Steve Vickers Department of Computing, Imperial College 180...  Home/Search
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Abstract: We present an introduction to geometric logic and the mathematical structures associated with it, such as categorical logic and toposes. We also describe some of its applications in computer science including its potential as a logic for specification languages. (Update)
Context of citations to this paper: More
...are preserved by the inverse image functors of geometric morphisms. We shall actually use a different language, analogous to that of [18, 20], that makes a systematic distinction between toposes as generalized topological spaces for which we reserve the word topos...
...discussed briefly in connection with schema connectives, and with specifying and implementing operations. 1 Introduction In Vickers [10, 9] it was suggested rather briefly that an observational content of geometric logic made it a good candidate as a logic appropriate to...
Cited by: More
Geometric Theories and Modal Logic in the Calculus of Structures - Hein (2005) (Correct)
Purity through Unravelling - Hein, Stewart (2005) (Correct)
Geometric Logic As A Specification Language - Vickers (Correct)
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0.3: Toposes Pour Les Vraiment Nuls - Vickers (1996) (Correct)
0.3: Localic Completion Of Quasimetric Spaces - Vickers (1997) (Correct)
0.3: Locales Are Not Pointless - Vickers (1994) (Correct)
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5: Topology via Logic (context) - Vickers - 1989
3: Cambridge University Press (context) - Johnstone - 1982
2: URL: http://iccl (context) - Guglielmi, Manuscript - 2004
BibTeX entry: (Update)
S. Vickers. Geometric logic in computer science. In G. Burn, S. Gay, and M. Ryan, editors, Theory and Formal Methods 1993, pages 37--54. Springer-Verlag, 1993. This article was processed using the L a T E X macro package with LLNCS style http://citeseer.ist.psu.edu/vickers93geometric.html More
@inproceedings{ vickers93geometric,
author = "Steven Vickers",
title = "Geometric Logic in Computer Science",
booktitle = "Theory and Formal Methods 1993",
publisher = "Springer-Verlag",
editor = "Geoff Burn and Simon Gay and Mark Ryan",
pages = "37--54",
year = "1993",
url = "citeseer.ist.psu.edu/vickers93geometric.html" }
Citations (may not include all citations):359 Introduction to Higher Order Categorical Logic (context) - Lambek, Scott - 1986
83 Topos theory (context) - Johnstone - 1977
73 Topology via Logic (context) - Vickers - 1989
53 Cambridge University Press (context) - Johnstone, Spaces - 1982
25 First Order Categorical Logic (context) - Makkai, Reyes - 1977
10 Geometric theories and databases (context) - Vickers
5 Another Semantics for Z (context) - Hodges
5 bagdomains and hyperlocal toposes (context) - Johnstone, products
3 Topical categories of domains - Vickers
1 in Annals of Pure and Applied Logic vol (context) - Abramsky, in et al. - 1991
1 London Mathematical Society Lecture Note Series vol (context) - Fourman, Johnstoneand et al. - 1992
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://theory.doc.ic.ac.uk/~sjv/): More
Topology via Constructive Logic - Vickers (1999) (Correct)
Localic Completion Of Quasimetric Spaces - Vickers (1997) (Correct)
Locales Are Not Pointless - Vickers (1994) (Correct)
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