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Glueing and orthogonality for models of linear logic

Martin Hyland, Andrea Schalk
2003 Theoretical Computer Science  
We present the general theory of the method of glueing and associated technique of orthogonality for constructing categorical models of all the structure of linear logic: in particular we treat the exponentials  ...  We indicate simple applications of the methods and show that they cover familiar examples. (M. Hyland), a.schalk@cs.man.ac.uk (A.  ...  We are also grateful for comments from Thomas Ehrhard and Laurent Regnier, members of the EU TMR project 'Linear Logic in Computer Science' centred at Marseille.  ... 
doi:10.1016/s0304-3975(01)00241-9 fatcat:lzi46y7gazdwxpn6i7w27swura

Author index

2003 Theoretical Computer Science  
amek (1-2) 1-1 Hyland, M. and A. Schalk, Glueing and orthogonality for models of linear logic (1-2) 183-231 Joinet, J.-B., see V. Danos (3) 353-378 Kanovich, M.I., M. Okada and A.  ...  Okada, A graph-theoretic characterization theorem for multiplicative fragment of non-commutative linear logic (3) 551-573 Okada, M., see J. Girard (3) 333-333 Okada, M., see M.I.  ... 
doi:10.1016/s0304-3975(03)00024-0 fatcat:azmdpkkrxvcwplluu5qfnsxktm

Abstract Games for Linear Logic Extended Abstract⋆ ⋆Research funded by EPSRC project GR/L27848

Martin Hyland, Andrea Schalk
1999 Electronical Notes in Theoretical Computer Science  
We draw attention to a number of constructions which lie behind many concrete models for linear logic we develop an abstract context for these and describe their general theory.  ...  Using these constructions we give a model of classical linear logic based on an abstract notion of game.  ...  Acknowledgement It will be clear that we h a ve been in uenced in a general way b y colleagues who have w orked on models for linear logic.  ... 
doi:10.1016/s1571-0661(05)80312-3 fatcat:v6zzhk2hhjasthvhqn4g7uxeyq

From Dynamic to Static Semantics, Quantitatively [article]

Thomas Seiller
2016 arXiv   pre-print
We then show how this category is mapped to weighted relational models of linear logic.  ...  This brings into vision a new bridge between the dynamic and static approaches, and provides formal grounds for considering interaction graphs models as quantitative versions of GoI and game semantics  ...  The author also thanks Hugh Steele for his interest in this work, and his numerous comments about earlier versions of this paper.  ... 
arXiv:1604.05047v1 fatcat:xlsxavqb5vbbjhs47rozukfw5a

A Linear Exponential Comonad in s-finite Transition Kernels and Probabilistic Coherent Spaces [article]

Masahiro Hamano
2021 arXiv   pre-print
The model supports an orthogonality in terms of an integral between measures and measurable functions, which can be seen as a continuous extension of Girard-Danos-Ehrhard's linear duality for probabilistic  ...  This paper concerns a stochastic construction of probabilistic coherent spaces by employing novel ingredients (i) linear exponential comonads arising properly in the measure-theory (ii) continuous orthogonality  ...  , hence a categorical model of the exponential modality of linear logic [2, 23, 26] .  ... 
arXiv:1909.07589v2 fatcat:jt5t4345trdrplc55x53ww35li

Intensional Double Glueing, Biextensional Collapse, and the Chu Construction

Dominic Hughes
2003 Electronical Notes in Theoretical Computer Science  
full monoidal embedding of the category Chu(Set, K) of Chu spaces over K into IG(Rel K ), where we define IG, the intensional double glueing construction, by substituting multisets for sets in G.  ...  We show that double glueing on relations subsumes the Chu construction on sets: we present a full monoidal embedding of the category chu(Set, K) of biextensional Chu spaces over K into G(Rel K ), and a  ...  Acknowledgement Many thanks to Martin Hyland, Duško Pavlović and Vaughan Pratt for their interest and feedback during the development of this work.  ... 
doi:10.1016/s1571-0661(03)50007-x fatcat:xb3rxcpyf5hkvovqwwst7wwolq

Speeding-Up Expensive Evaluations in High-Level Synthesis Using Solution Modeling and Fitness Inheritance [chapter]

Christian Pilato, Daniele Loiacono, Antonino Tumeo, Fabrizio Ferrandi, Pier Luca Lanzi, Donatella Sciuto
2010 Computational Intelligence in Expensive Optimization Problems  
any human intervention, (ii) we replace the expensive evaluation process of candidate solutions with a quite accurate regression model, and (iii) we reduce the number of evaluations with a fitness inheritance  ...  It involves three interdependent and NP-complete optimization problems: (i) the operation scheduling, (ii) the resource allocation, and (iii) the controller synthesis.  ...  The fitness surrogate was computed with a linear regression model that takes into account the contributions of all the components of the design (e.g., interconnections or glue logic) and the effect of  ... 
doi:10.1007/978-3-642-10701-6_26 fatcat:uf6kjwnlzrcihfzafgkce6yzyu

Page 1489 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
Girard’s proof nets for the multiplicative frag- ment of linear logic (among arbitrary paired graphs), and stated that for any proof net G there exists a Jordan-Hdlder decom- position of the homology group  ...  Summary: “A main concern of this paper is a Curry-Howard in- 99¢:03099 terpretation of intuitionistic linear logic.  ... 

