This paper presents three explanations of why Frege took the universal, rather than existential, quantifier as primitive in his formalization logic. The first two provide technical reasons related to how formalizes logic truth-functions and quantification. third, philosophical explanation locates reason Frege's logicist goal analyzing arithmetical concepts---especially concepts 0 1---in purely ...

In Japanese a certain kind of phrase, which Kuroda (1965) calls "indetenninate", can function as a wh-phrase, existential quantifier or universal quantifier depending on context and the use of particles. I argue that "indetenninates" are contrastive-focused, and that the meanings of existential and universal quantifiers are made of (in)finite application of disjunction ("ka") and conjunction ("...

Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar fo...

This paper addresses the issue of Floating Quantifier phenomena in Hebrew, focusing on the case of the universal quantifier kol (‘all’) and proposes a new, non-derivational analysis in the LFG framework in which the floating and the non-floating quantifier constructions are treated separately. This is based on semantic evidence showing that the quantifiers in these constructions have non-identi...

We present the first complete problems for dynamic complexity classes including the classes Dyn-FO and Dyn-ThC , the dynamic classes corresponding to relational calculus and (polynomially bounded) SQL, respectively. The first problem we show complete for Dyn-FO is a singlestep version of the circuit value problem (SSCV). Of independent interest, our construction also produces a first-order form...

Quantified Boolean formulas (QBFs) generalize propositional formulas by admitting quantifications over propositional variables. QBFs can be viewed as (restricted) formulas of first-order predicate logic and easy translations of QBFs into first-order formulas exist. We analyze different translations and show that first-order resolution combined with such translations can polynomially simulate we...

Abstract The problem of invariant checking in parametric systems – which are required to operate correctly regardless the number and connections their components is gaining increasing importance various sectors, such as communication protocols control software. Such typically modeled using quantified formulae, describing behaviour an unbounded (identical) components, automatic verification ofte...

Convergent realists desire scientific methods that converge reliably to informative, true theories over a wide range of theoretical possibilities. Much attention has been paid to the problem of induction from quantifier-free data. In this paper, we employ the techniques of formal learning theory and model theory to explore the reliable inference of theories from data containing alternating quan...

where , the existential quantifier, denotes “there exists’’ and is the conjunction that denotes “and.’’ Notice that while both sides of the equivalence, , are in fact equivalent, the right hand side does not involve y, i.e., the variable y has been eliminated. In fact, the quantifier has been also eliminated; for this reason, the procedure is also called “quantifier elimination.’’ A serious def...