MGTP Applications (1) Abductive Reasoning System
Abstract We have developed several parallel abductive reasoning systems using the MGTP. We will describe two implementations of the abductive reasoning system shown in Figure 1: one is the MGTP+MGTP method, and the other is the Skip method. In each method, the given input formulas are translated into MGTP rules in a different way. We demonstrated them by applying them to a logic circuit design problem.
P.71 Figure 1
Figure 1: Abductive Reasoning System based on the MGTP
Abduction We considered the first-order abductive framework (Sigma,Gamma), where Sigma is a set of Horn clauses and Gamma is a set of atoms (abducibles). A set E of ground instances of elements of Gamma is an explanation of a closed formula G from (Sigma, Gamma) if: (1) SigmaCup E G, and (2) SigmaCupE is consistent. Given Sigma, Gamma and G, the task of abduction is to find the explanations of G from (Sigma, Gamma). MGTP+MGTP Each ground hypothesis H from Gamma is represented by fact(H, {H}), and each Horn clause in Sigma of the form:
P.71 Function 3
is translated into the MGTP rule of the form:
P.71 Function 4
- 71 -