Fauconnier (1975a) noticed that existential quantification, if it is related to a scale endpoint, can force entailment along the scale and as such have the effect of universal quantification: assume a partially ordered set (X, ) and a predicate φ such that for all x, y X, x y, if φ is true of x, it is also true of y; then if there exists an element z that is ordered before all other elements an...

This article studies the monotonicity behavior of plural determiners that quantify over collections. Following previous work, we describe the collective interpretation of determiners such as all, some and most using generalized quantifiers of a higher type that are obtained systematically by applying a type shifting operator to the standard meanings of determiners in Generalized Quantifier Theo...

We begin with a definition Definition 1. A one-parameter family T (t) for 0 ≤ t < ∞ of bounded linear operators on a Banach space X is a C 0 (or strongly continuous) Semigroup on X if 1. T (0) = I (the identity on X). 2. T (t + s) = T (t)T (s) (semigroup property) 3. lim t↓0 T (t)v = v for all v ∈ X (This the Strong Continuity at t = 0, i.e., continuous at t = 0 in the strong operator topology)...

We show that the continuous existential quantifier ∃ω is not definable in Escardó’s Real-PCF from all functionals equivalent to a given total one in a uniform way. We further prove that relative to any total functional of type (I → I) → I which gives the maximum-value for any total input, we may, given a computable, total functional Φ of type (R → R) → R find a Real-PCF definable total Ψ equiva...

To Hehzut Hasse on his 6~. birthday Let f(a) be a holomorphic. function in the open unit disk D in the complex plane. (b) given any 8 > 0, there exists an n, = no(&) suc,h that, for every IL > rtO, J, lies in the region 1-E < 1 z 1 < 1. Set p!c, = p$ I f(z) I If lim pu, = 00, then we call f, for brevity, an annular function.-CO As is evident from this definition, an annular fun&ion f is not ide...

This paper argues that exhaustification is empirically and theoretically important as a tool in the semantic description of various constructions in natural language. Discussion focuses on the comparative construction, and presents a view of exhaustification as a ‘control element’ that influences the interpretation of a more basic element: the existential quantifier.

We propose a technique for specifying universal quantification and existential quantification (combined with negation) in a two-dimensional (graphical) database query language. Unlike other approaches that provide set operators to simulate universal quantification, this technique allows a direct representation of universal quantification. We present syntactic constructs for specifying universal...

The hydroxyl radical (OH•) is a powerful oxidant produced as a consequence of cavitation in water. It can react nonspecifically in breaking down persistent organic pollutants in water into their mineral form. It can also recombine to form hydrogen peroxide which is very useful in water treatment. In this study, terephthalic acid (TA) and potassium iodide dosimetry were used to quantify and inve...

20.2 Applications of quantification 20.4 20.3 Issues to consider in quantification 20.5 Preparing an action plan for quantification • Using centralized or decentralized quantification • Using manual or computerized methods for quantification • Estimating the time required • Developing and organizing the medicines list • Filling the supply pipeline • Estimating the procurement period • Consideri...