关于槽状语言的齐次模型
On Homogeneous Model of Fluted Languages
AI总结：
本文研究一阶逻辑的槽状片段，证明其可满足句子存在全局/局部齐次模型，据此简化带计数量词的槽状逻辑分析方法，确定带周期计数的槽状片段（有限）可满足性问题为TOWER完全，两变量时为NEXPTIME完全，并补充了槽状逻辑推广的复杂度结果。
摘要：
我们研究一阶逻辑的槽状片段，该片段常被视为缺乏角色逆的各种描述逻辑系统的多变量非受护扩展。本文表明，可满足的槽状句子（即使在合理扩展下）允许存在特殊类型的“良好”模型，我们称之为全局/局部齐次模型。齐次模型使我们能够简化分析带计数量词的槽状逻辑的方法，并为带周期计数的槽状片段的（有限）可满足性问题的可判定性建立新结果。更具体地说，我们将证明该语言的（有限）可满足性问题是TOWER完全的。若仅使用两个变量，计算复杂度降至NEXPTIME完全。我们通过证明槽状逻辑的推广（如相邻片段）的有限和一般可满足性问题分别是Π¹₀完全和Σ¹₀完全的，来补充研究结果。此外，若允许周期计数量词，可满足性变为Σ¹₁完全的。
英文摘要：
We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even under reasonable extensions) admit special kinds of ``nice'' models which we call globally/locally homogeneous. Homogeneous models allow us to simplify methods for analysing fluted logics with counting quantifiers and establish a novel result for the decidability of the (finite) satisfiability problem for the fluted fragment with periodic counting. More specifically, we will show that the (finite) satisfiability problem for the language is ${\rm T{\small OWER}}$-complete. If only two variable are used, computational complexity drops to ${\rm NE{\small XP}T{\small IME}}$-completeness. We supplement our findings by showing that generalisations of fluted logics, such as the adjacent fragment, have finite and general satisfiability problems which are, respectively, $Π^0_1$- and $Σ^0_1$-complete. Additionally, satisfiability becomes $Σ^1_1$-complete if periodic counting quantifiers are permitted.
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