Deductive Inference for the Interiors and Exteriors of Horn Theories

Kaz Makino

 

abstract:

In this paper, we investigate the deductive inference

for the interiors and exteriors of Horn knowledge bases,

where the interiors and exteriors were introduced by Makino and Ibaraki

\cite{interior} to study stability properties of knowledge bases.

We present a linear time algorithm for the deduction for the interiors and

show that it is co-NP-complete for the deduction for  the exteriors.

Under model-based representation, we show that the deduction problem

for interiors is NP-complete while the one for exteriors is co-NP-complete.

As for Horn envelopes of the exteriors, we show that it is linearly solvable

under model-based representation, while it is co-NP-complete under formula-based

representation. We also discuss the polynomially solvable cases

for all the intractable problems.

 

This is a joint work with Hirotaka Ono (Kyusyu University).