利用Tableau确定具有全角色否定和全角色同一的描述逻辑
Using Tableau to Decide Description Logics with Full Role Negation and Identity
摘要：
本文提出了一种确定具有完全角色否定和角色恒等式的表达性描述逻辑的表方法。我们考虑的描述逻辑ALBOid，这是扩展的ALC与布尔角色操作符，逆的角色，身份的角色，并包括完全支持个人和单例概念。ALBOid在表达上等价于一阶逻辑的两变量片段，并包含布尔模态逻辑。在本文中，我们定义了一个健全的和完整的表演算的ALBOid，提供了一个基础，决策程序的逻辑及其所有的子逻辑。我们的方法的一个重要的新颖性是使用一个通用的无限制的阻塞机制。基于概念上简单的规则，无限制分块执行两个个体是否相等的情况区分和等式推理以找到有限模型。阻塞机制将Tableau导子的终止性证明与ALBOid的有限模型性质联系起来。
英文摘要：
This paper presents a tableau approach for deciding expressive description logics with full role negation and role identity. We consider the description logic ALBOid, which is the extension of ALC with the Boolean role operators, inverse of roles, the identity role, and includes full support for individuals and singleton concepts. ALBOid is expressively equivalent to the two-variable fragment of first-order logic with equality and subsumes Boolean modal logic. In this paper we define a sound and complete tableau calculus for the ALBOid that provides a basis for decision procedures for this logic and all its sublogics. An important novelty of our approach is the use of a generic unrestricted blocking mechanism. Being based on a conceptually simple rule, unrestricted blocking performs case distinctions over whether two individuals are equal or not and equality reasoning to find finite models. The blocking mechanism ties the proof of termination of tableau derivations to the finite model property of ALBOid.
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