Equating categorially names and quantifiers within first-order logic

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...

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 ...

Nominal Logic: A First Order Theory of Names and Binding

This paper formalises within first-order logic some common practices in computer science to do with representing and reasoning about syntactical structures involving lexically scoped binding constructs. It introduces Nominal Logic, a version of first-order many-sorted logic with equality containing primitives for renaming via name-swapping, for freshness of names, and for name-binding. Its axio...

First-order and Second-order Equity in Equating

iii Brennan Equity The notion of equity in equating was introduced by Lord (1980. pp. 195ff). The basic idea is that for any true score on Form Y, the distribution of observed scores on Form Y should be the same as the distribution of converted scores on Form X (see Kolen & Brennan, 2004. pp. 10–11). If this goal is achieved, Lord argued, then it should be a matter of indifference to each and e...