Quantitative Competence

One of the first “tests” humans impose on chatbots (or at least would
like to impose if the chatbots could handle it) is what I would now
like to refer to as “quantitative competence”.

QA in the form of

1)
Q: “A cat has four legs. How many legs have two cats?”
A: “eight.”

or even more tricky:

2)
Q: “Cats are mammals. Mammals are tetrapods. Tetrapods have four legs.”
...
Q: “How many legs have eighteen cats?”
A: “seventy-two”

While working on the PetaMem Discourse Engine to enable this feature,
it became apparent that this would be just a gimmick - some kind of
special case to provide a nice effect but of limited use for the
general case of quantitative competence (which I personally consider a
subset of mathematical competence) in human-machine conversation.

If you look at the computational abilities of Wolfram Alpha
(http://www.wolframalpha.com), the two examples above seem trivial.  So we
inspected our knowledge representation formalism and also the
associated inferential algorithms.

The first modification was to use intervals instead of numbers, which
of course required to replace regular arithmetics with interval
arithmetics. The second modification was to make use of conditional
information in the KR formalism. (Something is something else IF some
condition is met).

And these allow us now to do not only 1) and 2), but also this:

3)
Q: “A female ostrich weighs 90 to 110 kg.”
Q: “A female ostrich is 175 to 190 cm tall.”
...
Q: “What is the BMI of a female ostrich?”
A: “The BMI of a female ostrich is within the range 24.9 to 35.9.”

The interesting thing is that “female ostrich” in this case is not a
lexical entity, but just some feature of an ostrich. So if you ask

...
Q: “What is the weight of an ostrich?”
A: “That depends. A female ostrich weighs 90 to 110 kg, a male ostrich weighs 135 to 155 kg.”

Interval arithmetics offers quite naturally an elegant way to provide
quantitative values of seemingly fuzzy nature.

“Up to/no more than a thousand individuals.” [1,1000]
“About 31 kilograms.” [30,32]
“70 years or more.” [70,inf]
...

Where the real representation of the intervals might be different from
case to case, or even debatable, but as a first approximation to the
problem it is usable.

So that milestone has been reached, albeit with 3 weeks delay. I
think it’s worth it, as the achievement is quite more than what was in the
initial specification.

Now we’ll update the backend of our NLP portal with the new version so
you can test it. There are still a few glitches, which I have manually
corrected in the above examples (e.g. the answer for the BMI values is
more like 24.9307479224377 to 35.9183673469388) but I think it is a
pretty nice achievement already.

Considering, that all what you see is language independent in
principle (our next milestone is that you can teach the Discourse
Engine facts about ostriches e.g. in german and ask them in english - or
vice versa.), I’m sufficiently confident to state that we’re “leading the pack”.

Richard