Akinori Abe

Abstract

In AI, generally abduction is such an inference that explains an observation by adopting consistent hypotheses included in the knowledge base. One example of this sort of inference is a hypothetical reasoning (Theorist etc.). Of course, this type of abduction is also a defeasible one, but it can not make an inference when the knowledge base lacks necessary hypotheses. Therefore, in that case, missing hypotheses need to be generated. On the other hand, although CMS [Reiter 1987] works as the clause management system, from the abductive point of view, the negated minimal support clauses returned from it can be regarded as abductive hypotheses. Therefore, CMS seems to be able to generate missing hypotheses.
In CMS, hypotheses are abduced from an observation. Therefore, only hypotheses which will not be placed on the real leaves (that is, be placed on the middle of the inference path) or short-cut hypotheses can be generated. That is, even if the knowledge base includes clauses on its leaves which can be used to explain an observation, an abductive inference path can not reach the leaves, so they can not be used as hypotheses.
For example, let the knowledge base be as shown in the following table. When a query palace is given by the user, since the knowledge base lacks necessary hypotheses to explain an observation, during the CMS inference, a set of minimal support clauses are returned; they are the negation of the missing hypotheses. The negations of the minimal support clause (candidate hypotheses) are {east, ride, car ∨ fuel, horse, village, fuel ∨ town}. This result shows that abduction is done without regarding a leaf hypothesis ``desert''. This is because it is hard to find the possible leaf hypotheses like ``desert'' in the separated inference paths which can be used to explain an observation. During abduction, the inference path will stop when there is no other clauses to be adopted abductively.
In order to avoid this sort of incorrect hypotheses generation, the hypotheses generation could be done by coupling deduction from the leaf hypotheses with abduction from an observation, and supplementing the missing inference paths by generating some new hypotheses. However, when some clauses are missing, there is no information about which clauses must be adopted to complete the inference path. Also there exist some possibilities of over-abduction or wrong-directed-deduction.
This page shows a method that can explain an observation not only by adopting hypotheses in the knowledge base but also by generating missing ones. The method also enables missing hypotheses to be found in the middle of the inference path by both abductive and deductive mechanisms. That is, at first, the hypotheses are searched abductively from the observation, and then they are searched deductively from the leaves. Then, even if the inference path is not a complete one, the possible location of hypotheses in the inference path can be found, and plausible hypotheses can be generated by analogical mapping from the clauses in the knowledge base.

References:

1. Abe, A.: Hypotheses Generation in Abduction, Proc. of the 54th. Annual Conf. of IPSJ, Vol. 2, 6G-01, pp. 155--156 (1997) (in Japanese).
2. Abe A.: Two-sided Hypotheses Generation for Abductive Analogical Reasoning, Proc. of ICTAI99, pp. 145--152 (1999)

• [Reiter 1987] Reiter R. and de Kleer J.: Foundation of assumption-based truth maintenance systems: preliminary report, Proc. of AAAI87, pp.183--188 (1987)