Deductive Inference for the Interiors and Exteriors of Horn Theories

TL;DR

This paper explores the computational complexity of deductive inference for the interiors and exteriors of Horn knowledge bases, providing algorithms and complexity results for different representations and cases.

Contribution

It introduces a linear time algorithm for interior deduction and characterizes the complexity of exterior deduction in Horn theories, including various representations.

Findings

Linear time algorithm for interior deduction

Exterior deduction is co-NP-complete under formula-based representation

Horn envelope deduction is linearly solvable under model-based representation

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 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.