Dealing with context dependent knowledge has led to different formalizations of the notion of context. Among them is the Contextualized Knowledge Repository (CKR) framework, which is rooted in description logics but links on the reasoning side strongly to logic programs and Answer Set Programming (ASP) in particular. The CKR framework caters for reasoning with defeasible axioms and exceptions in contexts, which was extended to knowledge inheritance across contexts in a coverage (specificity) hierarchy. However, the approach supports only this single type of contextual relation and the reasoning procedures work only for restricted hierarchies, due to non-trivial issues with model preference under exceptions. In this paper, we overcome these limitations and present a generalization of CKR hierarchies to multiple contextual relations, along with their interpretation of defeasible axioms and preference. To support reasoning, we use ASP with algebraic measures, which is a recent extension of ASP with weighted formulas over semirings that allows one to associate quantities with interpretations depending on the truth values of propositional atoms. Notably, we show that for a relevant fragment of CKR hierarchies with multiple contextual relations, query answering can be realized with the popular asprin framework. The algebraic measures approach is more powerful and enables e.g. reasoning with epistemic queries over CKRs, which opens interesting perspectives for the use of quantitative ASP extensions in other applications. Under consideration for acceptance in Theory and Practice of Logic Programming (TPLP).
翻译:与背景相关知识的处理导致上下文概念的不同形式化,其中之一是背景化知识存储库(CKR)框架(CKR)框架,其根基是描述逻辑,但将逻辑方面的推理与逻辑程序和答案设定程序(ASP)特别地联系起来。CKR框架在背景中采用推理,其推理与不可行的轴和例外,其范围(具体性)等级扩大到跨背景的知识继承。不过,该方法仅支持单一类型的开放背景关系和推理程序,仅用于有限的等级结构,因为非三角问题和模式性应用有例外。在本文件中,我们克服了这些局限性,并将CKSR的分级结构与多背景关系加以概括化。为了支持推理,我们使用ASP与代数衡量措施,这是ASP的近期扩展公式,允许将数量与解释联系起来,这取决于Putal-Roms的真理值,而模式适用有例外。在本文中,我们克服了这些限制,CKRR的分级分级结构,我们用C级的分级的分级的分级的分数法,用来解释。