Reasoning about Evolving Nonmonotonic Knowledge Bases

TL;DR

This paper introduces a formal framework for reasoning about evolving nonmonotonic knowledge bases modeled as extended logic programs, analyzing their properties, semantics, and computational complexity.

Contribution

It provides a formal model and logical language for evolving knowledge bases, along with complexity and decidability results for various classes.

Findings

Finitary characterizations of knowledge base evolution.

Decidability results for specific framework classes.

Complexity analysis ranging from polynomial to double exponential space.

Abstract

Recently, several approaches to updating knowledge bases modeled as extended logic programs have been introduced, ranging from basic methods to incorporate (sequences of) sets of rules into a logic program, to more elaborate methods which use an update policy for specifying how updates must be incorporated. In this paper, we introduce a framework for reasoning about evolving knowledge bases, which are represented as extended logic programs and maintained by an update policy. We first describe a formal model which captures various update approaches, and we define a logical language for expressing properties of evolving knowledge bases. We then investigate semantical and computational properties of our framework, where we focus on properties of knowledge states with respect to the canonical reasoning task of whether a given formula holds on a given evolving knowledge base. In particular, we present finitary characterizations of the evolution for certain classes of framework instances, which can be exploited for obtaining decidability results. In more detail, we characterize the complexity of reasoning for some meaningful classes of evolving knowledge bases, ranging from polynomial to double exponential space complexity.