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Abstract: We give a uniform representation of the objects of mathematical practice as Chu spaces, forming a concrete self-dual bicomplete closed category and hence a constructive model of linear logic. This representation distributes mathematics over a two-dimensional space we call the Stone gamut. The Stone gamut is coordinatized horizontally by coherence, ranging from \Gamma1 for sets to 1 for complete atomic Boolean algebras (CABA's), and vertically by complexity of language. Complexity 0 contains... (Update)
Context of citations to this paper: More
.... category first studied by Barr and Chu [Bar79] which has found applications elsewhere in proof theory, game theory, and Stone duality [Pra95] Chu spaces are the subject of Vaughan Pratt s position statement, accessible by http: boole.stanford.edu stmt.html. 3.3 Design and...
...an object x and a (not completely known) measuring device y. Such a function describes a so called Chu space (see, e.g. [1, 2, 7, 8, 20, 21, 22, 23, 24, 25, 26]) 1.3 Precise Definition of a Chu Space To be more precise, to define a Chu space, we must fix a set K (of possible...
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BibTeX entry: (Update)
V.R. Pratt (1995), The Stone Gamut: A Coordinatization of Mathematics. In Proceedings of the conference Logic in Computer Science IEEE Computer Society. http://citeseer.ist.psu.edu/pratt95stone.html More
@inproceedings{ pratt95stone,
author = "Vaughan R. Pratt",
title = "The Stone Gamut: {A} Coordinatization of Mathematics",
booktitle = "Tenth Annual Symposium on Logic in Computer Science",
publisher = "IEEE Computer Society",
address = "San Diego, California",
pages = "444--454",
year = "1995",
url = "citeseer.ist.psu.edu/pratt95stone.html" }
Citations (may not include all citations):982 Theoretical Computer Science (context) - Girard - 1987
248 The mathematics of sentence structure (context) - Lambek - 1958
126 Cambridge University Press (context) - Johnstone - 1982
43 Games semantics for linear logic (context) - Lafont, Streicher - 1991
39 The theory of representations for Boolean algebras (context) - Stone - 1936
37 Action logic and pure induction - Pratt - 1990
36 Chu Spaces: A Model of Concurrency - Gupta - 1994
34 A categorical linear framework for Petri nets (context) - Brown, Gurr - 1990
31 Gates accept concurrent behavior - Gupta, Pratt - 1993
28 Autonomous categories (context) - Barr - 1979
27 Configuration structures - Van Glabbeek, Plotkin - 1995
26 The second calculus of binary relations - Pratt - 1993
19 Atomless parts of spaces (context) - Isbell - 1972
16 Event spaces and their linear logic - Pratt - 1992
14 A dialectica-like model of linear logic (context) - de Paiva - 1989
13 The duality of time and information - Pratt - 1992
12 Math Structures in Comp (context) - Barr, categories et al. - 1991
9 Concurrent Kripke structures - Gupta - 1993
8 Rational mechanics and natural mathematics - Pratt - 1995
7 How comprehensive is the category of semigroups (context) - Hedrl'in, Lambek - 1969
7 Algebraic and Topological Representations of Groups (context) - Pultr, Trnkov'a - 1980
4 An adjoint characterization of the category of sets - Rosebrugh, Wood - 1994
2 The chu construction and cofree models of linear logic (context) - Pavlovi'c - 1993
2 A categorytheoretical approach to hypergraphs (context) - Dorfler, Waller - 1980
2 and constructivity (context) - Pratt, linear - 1992
The graph only includes citing articles where the year of publication is known.
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