On Linear Information Systems

TL;DR

This paper introduces linear information systems as a new model for intuitionistic linear logic, connecting domain theory with linear logic through categorical and set-theoretic interpretations.

Contribution

It defines linear information systems, establishing their equivalence to prime algebraic Scott domains and providing a novel categorical model of linear logic.

Findings

Linear information systems model intuitionistic linear logic.

They are equivalent to prime algebraic Scott domains.

The model recovers Scott continuous functions via the co-Kleisli construction.

Abstract

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.