Abstract

We prove that the satisfiability problem for C² is decidable. C² is first-order logic with only two variables in the presence of arbitrary counting quantifiers 9 ?m , m ? 1. It considerably extends L², plain first-order with only two variables, which is known to be decidable by a result of Mortimer. Unlike L², C² does not have the finite model property. As C² extends L² by expressive means for counting, significant applications arise from the fact that C² embeds corresponding counting extensions of modal logics.

Citations