We consider the one-variable fragment of first-order logic extended with Presburger constraints. The logic is designed in such a way that it subsumes the previously-known fragments extended with counting, modulo counting or cardinality comparison and combines their expressive powers. We prove NP-completeness of the logic by presenting an optimal algorithm for solving its finite satisfiability problem.
翻译:我们认为第一阶逻辑的一成不变的片段随普雷斯堡的限制而延伸。 逻辑的设计方式是将先前已知的片段以计数、摩杜罗计数或基点比较来进行,并结合其表达力。 我们通过提出解决其有限相对性问题的最佳算法来证明逻辑的完整性。