Q:

What do "KAL." and "A.S." stand for in this inscription?

The inscription below has this line:

MORTUO XV KAL. OCT. A.S. MDCCCLVII 

I'm not sure what KAL. nor A.S. stand for. The source of the image states that the person died the 17th of September. The inscription says instead that he died the 15th of October. What is KAL. to do with it? Is some sort of calendar correction? The year is correct.
And regarding A.S., is this anno sancti? I was surprised not to find A.D., as usual in these inscriptions.

A:

The source of the image states that the person died the 17th of September. The inscription says instead that he died the 15th of October. What is KAL. to do with it? Is some sort of calendar correction?

This is how the Roman calendar works.
The day is ante diem quintum decimum Kalendas Octobres, "on the fifteenth day before the first of October".
With the Roman inclusive counting1, this amounts to 17th of September.
This question on writing dates contains a detailed description of how the dates work.

And regarding A.S., is this anno sancti? I was surprised not to find A.D., as usual in these inscriptions.

Indeed, Anno Domini is far more common in my experience.
This one might have Anno Sancto, "on the holy year" but not "on the year of the holy".
A more common choice appears to be Anno Salvatoris as Tom Cotton suggests.

1
We would call it the fourteenth day.
For the Romans the day before yesterday would be the third day before today — you have to count today, yesterday, and the day before.

A:

The Romans counted backwards from one of three datum days,and  included both the datum and the day itself. KAL is short for Kalendis, the first day of the month, so 15 KAL indicates 13 days between  the 1st October,and the day itself, giving us the 17th September. This inscription appears to be unusual in two ways.
First, it's usual to find A.D. before the numeral (ante diem, literally the day  before the numbered day). The other datum points are the Nones and the Ides, both of which have a rule for the day on which they fall after the Kalends that preceded them. It's very confusing to the uninitiated! 
Secondly, A.S. is sometimes (if rarely) used instead of A.D. It stands for Anno Salvatoris, 'Year of the Saviour', where A.D. is the familiar Anno Domini, 'Year of the Lord'.

A:

The other answers have correctly explained "Kal".
AS stands for anno salutis. The English equivalent is "in the year of grace".
https://de.wikipedia.org/wiki/Anno_Salutis

