.levelname
        if self.use_color and levelname in COLORS:
            levelname_color = COLOR_SEQ % (30 + COLORS[levelname]) + levelname + RESET_SEQ
            record.levelname = levelname_color
        return logging.Formatter.format(self, record)

And to use it, create your own Logger:

# Custom logger class with multiple destinations
class ColoredLogger(logging.Logger):
    FORMAT = "[$BOLD%(name)-20s$RESET][%(levelname)-18s]  %(message)s ($BOLD%(filename)s$RESET:%(lineno)d)"
    COLOR_FORMAT = formatter_message(FORMAT, True)
    def __init__(self, name):
        logging.Logger.__init__(self, name, logging.DEBUG)                

        color_formatter = ColoredFormatter(self.COLOR_FORMAT)

        console = logging.StreamHandler()
        console.setFormatter(color_formatter)

        self.addHandler(console)
        return


logging.setLoggerClass(ColoredLogger)

Just in case anyone else needs it.

Be careful if you're using more than one logger or handler: ColoredFormatter is changing the record object, which is passed further to other handlers or propagated to other loggers. If you have configured file loggers etc. you probably don't want to have the colors in the log files. To avoid that, it's probably best to simply create a copy of record with copy.copy() before manipulating the levelname attribute, or to reset the levelname to the previous value, before returning the formatted string (credit to Michael in the comments).