Bibliography on Realizability

AbstractThis document is a bibliography on realizability and related matters. It has been collected by Lars Birkedal based on submissions from the participants in “A Workshop on Realizability Semantics and Its Applications”, Trento, Italy, June 30–July 1, 1999. It is available in BibTEX format at the following URL: http://www.cs.cmu.edu./~birkedal/realizability-bib.html

A Normalizing Intuitionistic Set Theory with Inaccessible Sets

We propose a set theory strong enough to interpret powerful type theories underlying proof assistants such as LEGO and also possibly Coq, which at the same time enables program extraction from its constructive proofs. For this purpose, we axiomatize an impredicative constructive version of Zermelo-Fraenkel set theory IZF with Replacement and $\omega$-many inaccessibles, which we call \izfio. Our axiomatization utilizes set terms, an inductive definition of inaccessible sets and the mutually recursive nature of equality and membership relations. It allows us to define a weakly-normalizing typed lambda calculus corresponding to proofs in \izfio according to the Curry-Howard isomorphism principle. We use realizability to prove the normalization theorem, which provides a basis for program extraction capability.Comment: To be published in Logical Methods in Computer Scienc

Emergence, Function and Realization

“Realization” and “emergence” are two concepts that are sometimes used to describe same or similar phenomena in philosophy of mind and the special sciences, where such phenomena involve the synchronic dependence of some higher-level states of affairs on the lower-level ones. According to a popular line of thought, higher-level properties that are invoked in the special sciences are realized by, and/or emergent from, lower-level, broadly physical, properties. So, these two concepts are taken to refer to relations between properties from different levels where the lower-level ones somehow “bring about” the higher-level ones. However, for those who specialise in inter-level relations, there are important differences between these two concepts – especially if emergence is understood as strong emergence. The purpose of this chapter is to highlight these differences

Emergence, Function and Realization

“Realization” and “emergence” are two concepts that are sometimes used to describe same or similar phenomena in philosophy of mind and the special sciences, where such phenomena involve the synchronic dependence of some higher-level states of affairs on the lower-level ones. According to a popular line of thought, higher-level properties that are invoked in the special sciences are realized by, and/or emergent from, lower-level, broadly physical, properties. So, these two concepts are taken to refer to relations between properties from different levels where the lower-level ones somehow “bring about” the higher-level ones. However, for those who specialise in inter-level relations, there are important differences between these two concepts – especially if emergence is understood as strong emergence. The purpose of this chapter is to highlight these differences

An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics

We revisit the Mittag-Leffler functions of a real variable $t$, with one, two and three order-parameters $\{\alpha, \beta, \gamma\}$, as far as their Laplace transform pairs and complete monotonicty properties are concerned. These functions, subjected to the requirement to be completely monotone for $t>0$, are shown to be suitable models for non--Debye relaxation phenomena in dielectrics including as particular cases the classical models referred to as Cole-Cole, Davidson-Cole and Havriliak-Negami. We show 3D plots of the response functions and of the corresponding spectral distributions, keeping fixed one of the three order-parameters.Comment: 22 pages, 6 figures, Second Revised Versio