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From proof nets to the free * autonomous category
 Logical Methods in Computer Science, 2(4:3):1–44, 2006. Available from: http://arxiv.org/abs/cs/0605054. [McK05] Richard McKinley. Classical categories and deep inference. In Structures and Deduction 2005 (Satellite Workshop of ICALP’05
, 2005
"... Vol. 2 (4:3) 2006, pp. 1–44 www.lmcsonline.org ..."
Chu Spaces as a Semantic Bridge Between Linear Logic and Mathematics
 Theoretical Computer Science
, 1998
"... The motivating role of linear logic is as a "logic behind logic." We propose a sibling role for it as a logic of transformational mathematics via the selfdual category of Chu spaces, a generalization of topological spaces. These create a bridge between linear logic and mathematics by soundly interp ..."
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Cited by 12 (2 self)
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The motivating role of linear logic is as a "logic behind logic." We propose a sibling role for it as a logic of transformational mathematics via the selfdual category of Chu spaces, a generalization of topological spaces. These create a bridge between linear logic and mathematics by soundly interpreting linear logic while fully and concretely embedding a comprehensive range of concrete categories of mathematics. Our main goal is to treat each end of this bridge in expository detail. In addition we introduce the dialectic lambdacalculus, and show that dinaturality semantics is not fully complete for the Chu interpretation of linear logic. 1 Introduction Linear logic was introduced by J.Y. Girard as a "logic behind logic." It separates logical reasoning into a core linear part in which formulas are merely moved around, and an auxiliary nonlinear part in which formulas may be deleted and copied. The core, multiplicative linear logic (MLL), is a substructural logic whose basic connect...
THE CHU CONSTRUCTION
, 1996
"... We take another look at the Chu construction and show how to simplify it by looking at ..."
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Cited by 12 (1 self)
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We take another look at the Chu construction and show how to simplify it by looking at
Chu Spaces From the Representational Viewpoint
 Ann. Pure Appl. Logic
, 1998
"... We give an elementary introduction to Chu spaces viewed as a set of strings all of the same length. This perspective dualizes the alternative view of Chu spaces as generalized topological spaces, and has the advantage of substituting the intuitions of formal language theory for those of topology. 1 ..."
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Cited by 8 (0 self)
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We give an elementary introduction to Chu spaces viewed as a set of strings all of the same length. This perspective dualizes the alternative view of Chu spaces as generalized topological spaces, and has the advantage of substituting the intuitions of formal language theory for those of topology. 1 Background Chu spaces provide a simple, uniform, and wellstructured approach to the representation of objects that may possess algebraic, relational, or other structure, and that can transform into one another in ways that respect that structure. Chu spaces are simple by virtue of being merely a rectangular array, with no further machinery. They are uniform in the sense that all transformable objects, whether sets, groups, Boolean algebras, vector spaces, or manifolds, are representable by Chu spaces within the same framework, and hence can coexist in a single typeless universe of mathematical objects. And they are wellstructured in that this seemingly featureless universe in fact has a na...
Types as Processes, via Chu spaces
 EXRESS'97 Proceedings
, 1997
"... We match up types and processes by putting values in correspondence with events, coproduct with (noninteracting) parallel composition, and tensor product with orthocurrence. We then bring types and processes into closer correspondence by broadening and unifying the semantics of both using Chu spaces ..."
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Cited by 2 (0 self)
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We match up types and processes by putting values in correspondence with events, coproduct with (noninteracting) parallel composition, and tensor product with orthocurrence. We then bring types and processes into closer correspondence by broadening and unifying the semantics of both using Chu spaces and their transformational logic. Beyond this point the connection appears to break down; we pose the question of whether the failures of the corrrespondence are intrinsic or cultural. 1 Introduction Typesasprocesses modernizes dataasprograms. It is the CurryHoward propositionsastypes correspondence with propositions replaced by processes. To the extent that types and processes are both part of the working programmer 's toolkit, even more than propositions, the typesasprocesses correspondence is more central to the practice of programming than propositionsastypes. Moreover the connection works out very well mathematically, at least up to a point. The similarities and differences ...
Dedicated to the memory of Heinrich Kleisli, 1930–2011.
"... Abstract. In [Barr & Kleisli 2001] we described ⋆autonomous structures on two full subcategories of topological abelian groups. In this paper we do the same for sup semilattices except that uniform structures play the role that topology did in the earlier paper. 1. ..."
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Abstract. In [Barr & Kleisli 2001] we described ⋆autonomous structures on two full subcategories of topological abelian groups. In this paper we do the same for sup semilattices except that uniform structures play the role that topology did in the earlier paper. 1.