Guards, Bounds, and Generalized Semantics
Guards, Bounds, and Generalized Semantics
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守卫、界限和广义语义
DOI：
10.1007/s10849-005-5786-y
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
J. Benthem
中科院分区：
文献类型：
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作者：
J. Benthem
守护片段的一些最初动机似乎仍然对进一步开展其计划感兴趣。首先，我们强调两个观点之间的等价性：（a）标准模型的可满足性的保护一阶公式，和（B）一般分配模型的可满足性的任意一阶公式。特别是，我们给出了一个新的直接减少从前者的概念，后者。我们还展示了如何视角转移到一般的分配模型提供了一个新的视角在一阶逻辑的定点扩展LFP（FO），使其可判定。接下来，我们将守护语法与早期的量词限制策略联系起来，以实现二阶逻辑中的有效公理化-指向具有“持久性”公式的类比，这些公式基本上是在许多排序的一阶逻辑的有界片段中。最后，我们看一些进一步的未探索的方向，包括系统地使用“准模型”本身作为一个语义。
Some initial motivations for the Guarded Fragment still seem of interest in carrying its program further. First, we stress the equivalence between two perspectives: (a) satisfiability on standard models for guarded first-order formulas, and (b) satisfiability on general assignment models for arbitrary first-order formulas. In particular, we give a new straightforward reduction from the former notion to the latter. We also show how a perspective shift to general assignment models provides a new look at the fixed-point extension LFP(FO) of first-order logic, making it decidable. Next, we relate guarded syntax to earlier quantifier restriction strategies for achieving effective axiomatizability in second-order logic – pointing at analogies with ‘persistent’ formulas, which are essentially in the Bounded Fragment of many-sorted first-order logic. Finally, we look at some further unexplored directions, including the systematic use of ‘quasi-models’ as a semantics by itself.