Some applications of logic to feasibility in higher types

In this paper we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalize the corresponding properties of the class of feasible functions. We also improve the Kapron - Cook result on mashine representation of basic feasible functionals. Our proofs are based on essential applications of logic. We introduce a weak fragment of second order arithmetic with second order variables ranging over functions from N into N which suitably characterizes basic feasible functionals, and show that it is a useful tool for investigating the properties of basic feasible functionals. In particular, we provide an example how one can extract feasible "programs" from mathematical proofs which use non-feasible functionals (like second order polynomials)

Knowledge Management Systems in Museums: the Next Generation for Assimilating Museum Information Resources in an Electronic Environment

This thesis focuses on knowledge management practices, tools, and systems and how it can play a vital role for managing collections in museums. The purpose of knowledge management would be to control information across disparate collections and departments within museums. The process of gathering. collecting and storing various data will help institutions achieve cost-effective solutions for a successful information management system. Implementing the concept and applications of knowledge management would create a culture that would encourage knowledge sharing among curators, registrars, directors of development and exhibition designers, to name a few. Further, it would establish museum-wide shared resources that would be available in one relational database for all to access, navigate, and contribute. However, facilitating this new museological concept presents many challenges and barriers. Advancements are being made through the development of knowledge tools, standards and other forms of technology. Overall, knowledge management would be beneficial in supporting the integration of museum informational resources (i.e, exhibition catalogs, press releases, memberships) in an electronic environment

Characterising polynomial time computable functions using theories with weak set existence principles

AbstractSeveral authors have independently introduced second order theories whose provably total functionals are polynomial time computable functions on strings (e.g. [4], [6] and [7]), including the first author ([3], meant to be the second part of [2]). In this paper we give a detailed proof of the bi-interpretability result between such a second order theory and Buss' first order bounded arithmetic, based on an elegant definition of multiplication due to the second author