Local Realizability Toposes and a Modal Logic for Computability (Extended Abstracts) (1999)
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| Venue: | Presented at Tutorial Workshop on Realizability Semantics, FLoC'99 |
| Citations: | 21 - 6 self |
BibTeX
@INPROCEEDINGS{Awodey99localrealizability,
author = {Stephen Awodey and Lars Birkedal and Dana S. Scott},
title = {Local Realizability Toposes and a Modal Logic for Computability (Extended Abstracts)},
booktitle = {Presented at Tutorial Workshop on Realizability Semantics, FLoC'99},
year = {1999},
publisher = {Elsevier}
}
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Abstract
) Steven Awodey 1 Lars Birkedal 2y Dana S. Scott 2z 1 Department of Philosophy, Carnegie Mellon University 2 School of Computer Science, Carnegie Mellon University April 15, 1999 Abstract This work is a step toward developing a logic for types and computation that includes both the usual spaces of mathematics and constructions and spaces from logic and domain theory. Using realizability, we investigate a configuration of three toposes, which we regard as describing a notion of relative computability. Attention is focussed on a certain local map of toposes, which we study first axiomatically, and then by deriving a modal calculus as its internal logic. The resulting framework is intended as a setting for the logical and categorical study of relative computability. 1 Introduction We report here on the current status of research on the Logic of Types and Computation at Carnegie Mellon University [SAB + ]. The general goal of this research program is to develop a logical fra...
