机器级与结构级的可表达性：ESO通用Horn逻辑和P类
Expressibility at the machine level versus structure level: ESO universal Horn Logic and the class P
摘要：
我们表明，ESO通用霍恩逻辑（存在的第二逻辑，其中第一阶部分是一个通用的霍恩公式）是不足以捕捉P，一类问题的决定在多项式时间。在输入词汇表中存在后继关系时，此语句为真。我们提供了两个证明-一个基于两个结构的约化积，另一个基于可逼近性理论（第二个证明是在假设P与NP不相同的情况下）。我们表明，这里的结果与Grädel（1991）中的结果之间的差异是由于本文处理的表达式是在“结构层面”，而Grädel（1991）中的表达式是在“机器层面”-一个比说的更容易的例子。
英文摘要：
We show that ESO universal Horn logic (existential second logic where the first order part is a universal Horn formula) is insufficient to capture P, the class of problems decidable in polynomial time. This statement is true in the presence of a successor relation in the input vocabulary. We provide two proofs --- one based on reduced products of two structures, and another based on approximability theory (the second proof is under the assumption that P is not the same as NP). We show that the difference between the results here and those in Grädel (1991), is due to the fact that the expressions this paper deals with are at the "structure level", whereas the expressions in Grädel (1991) are at the "machine level" --- a case of Easier done than said.
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