When is reasoning with distributed knowledge bases same as reasoning about update of a single knowledge base?
In some cases, a problem of drawing conclusions from distributed Knowledge Bases (KB) can be treated as the problem of belief update, and that a formalism which supports dialectical inference (such as Dung’s abstract argumentation) can model such reasoning, provided that one wants to have dialectical inference in the first place. (Dung’s argumentation is not the only way, but that doesn’t matter much below.)
Consider the following problem: There are several knowledge bases, KB1…KBn. Each is just a set of propositions (ground formulas). There is an observer who wants to know if some proposition p follows from the propositions revealed from these KBs. By revealed, I mean that the propositions in the different KBs become accessible to the observer in a sequence, not all at the same time.
This looks like the problem of a judge in a trial, to whom the defense and prosecution reveal pieces of information. As the trial progresses, the judge forms and changes her opinion on the person being innocent.
It is also the problem of the patient who asks several doctors for opinion on the same symptoms, and tries to draw her own conclusions as she goes from one doctor to the next.
My argument is that, while this looks like a distributed KB problem, it seems easier to me to see it as a problem of updating a single KB, as long as the observer just wants to see if that proposition p follows from the revealed propositions.
In the judge’s problem, it seems reasonable to assume that the aim of the judge is to decide on innocence, based on the arguments and evidence offered by the defense and the prosecution, while the aim of prosecution both prosecution and defense is to offer arguments in favor of their own, and against the claims and arguments of the other.
It is clear that this is a setting with distributed knowledge, but if the aim is to compute acceptable arguments (which in the example clearly is relevant for all of the involved – judge, prosecution, and defense), it is enough to compute acceptability on a new KB, which includes only arguments and attack relations revealed up to the time when acceptability is computed. So the new KB is updated with any newly revealed argument and attack relation, each time prosecution and defense offer them.
The reason I mention Dung’s argumentation is that, if the problem is seen as one of belief update, it seems simpler to take Dung’s argumentation, rather than Alchourrón, Gärdenfors and Makinson. I think that any argumentation à la John Pollock is by definition about update. Dung’s argumentation for example, belongs to this line of work, but not Elvang-Goransson and Hunter, because as far as I know, there is no notion of dialectical reasoning there.
But it is interesting to consider the problems above as problems of distributed KBs, when considering such questions as:
– Based on agent X’s assumption of the content of agent Y’s KB, what is the minimal set of propositions A should reveal to B, in order to ensure some argument which is known by both A and B is acceptable?
– What is the minimal number of propositions an agent should reveal to others, in order to determine whom to cooperate with, and whom to conflict with?
Let me know if you disagree.