scholarly journals A Linear/Producer/Consumer Model of Classical Linear Logic

2015 ◽  
Vol 176 ◽  
pp. 9-23
Author(s):  
Jennifer Paykin ◽  
Steve Zdancewic
Keyword(s):  
Linear Logic ◽  
Consumer Model

scholarly journals A linear/producer/consumer model of classical linear logic

2016 ◽  
Vol 28 (5) ◽  
pp. 710-735
Author(s):  
JENNIFER PAYKIN ◽  
STEVE ZDANCEWIC
Keyword(s):  
Category Theory ◽  
Linear Logic ◽  
Linear Formulation ◽  
Linear Regime ◽  
Non Linear ◽  
Consumer Model ◽  
Intuitionistic Linear Logic

This paper defines a new proof- and category-theoretic framework forclassical linear logicthat 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/non-linear formulation of intuitionistic linear logic. Semantically, LPC corresponds to a system of three categories connected by adjunctions reflecting the LPC structure. The paper's meta-theoretic results include admissibility theorems for the cut and duality rules, and a translation of the LPC logic into category theory. The work also presents several concrete instances of the LPC model.

scholarly journals Cartesian Differential Categories as Skew Enriched Categories

2021 ◽  
Author(s):  
Richard Garner ◽  
Jean-Simon Pacaud Lemay
Keyword(s):  
Linear Logic ◽  
Usual Sense ◽  
Enriched Category ◽  
Enriched Categories ◽  
Full Structure ◽  
Monoidal Closed Category ◽  
Category Of Modules ◽  
Differential Categories ◽  
Linear Category ◽  
Open Question

AbstractWe exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular kind of enriched category. The base for the enrichment is the category of commutative monoids—or in a straightforward generalisation, the category of modules over a commutative rig k. However, the tensor product on this category is not the usual one, but rather a warping of it by a certain monoidal comonad Q. Thus the enrichment base is not a monoidal category in the usual sense, but rather a skew monoidal category in the sense of Szlachányi. Our first main result is that cartesian differential categories are the same as categories with finite products enriched over this skew monoidal base. The comonad Q involved is, in fact, an example of a differential modality. Differential modalities are a kind of comonad on a symmetric monoidal k-linear category with the characteristic feature that their co-Kleisli categories are cartesian differential categories. Using our first main result, we are able to prove our second one: that every small cartesian differential category admits a full, structure-preserving embedding into the cartesian differential category induced by a differential modality (in fact, a monoidal differential modality on a monoidal closed category—thus, a model of intuitionistic differential linear logic). This resolves an important open question in this area.

scholarly journals The Doctor as Parent, Partner, Provider… or Comrade? Distribution of Power in Past and Present Models of the Doctor–Patient Relationship

2021 ◽  
Author(s):  
Mani Shutzberg
Keyword(s):  
Patient Relationship ◽  
Sickness Certification ◽  
Doctor Patient Relationship ◽  
Partnership Model ◽  
Distribution Of Power ◽  
Consumer Model ◽  
Patient Relationships ◽  
Point Of Departure

AbstractThe commonly occurring metaphors and models of the doctor–patient relationship can be divided into three clusters, depending on what distribution of power they represent: in the paternalist cluster, power resides with the physician; in the consumer model, power resides with the patient; in the partnership model, power is distributed equally between doctor and patient. Often, this tripartite division is accepted as an exhaustive typology of doctor–patient relationships. The main objective of this paper is to challenge this idea by introducing a fourth possibility and distribution of power, namely, the distribution in which power resides with neither doctor nor patient. This equality in powerlessness—the hallmark of “the age of bureaucratic parsimony”—is the point of departure for a qualitatively new doctor–patient relationship, which is best described in terms of solidarity between comrades. This paper specifies the characteristics of this specific type of solidarity and illustrates it with a case study of how Swedish doctors and patients interrelate in the sickness certification practice.

scholarly journals On Polymorphic Sessions and Functions

2021 ◽  
Vol 43 (2) ◽  
pp. 1-55
Author(s):  
Bernardo Toninho ◽  
Nobuko Yoshida
Keyword(s):  
Natural Deduction ◽  
Sequent Calculus ◽  
Linear Logic ◽  
Linear Formulation ◽  
Session Types ◽  
Logical Foundation ◽  
Π Calculus ◽  
Soundness And Completeness ◽  
System F ◽  
Algebraic Representations

This work exploits the logical foundation of session types to determine what kind of type discipline for the Λ-calculus can exactly capture, and is captured by, Λ-calculus behaviours. Leveraging the proof theoretic content of the soundness and completeness of sequent calculus and natural deduction presentations of linear logic, we develop the first mutually inverse and fully abstract processes-as-functions and functions-as-processes encodings between a polymorphic session π-calculus and a linear formulation of System F. We are then able to derive results of the session calculus from the theory of the Λ-calculus: (1) we obtain a characterisation of inductive and coinductive session types via their algebraic representations in System F; and (2) we extend our results to account for value and process passing, entailing strong normalisation.

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