scholarly journals Categorical Models of Syntactic Control of Intereference Revisited, Revisited

2007 ◽  
Vol 10 ◽  
pp. 176-206 ◽  
Author(s):  
Guy McCusker
Keyword(s):  
Type System ◽  
General Notion ◽  
Coherence Property ◽  
Game Semantics ◽  
Proof Sketch ◽  
Categorical Structure ◽  
Categorical Models

AbstractThe question of what categorical structure is required to give semantics to O‘Hearn et al.'s type system Syntactic Control of Interference Revisited (SCIR) is considered. The previously proposed notion of bireflective model is rejected as being too restrictive to accommodate important concrete models based on game semantics and object spaces; furthermore it is argued that the existing proof-sketch of the important property of coherence for these models is incorrect. A new, more general notion of model is proposed and the coherence property proved.

scholarly journals On geometry of interaction for polarized linear logic

2017 ◽  
Vol 28 (10) ◽  
pp. 1639-1694
Author(s):  
MASAHIRO HAMANO ◽  
PHILIP SCOTT
Keyword(s):  
Proof Theory ◽  
Monoidal Category ◽  
Linear Logic ◽  
Cut Elimination ◽  
List Type ◽  
Monoidal Categories ◽  
Categorical Structure ◽  
Categorical Models ◽  
Focusing Property ◽  
Special Case

We present Geometry of Interaction (GoI) models for Multiplicative Polarized Linear Logic, MLLP, which is the multiplicative fragment of Olivier Laurent's Polarized Linear Logic. This is done by uniformly adding multi-points to various categorical models of GoI. Multi-points are shown to play an essential role in semantically characterizing the dynamics of proof networks in polarized proof theory. For example, they permit us to characterize the key feature of polarization, focusing, as well as being fundamental to our construction of concrete polarized GoI models.Our approach to polarized GoI involves following two independent studies, based on different categorical perspectives of GoI: (i)Inspired by the work of Abramsky, Haghverdi and Scott, a polarized GoI situation is defined in which multi-points are added to a traced monoidal category equipped with a reflexive object U. Using this framework, categorical versions of Girard's execution formula are defined, as well as the GoI interpretation of MLLP proofs. Running the execution formula is shown to characterize the focusing property (and thus polarities) as well as the dynamics of cut elimination.(ii)The Int construction of Joyal–Street–Verity is another fundamental categorical structure for modelling GoI. Here, we investigate it in a multi-pointed setting. Our presentation yields a compact version of Hamano–Scott's polarized categories, and thus denotational models of MLLP. These arise from a contravariant duality between monoidal categories of positive and negative objects, along with an appropriate bimodule structure (representing ‘non-focused proofs’) between them.Finally, as a special case of (ii) above, a compact model of MLLP is also presented based on Rel (the category of sets and relations) equipped with multi-points.

scholarly journals An interpretation of dependent type theory in a model category of locally cartesian closed categories

2021 ◽  
pp. 1-26
Author(s):  
Martin E. Bidlingmaier
Keyword(s):  
Type Theory ◽  
Model Category ◽  
Model Categories ◽  
Dependent Type Theory ◽  
Categorical Structure ◽  
Categorical Models ◽  
Cartesian Closed Categories ◽  
Cartesian Closed ◽  
Original Interpretation ◽  
Dependent Type

Abstract Locally cartesian closed (lcc) categories are natural categorical models of extensional dependent type theory. This paper introduces the “gros” semantics in the category of lcc categories: Instead of constructing an interpretation in a given individual lcc category, we show that also the category of all lcc categories can be endowed with the structure of a model of dependent type theory. The original interpretation in an individual lcc category can then be recovered by slicing. As in the original interpretation, we face the issue of coherence: Categorical structure is usually preserved by functors only up to isomorphism, whereas syntactic substitution commutes strictly with all type-theoretic structures. Our solution involves a suitable presentation of the higher category of lcc categories as model category. To that end, we construct a model category of lcc sketches, from which we obtain by the formalism of algebraically (co)fibrant objects model categories of strict lcc categories and then algebraically cofibrant strict lcc categories. The latter is our model of dependent type theory.

Ultrastructural characteristics of sporidia of Ustilago

1989 ◽  
Vol 47 ◽  
pp. 786-787
Author(s):  
Patricia N. Hackney
Keyword(s):  
Electron Microscope ◽  
Type System ◽  
Tube Formation ◽  
High Voltage Electron Microscopy ◽  
Voltage Electron ◽  
University Of Wisconsin ◽  
Transmission Electron ◽  
Ustilago Hordei ◽  
Silene Alba ◽  
The University

Ustilago hordei and Ustilago violacea are yeast-like basidiomycete pathogens ofHordeum vulgare and Silene alba respectively. The mating type system in both species of Ustilago is bipolar, with alleles, A,a, (U.hordei) and a1, a2 (U.violacea) at a single locus. Haploid sporidia maintain the asexual phase by budding, while the sexual phase is initiated by conjugation tube formation between the mating types during budding and conjugation.For observation of budding, sporidia were prepared by culturing the four types on YEG (yeast extract glucose) broth for 24 hours. After centrifugation at 5000g cells were either left unmated or mated in a1/a2,A/a combinations. The sporidia were then mixed 1:1 with 4% agar and the resulting 1mm cubes fixed in 8% gluteraldehyde and post fixed in osmium tetroxide. After dehydration and embedding cubes were thin sectioned with a LKB ultratome and photographed in a Zeiss 9s transmission electron microscope or in an AE1 electron microscope of MK11 1MEV at the High Voltage Electron Microscopy Center of the University of Wisconsin-Madison.

Nominal Game Semantics

2016 ◽  
Author(s):  
Andrzej S. Murawski ◽  
Nikos Tzevelekos
Keyword(s):  
Game Semantics

Thermal comfort conditions in a classroom conditioned by a split-type system

2017 ◽  
Author(s):  
Rogério Vilain ◽  
Marcelo Pereira ◽  
Nathan Mendes ◽  
katia cordeiro ◽  
anastacio da silva junior
Keyword(s):  
Thermal Comfort ◽  
Type System

Spontaneous Discovery and Use of Categorical Structure

1993 ◽  
Author(s):  
John P. Clapper ◽  
Gordon H. Bower
Keyword(s):  
Categorical Structure

Modelling of impregnation of γ-alumina with cobalt and molybdenum salts. CoCl2-(NH4)2MoO4-γ-Al2O3 (aluminate type) system

1987 ◽  
Vol 52 (3) ◽  
pp. 663-671 ◽  
Author(s):  
Jiří Hanika ◽  
Vladimír Janoušek ◽  
Karel Sporka
Keyword(s):  
Effective Diffusion ◽  
Type System ◽  
Catalyst Particle ◽  
Ammonium Molybdate ◽  
Active Components ◽  
Model Set ◽  
Cobalt Dichloride ◽  
Set Up ◽  
Electron Microanalysis ◽  
Kinetics Of

Adsorption data for the impregnation of alumina with an aqueous solution of cobalt dichloride and ammonium molybdate were treated in terms of the Langmuir adsorption isotherm and compared with a mathematical model set up to describe the kinetics of simultaneous impregnation of a support by two components. The effective diffusion coefficients of the two components at 25 °C in a cylindrical particle of alumina were obtained. The validity of the model used was verified qualitatively by comparing the numerical results with the experimental time dependent concentration profiles of the active components in a catalyst particle, measured by electron microanalysis technique.

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