Semantic Vector Models and Functional Models for Pregroup Grammars

Anne Preller, Mehrnoosh Sadrzadeh
2011 Journal of Logic, Language and Information  
It includes the semantic vector models of Information Retrieval Systems and has an interior logic admitting a comprehension schema.  ...  We show that vector space semantics and functional semantics in twosorted first order logic are equivalent for pregroup grammars.  ...  Acknowledgement The authors would like to thank two anonymous referees for constructive comments.  ... 
doi:10.1007/s10849-011-9132-2 fatcat:pkp255vaxfdcbjngtiex3dlcyq

Comparison of two model approaches in the Zambezi river basin with regard to model reliability and identifiability

H. C. Winsemius, H. H. G. Savenije, A. M. J. Gerrits, E. A. Zapreeva, R. Klees
2005 Hydrology and Earth System Sciences Discussions  
Both models are threshold models, where the non-linear behaviour of the Zambezi river basin is explained by a combination of thresholds and linear reservoirs.  ...  It underlines the need and potential for independent observations of terrestrial storage to enhance our understanding and modelling capacity of the hydrological processes.  ...  This research is being funded by the Netherlands Organisation for Scientific Research (NWO). We are grateful for their support. Edited by: A. Montanari  ... 
doi:10.5194/hessd-2-2625-2005 fatcat:icuchcezvbfznbf27ijtsq2r4q

Algebraic Totality, towards Completeness [chapter]

Christine Tasson
2009 Lecture Notes in Computer Science  
Finiteness spaces constitute a categorical model of Linear Logic (LL) whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and  ...  Then we give an interpretation of LL based on linear algebra.  ...  Acknowledgements I want to thank Thomas Ehrhard and Pierre-Louis Curien for their constant support.  ... 
doi:10.1007/978-3-642-02273-9_24 fatcat:pjq4yhppwbgrppkzq2k33xulce

Zeta Functions and the (Linear) Logic of Markov Processes [article]

Thomas Seiller
2021 arXiv   pre-print
In a series of papers, the author introduced models of linear logic known as "Interaction Graphs".  ...  We further extend previous constructions to provide a model of second-order linear logic as a type system over the set of all (discrete-time) sub-Markov processes.  ...  A first model of Linear Logic To obtain a model of linear logic, one has to consider sub-Markov kernels with a set of states.  ... 
arXiv:2001.11906v3 fatcat:enlj7tf5lzfarltthaka45xjna

Book announcements

2000 Discrete Applied Mathematics  
Quotient Spaces Denseness and Separability Problems References 3. HILBERT SPACE 3.1  ...  point onto the optimal face Introduction 1.1 Logic and Mathematics: The Twain Shall Meet 1.2 Inference Methods for Logic Models 1.3 Logic Modeling Meets Mathematical Modeling 1.4 The Difficulty  ...  Hypergraphs 5.4 An Infinite O-l Programming Model 5.5 The Logic of Arithmetic Chapter 6 Nonclassical and Many-Valued Logics 6.1 Nonmonotonic Logics 6.2 Many-Valued Logics 6.3 Modal Logics 6.4  ... 
doi:10.1016/s0166-218x(00)90007-6 fatcat:cemhaoz7rzdmdoec7pjjqiur2a

Comparison of two model approaches in the Zambezi river basin with regard to model reliability and identifiability

H. C. Winsemius, H. H. G. Savenije, A. M. J. Gerrits, E. A. Zapreeva, R. Klees
2006 Hydrology and Earth System Sciences  
It underlines the 25 need and potential for independent observations of terrestrial storage to enhance our understanding and modelling capacity of the hydrological processes.  ...  Comparison of two model approaches in the Zambezi river basin with regard to model reliability and identifiability.  ...  This research is being funded by the Netherlands Organisation for Scientific Research (NWO). We are grateful for their support. Zambezi river basin  ... 
doi:10.5194/hess-10-339-2006 fatcat:cucfj4ybbbdhhpozsuqvhqezoe

A gentle introduction to Girard's Transcendental Syntax for the linear logician [article]

Boris Eng
2022 arXiv   pre-print
An initial goal of the transcendental syntax is to retrieve linear logic from this new framework. In particular, this model naturally encodes cut-elimination for proof-structures.  ...  All the logical entities and activities will be presented as formatting/structuring on a given model of computation which should be as general, simple and natural as possible.  ...  Par and linear implication As usual in linear logic, the par and linear implication are defined from the tensor and the orthogonal: A `B := (A ⊥ ⊗ B ⊥ ) ⊥ and A ⊸ B := A ⊥ `B.  ... 
arXiv:2012.04752v5 fatcat:6lwhknoeafabdjnc5quar5kdtq
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