The print here is by
Tatsuo Horiuchi, who uses Excel to draw beautiful Japanese pictures. This is strangely apt as a caption for a post on question answering, actually.
Some
times bits of information get stuck in your head and keep coming back
when you're having a shower or driving, pestering you for no good
reason...
Right now the bit of information that is annoying me like food-stuck-between-your-teeth is the
Standard Model of Question Answering using knowledge bases or KBs. Say you have a question Q, a proposed answer A for the question and a knowledge base KB that is supposed to help you answer the question.
It is usual to say that
A is a good answer for Q, provided by the knowledge base KB, which we could write as
Answers(A, Q, KB) if the declarative form of the question Q matches the assertion A and A is entailed by the contents of the KB.
A simple example of question Q is "What is the capital of France?" The declarative version of this question could be written as
capital(France, ?) where I am writing
? for the thing I don't know
. So if the KB has a triple "capital(France, Paris)", then the KB entails a good answer for Q, or KB |- A and A is a good answer for Q, using the traditional symbol of entailment so loved by logicians.
Thus in the standard model we have to do two things:
1. we need to show that KB entails A (proof theory in databases? how long can the proof be?) and
2. we need to show that A matches (how closely?) the declarative form of the question Q.
There are plenty of deficiencies of this standard model:
1. Sometimes answers do not directly match the form of the question, but imply it in conjunction with additional (background) knowledge, you could call it More-Informative answers. For example, if the question was:
Q: Is Paris in France?
A: Paris is the capital of France (Since being the 'capital of' a country implies being 'in the country', this is a more informative answer than the question you asked. You have to do some inference to obtain the answer really asked for.)
2. Sometimes you'd prefer to see
Qualified answers
Q: How much for "The Dark Knight"?
A: To see it now, you have to pay $13.95 On Demand, Netflix announced it will have for free next week.
Another example:
Q: What is the dosage of aspirin for fever?
A: For infants 100 mg, for children 200 mg, for adults 300 mg...
3. Sometimes more than qualified answers, you want
Ranked Answers
Q: How do I get to Boston?
A: There are multiple flights or train or bus itineraries, depending on who you
are, where you are, how much money you want to spend, etc..
Multiple correct answers but of varying relevance...
Given that we do want these kinds of answers, which are more informative,
Dick Crouch describes an improved model of KB-based question answering. Say A answers question Q using KB and a collection of backgroung assumptions B plus a set of extra suppositions S if
Answers(A, Q, KB, B, S) if:
1. KB |- A the answer A 'follows from' the KB;
2.
the declarative form of the question Q follows from some background
knowledge B, some extra suppositions S and the answer A, A&B&S
|- Q^d
3. the background knowledge follows from the KB, KB |- B (are these the same kinds of proofs as before?)
4. the additional suppositions do not follow from the KB, KB |-/- S
5. the additional suppositions do not entail the declarative form of the question S|-/- Q^d
But I wonder how S and B come about and from where.
It
looks like B ought to be part of a common stock of general knowledge
that my KB should have or would have if it knew about Common Sense, while S consists of extra assumptions that no amount of generic knowledge about the world would provide. Does this make sense?
Mike Barr posted in the cats mailing list the following:
