We consider the extension of two-variable guarded fragment logic with local Presburger quantifiers. These are quantifiers that can express properties such as ``the number of incoming blue edges plus twice the number of outgoing red edges is at most three times the number of incoming green edges'' and captures various description logics with counting, but without constant symbols. We show that the satisfiability of this logic is EXP-complete. While the lower bound already holds for the standard two-variable guarded fragment logic, the upper bound is established by a novel, yet simple deterministic graph theoretic based algorithm.

翻译：我们考虑在二变量保护片段逻辑中扩展局部Presburger量词。这些量词能够表达诸如“入蓝边的数量加上两倍的出红边数量最多是三倍的入绿边数量”等性质，并捕捉了各种带有计数但无常数符号的描述逻辑。我们证明该逻辑的可满足性是EXP完全的。下界已经适用于标准的二变量保护片段逻辑，而上界则通过一种新颖且简单的基于确定性图论算法得以建立。