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A Linear/Producer/Consumer model of Classical Linear Logic
, 2014
"... This paper defines a new proof and categorytheoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to! and?. The resulting linear/producer/consumer (LPC) logic puts the three classes of propositions on the same semant ..."
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This paper defines a new proof and categorytheoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to! and?. The resulting linear/producer/consumer (LPC) logic puts the three classes of propositions on the same semantic footing, following Benton’s linear/nonlinear formulation of intuitionistic linear logic. Semantically, LPC corresponds to a system of three categories connected by adjunctions that reflect the linear/producer/consumer structure. The paper’s metatheoretic results include admissibility theorems for the cut and duality rules, and a translation of the LPC logic into the category theory. The work also presents several concrete instances of the LPC model, including one based on finite vector spaces. 1
Dialectica and Chu Constructions: Cousins?
 In this Volume
, 2006
"... This note investigates two generic constructions used to produce categorical models of linear logic, the Chu construction and the Dialectica construction, in parallel. The constructions have the same objects, but are rather di#erent in other ways. We discuss similarities and di#erences and prove ..."
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This note investigates two generic constructions used to produce categorical models of linear logic, the Chu construction and the Dialectica construction, in parallel. The constructions have the same objects, but are rather di#erent in other ways. We discuss similarities and di#erences and prove that the dialectica construction can be done over a symmetric monoidal closed basis. We also point out several interesting open problems concerning the Dialectica construction.
Cartesian differential storage categories
, 2014
"... Cartesian differential categories were introduced to provide an abstract axiomatization of categories of differentiable functions. The fundamental example is the category whose objects are Euclidean spaces and whose arrows are smooth maps. Tensor differential categories provide the framework for cat ..."
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Cartesian differential categories were introduced to provide an abstract axiomatization of categories of differentiable functions. The fundamental example is the category whose objects are Euclidean spaces and whose arrows are smooth maps. Tensor differential categories provide the framework for categorical models of differential
Submitted to: LINEARITY 2014 A Linear/Producer/Consumer Model of Classical Linear Logic
"... This paper defines a new proof and categorytheoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to! and?. The resulting linear/producer/consumer (LPC) logic puts the three classes of propositions on the same semant ..."
Abstract
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This paper defines a new proof and categorytheoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to! and?. The resulting linear/producer/consumer (LPC) logic puts the three classes of propositions on the same semantic footing, following Benton’s linear/nonlinear formulation of intuitionistic linear logic. Semantically, LPC corresponds to a system of three categories connected by adjunctions reflecting the linear/producer/consumer structure. The paper’s metatheoretic results include admissibility theorems for the cut and duality rules, and a translation of the LPC logic into category theory. The work also
Categorical Semantics of Linear Logic For All
"... This paper is a survey of results on categorical modeling of linear ..."
Imperative Programs as Proofs via Game Semantics
"... This version is made available in accordance with publisher policies. Please cite only the published version using the reference above. ..."
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This version is made available in accordance with publisher policies. Please cite only the published version using the reference above.