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Full completeness of the multiplicative linear logic of chu spaces
 Proc. IEEE Logic in Computer Science 14
, 1999
"... We prove full completeness of multiplicative linear logic (MLL) without MIX under the Chu interpretation. In particular we show that the cutfree proofs of MLL theorems are in a natural bijection with the binary logical transformations of the corresponding operations on the category of Chu spaces on ..."
Abstract

Cited by 22 (8 self)
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We prove full completeness of multiplicative linear logic (MLL) without MIX under the Chu interpretation. In particular we show that the cutfree proofs of MLL theorems are in a natural bijection with the binary logical transformations of the corresponding operations on the category of Chu spaces on a twoletter alphabet. This is the online version of the paper of the same title appearing in the LICSâ€™99 proceedings. 1
Towards Semantics of SelfAdaptive Software
, 2000
"... When people perform computations, they routinely monitor their results, and try to adapt and improve their algorithms when a need arises. The idea of selfadaptive software is to implement this common facility of human mind within the framework of the standard logical methods of software engineering ..."
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Cited by 7 (0 self)
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When people perform computations, they routinely monitor their results, and try to adapt and improve their algorithms when a need arises. The idea of selfadaptive software is to implement this common facility of human mind within the framework of the standard logical methods of software engineering. The ubiquitous practice of testing, debugging and improving programs at the design time should be automated, and established as a continuing run time routine. Technically, the task thus requires combining functionalities of automated software development tools and of runtime environments. Such combinations lead not just to challenging engineering problems, but also to novel theoretical questions. Formal methods are needed, and the standard techniques do not suffice. As a first contribution in this direction, we present a basic mathematical framework suitable for describing selfadaptive software at a high level of semantical abstraction. A static view leads to a structure akin...
Physical Systems
, 2009
"... We revisit our earlier work on the representation of quantum systems as Chu spaces, and investigate the use of coalgebra as an alternative framework. On the one hand, coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimu ..."
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We revisit our earlier work on the representation of quantum systems as Chu spaces, and investigate the use of coalgebra as an alternative framework. On the one hand, coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimulation and coalgebraic logic. However, the standard coalgebraic framework does not accommodate contravariance, and is too rigid to allow physical symmetries to be represented. We introduce a fibrational structure on coalgebras in which contravariance is represented by indexing. We use this structure to give a universal semantics for quantum systems based on a final coalgebra construction. We characterize equality in this semantics as projective equivalence. We also define an analogous indexed structure for Chu spaces, and use this to obtain a novel categorical description of the category of Chu spaces. We use the indexed structures of Chu spaces and coalgebras over a common base to define a truncation functor from coalgebras to Chu spaces. This truncation functor is used to lift the full and faithful representation of the groupoid of physical symmetries on Hilbert spaces into Chu spaces, obtained in our previous work, to the coalgebraic semantics. 1