Beth Definability for the Guarded Fragment
Beth Definability for the Guarded Fragment
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Beth 受保护片段的可定义性
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
M. Otto
中科院分区：
文献类型：
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作者：
E. Hoogland;maarten marx;M. Otto
在[ABN98]中引入了Gueirded片段（GF），作为一阶逻辑的片段，将出色的表达能力与良好的模态行为结合在一起。它由一个关系的一阶公式组成，其Qucintiiiers以某种方式与原子相对。尽管在许多方面，GF HSI被确立为一阶逻辑的特别良好的片段，但插值限制在GF上失败了，[HM99]。在本文中，我们考虑了一阶逻辑的Beth属性，并表明，尽管插值失败，但仍限于GF。是关闭财产W.R.T.确定性，贝丝的属性在理论上和对于GF的典型潜在影响（例如，在描述逻辑的背景下）具有独立感兴趣。在这里，基于有限的插值形式建立了GF的BETH属性，该插值与通常以模态逻辑研究的插值属性更相似。从中，我们可以获得更具体地说的，即使是每个N-可保护的碎片，以及n-ary关系的最多具有贝丝的财产。
The gueirded fragment (GF) was introduced in [ABN98] as a fragment of first order logic which combines a great expressive power with nice modal behavior. It consists of relationeil first order formulas whose qucintiiiers are relativized by atoms in a certain way. While GF hsis been established as a particularly well-behaved fragment of first order logic in many respects, interpolation fails in restriction to GF, [HM99]. In this paper we consider the Beth property of first order logic and show that, despite the failure of interpolation, it is retained in restriction to GF. Being a closure property w.r.t. definability, the Beth property is of independent interest, both theoretically and for typical potential appUcations of GF, e.g., in the context of description logics. The Beth property for GF is here established on the basis of a limited form of interpolation, which more closely resembles the interpolation property that is usually studied in modal logics. From this we obtain that, more specifically, even every n-variable guarded fragment with up to n-ary relations has the Beth property.