One-variable logic meets Presburger arithmetic

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 Image 1 -completeness of the logic by presenting an optimal algorithm for solving its finite satisfiability problem.

Authors

• Bartosz Bednarczyk

Keywords

• Finite satisfiability
• Computational complexity
• Decidability
• Classical decision problem
• Arithmetics