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：我们考虑扩展二变量保护片段逻辑，引入局部Presburger量词。这些量词能够表达诸如“入站蓝边数量加上两倍出站红边数量不超过三倍入站绿边数量”之类的性质，并涵盖了多种带有计数功能但不含常元符号的描述逻辑。我们证明该逻辑的可满足性是EXP完全的。虽然下界已适用于标准的二变量保护片段逻辑，但上界是通过一种新颖且简单的基于确定性图论算法建立的。