On Linear Information Systems

A. Bucciarelli
A. Carraro
T. Ehrhard
A. Salibra

Scott's information systems provide a categorically equivalent, intensional description of Scott domains and continuous functions. Following a well established pattern in denotational semantics, we define a linear version of information systems, providing a model of intuitionistic linear logic (a new-Seely category), with a "set-theoretic" interpretation of exponentials that recovers Scott continuous functions via the co-Kleisli construction. From a domain theoretic point of view, linear information systems are equivalent to prime algebraic Scott domains, which in turn generalize prime algebraic lattices, already known to provide a model of classical linear logic.

In Mário Florido and Ian Mackie: Proceedings First International Workshop on Linearity (LINEARITY 2009), Coimbra, Portugal, 12th September 2009, Electronic Proceedings in Theoretical Computer Science 22, pp. 38–48.
Published: 30th March 2010.

ArXived at: https://dx.doi.org/10.4204/EPTCS.22.4 bibtex PDF

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