Merging First-Order Knowledge Using Dilation Operators

Abstract

The area of knowledge merging is concerned with merging conflicting information while preserving as much as possible. Most proposals in the literature work with knowledge bases expressed in propositional logic. We propose a new framework for merging knowledge bases expressed in (subsets of) first-order logic. Dilation operators (a concept originally introduced by Bloch and Lang) are employed and developed, and by combining them with the concept of comparison orderings we obtain a framework that is driven by model-based intuitions but that can be implemented in a syntax-based manner. We demonstrate specific dilation operators and comparison orderings for use in applications. We also show how postulates from the literature on knowledge merging translate into our framework and provide the conditions that dilation operators and comparison orderings must satisfy in order for the respective merging operators to satisfy the new postulates.

Belief Merging in Dynamic Logic of Propositional Assignments

“…There exist also tentatives to define merging operations in first order logic [6]. In the long run, we may plan to extend DL-PA with first order constructions in order to capture those merging operations.…”

A forgetting-based approach to merging knowledge bases

“…The aggregation of finite KBs into a collective one is studied by a recent discipline called belief merging (see [8], [2], [3]). A particular type of aggregation is called model-based merging.…”

“…As one of traditional ways of management, belief merging concerns with the problem of determining a group's beliefs from individual members' beliefs ( [2], [3]). The merging process from the point of logic is formalize as follows: let <I> = {CPl,···, CP n} be a group of KBs (which is composed of multiple formulae and can also be taken as conjunction of them from logic equivalence) where each logical formula CPi denotes a knowledge base(KB) from some information source.…”

Integração entre múltiplas ontologias: reúso e gerência de conflitos

“…Essa tarefaé dificultada quando lidamos com lógicas de primeira ordem, uma vez que axiomas simples podem possuir infinitos modelos. Assim, diversos autores como Gorogianis e Hunter [GH08], Qi et al [QLB06], Horridge [Hor11] e Kalyanpur [Kal06] propuseram estratégias baseadas em modificações de axiomas presentes em bases que estão sofrendo fusão para lidar com problemas de modelagem surgidos após a fusão de ontologias.…”

“…Gorogianis e Hunter, em [GH08], propõem uma estratégia de modificação iterativa através da substituição de quantificadores universais por existenciais. Eles aplicam essa ideia a lógica de predicados, e.g.…”