On Linear Information Systems

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

On F

We introduce a new construction—FS+-domain—and prove that the category with FS+-domains as objects and Scott continuous functions as morphisms is a Cartesian closed category. We obtain that the Plotkin powerdomain PP(L) over an FS-domain L is an FS+-domain

On linear information systems

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