Dynamics of Belief: Horn Knowledge Base and Database Updates

Abstract

The dynamics of belief and knowledge is one of the major components of any autonomous system that should be able to incorporate new pieces of information. In order to apply the rationality result of belief dynamics theory to various practical problems, it should be generalized in two respects: first it should allow a certain part of belief to be declared as immutable; and second, the belief state need not be deductively closed. Such a generalization of belief dynamics, referred to as base dynamics, is presented in this paper, along with the concept of a generalized revision algorithm for knowledge bases (Horn or Horn logic with stratified negation). We show that knowledge base dynamics has an interesting connection with kernel change via hitting set and abduction. In this paper, we show how techniques from disjunctive logic programming can be used for efficient (deductive) database updates. The key idea is to transform the given database together with the update request into a disjunctive (datalog) logic program and apply disjunctive techniques (such as minimal model reasoning) to solve the original update problem. The approach extends and integrates standard techniques for efficient query answering and integrity checking. The generation of a hitting set is carried out through a hyper tableaux calculus and magic set that is focused on the goal of minimality. The present paper provides a comparative study of view update algorithms in rational approach. For, understand the basic concepts with abduction, we provide an abductive framework for knowledge base dynamics. Finally, we demonstrate how belief base dynamics can provide an axiomatic characterization for insertion a view atom to the database. We give a quick overview of the main operators for belief change, in particular, belief update versus database update. Definition 1 (Horn Knowledge Base). A Horn knowledge base, KB is a finite set of Horn formulae from languageHorn knowledge base change deals with situations in which an agent has to modify its beliefs about the world, usually due to new or previously unknown 1 There are two major interpretations of belief bases. One of them, supported by Dalal 1998, uses belief bases as mere expressive devices; hence if Cn(B1) = Cn(B2) then Proof. Follows from the observation and the result of Konieczny 2011. Definition 8 ([3]). Let M=(W.w) be a K-model and µ a formula. A k-model M = (W , w ) is called a possible resulting k-model after updating M with µ if and only if the following conditions hold: 1. M'|= µ; 2. there does not exist another k-model M = (W , w ) such that M |= µ and M < M M .