Harmony-seeking computations, as proposed by Christopher Alexander, offer a way to tackle complexity. Smart, free agents, facing uncertainty, look for order in context powered fifteen attractors, or patterns. would then be relatively guided path across those idealized patterns, towards wholeness and beauty. However, individuals acting change the city must combine circumstances imposed external ...

A fragment of se ond-order lambda al ulus (System F) is de ned that hara terizes the elementary re ursive fun tions. Type quanti ation is restri ted to be non-interleaved and strati ed, i.e., the types are assigned levels, and a quanti ed variable an only be instantiated by a type of smaller level, with a slightly liberalized treatment of the level zero.

We give a survey of three implemented real quantiier elimination methods: partial cylindrical algebraic decomposition, virtual substitution of test terms, and a combination of Grr obner basis computations with multivariate real root counting. We examine the scope of these implementations for applications in various elds of science, engineering, and economics.

Most studies of the so-called Proportion Problem seek to understand how lexical and structural properties of sentences containing adverbial quanti ers give rise to various proportional readings. This paper explores a related but distinct problem: given a use of a particular sentence in context, why do only some of the expected proportional readings seem to be available? That is, why do some sen...

Various logical languages are compared regarding their expressive power with respect to models consisting of nitely bounded branching in nite trees The basic multimodal logic with backward and forward necessity operators is equivalent to restricted rst order logic by adding the binary temporal operators since and until we get the expressive power of rst order logic on trees Hence restricted pro...

This paper summarizes a mathematical model for characterizing hysteresis in ferroelectric materials. The model is based on the quanti cation of energy required to bend and translate domain walls and is developed in two steps. In the rst, the underlying anhysteretic polarization is quanti ed through constitutive equations derived using Boltzmann statistics. Three anhysteretic models are consider...

Quanti®ed statements are used in the resolution of a great variety of problems. Several methods have been proposed to evaluate statements of types I and II. The objective of this paper is to study these methods, by comparing and generalizing them. In order to do so, we propose a set of properties that must be ful®lled by any method of evaluation of quanti®ed statements, we discuss some existing...

In dynamic semantics three styles of quanti cation have been proposed that can be seen to involve two di erent ways of interpreting free and quanti ed variables: Variables as denoting single partial objects; Variables as ranging over a number of alternative total objects. I will show that the rst view leads to problems of underspeci cation and the second to problems of overspeci cation. I will ...

A combinatorial criterium is given when a monadic quantiier is expressible by means of universe-independent monadic quantiiers of width n. It is proved that the corresponding hierarchy does not collapse. As an application, it is shown that the second resumption (or vectorization) of the HH artig quantiier is not deenable by monadic quantiiers. The techniques rely on Ramsey theory.

While numerous extensions of Cardelli and Wegner's calculus of polymorphism and subtyping, Kernel Fun, have been studied during the past decade, one quite simple one has received little attention: the addition of a minimal type Bot, dual to the familiar maximal type Top. We develop basic meta-theory for this extension. Although most of the usual properties of Kernel Fun (existence of meets and ...