Arithmetic, first-order logic, and counting quantifiers

Two-Variable First Order Logic with Counting Quantifiers: Complexity Results

Etessami, Vardi and Wilke [5] showed that satisfiability of two-variable first order logic FO[<] on word models is Nexptime-complete. We extend this upper bound to the slightly stronger logic FO[<, succ,≡], which allows checking whether a word position is congruent to r modulo q, for some divisor q and remainder r. If we allow the more powerful modulo counting quantifiers of Straubing, Thérien ...

Characterizing Second Order Logic with First Order Quantifiers

First order quantifiers in~monadic second order logic

This paper studies the expressive power that an extra first order quantifier adds to a fragment of monadic second order logic, extending the toolkit of Janin and Marcinkowski [JM01]. We introduce an operation existsn(S) on properties S that says “there are n components having S”. We use this operation to show that under natural strictness conditions, adding a first order quantifier word u to th...

On the Role of Ramsey Quantifiers in First Order Arithmetic

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Decidable first-order modal logics with counting quantifiers

In this paper, we examine the computational complexity of various natural onevariable fragments of first-order modal logics with the addition of arbitrary counting quantifiers. The addition of counting quantifiers provides us a rich language with which to succinctly express statements about the quantity of objects satisfying a given property, using only a single variable. We provide optimal upp...