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The Free Exponential Modality of Probabilistic Coherence Spaces [chapter]

Raphaëlle Crubillé, Thomas Ehrhard, Michele Pagani, Christine Tasson
2017 Lecture Notes in Computer Science  
We prove here that the exponential modality is the free commutative comonad, giving a further mark of canonicity to the model.  ...  Probabilistic coherence spaces yield a model of linear logic and lambda-calculus with a linear algebra flavor.  ...  This work has been partly funded by the French project ANR-14-CE25-0005 Elica and by the French-Chinese project ANR-11-IS02-0002 and NSFC 61161130530 Locali.  ... 
doi:10.1007/978-3-662-54458-7_2 fatcat:uwfd7xwkivfc3f2ufsyhuo64sm

Linear-Algebraic Models of Linear Logic as Categories of Modules over Sigma-Semirings [article]

Takeshi Tsukada, Kazuyuki Asada
2022 arXiv   pre-print
Examples include models based on coherence spaces, finiteness spaces and probabilistic coherence spaces, as well as the relational and weighted relational models.  ...  cofree exponential.  ...  It is used to prove that the exponential modality of probabilistic coherence spaces given in [4] is actually free [3] . The relationship of our construction to [26, 27] is currently unclear.  ... 
arXiv:2204.10589v1 fatcat:fttbgqdvvjhilmu4opb7zbi2da

Coalgebraic Hybrid Logic [chapter]

Rob Myers, Dirk Pattinson, Lutz Schröder
2009 Lecture Notes in Computer Science  
This framework, coalgebraic hybrid logic, works at the same level of generality as coalgebraic modal logic, and in particular subsumes, besides normal hybrid logics such as hybrid K, a wide variety of  ...  logics with non-normal modal operators such as probabilistic, graded, or coalitional modalities and non-monotonic conditionals.  ...  The authors wish to thank Erwin R. Catesbeiana for detailed explanations of his views on consistent formulas.  ... 
doi:10.1007/978-3-642-00596-1_11 fatcat:ziyoci7gmja3npv76w5m5ohdiq

On Banach spaces of sequences and free linear logic exponential modality

2017 Mathematical Structures in Computer Science  
The main interest of the work is that our model gives a realization of the free linear logic exponentials construction.  ...  We introduce a category of vector spaces modelling full propositional linear logic, similar to probabilistic coherence spaces and to Koethe sequences spaces.  ...  Coherence spaces and vector spaces The first and best known model of linear logic, coherence spaces, has free exponentials.  ... 
doi:10.1017/s0960129517000251 fatcat:xf4dp4wl3rf75a6zjbvg577j4i

Nominals for Everyone

Lutz Schröder, Dirk Pattinson, Clemens Kupke
2009 International Joint Conference on Artificial Intelligence  
It has been recognised that the expressivity of description logics benefits from the introduction of non-standard modal operators beyond existential and number restrictions.  ...  Such operators support notions such as uncertainty, defaults, agency, obligation, or evidence, whose semantics often lies outside the realm of relational structures.  ...  Probabilistic hybrid logic, the hybrid extension of probabilistic modal logic [Larsen and Skou, 1991; Heifetz and Mongin, 2001] , has modal operators L p 'in the next step, it holds with probability at  ... 
dblp:conf/ijcai/SchroderPK09 fatcat:i57llnyuafd53mwaqj2onedwve

Linear logic in normed cones: probabilistic coherence spaces and beyond [article]

Sergey Slavnov
2019 arXiv   pre-print
of probabilistic coherence spaces.  ...  However, unlike the case of probabilistic coherence spaces, it remained unclear if the model could be refined to a model of classical linear logic.  ...  Probabilistic coherence spaces We briefly recall the notion of probabilistic coherence space (PCS). For more details see [4] . Let I be an at most countable index set.  ... 
arXiv:1803.06005v3 fatcat:vyqcm3r7nve6ni5wmy4urmuefa

Optimal Processing of Wind Tunnel Measurements in View of Stochastic Structural Design of Large Flexible Structures [chapter]

Vincent Denol, Nicolas Blaise
2011 Wind Tunnels and Experimental Fluid Dynamics Research  
Although standards usually neglect the imaginary part of the coherence and model the real part as a decreasing exponential (Dyrbye & Hansen, 1997) , we may observe that this model (adopted from free field  ...  Coherence does not decrease exponentially; it also diminishes with increasing distance between sensors.  ... 
doi:10.5772/19902 fatcat:cjtkjtsfargktg2n2whn7izzta

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

Masahiro Hamano
2021 arXiv   pre-print
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  ...  As an application to countable measurable spaces, a dagger compact closed category is obtained, whose double glueing gives rise to the familiar category of probabilistic coherent spaces.  ...  His investigation of duality leads Danos-Ehrhard [7] to formulate a probabilistic (fuzzy) version of duality in their probabilistic coherent spaces Pcoh.  ... 
arXiv:1909.07589v2 fatcat:jt5t4345trdrplc55x53ww35li

Strong Adequacy and Untyped Full-Abstraction for Probabilistic Coherence Spaces [chapter]

Thomas Leventis, Michele Pagani
2019 Green Chemistry and Sustainable Technology  
We consider the probabilistic untyped lambda-calculus and prove a stronger form of the adequacy property for probabilistic coherence spaces (PCoh), showing how the denotation of a term statistically distributes  ...  over the denotations of its head-normal forms.  ...  Probabilistic Coherence Spaces Girard introduced probabilistic coherence spaces (PCS) as a "quantitative refinement" of coherence spaces [9] .  ... 
doi:10.1007/978-3-030-17127-8_21 dblp:conf/fossacs/LeventisP19 fatcat:pegtpjfx2rfmxcoxneqbg7kvti

NP-containment for the coherence test of assessments of conditional probability: a fuzzy logical approach

Tommaso Flaminio
2007 Archive for Mathematical Logic  
In particular we will prove that the coherence of an assessment of conditional probability χ can be characterized by means of the logical consistency of a suitable theory Tχ defined on the modal-fuzzy  ...  Both [12] and [16] are devoted to the treatment of the coherence of assess-  ...  Acknowledgments The author feels deeply indebted to Lluís Godo and Franco Montagna for their useful comments and remarks about the present work, as well as to the anonymous referees for the nice improvements  ... 
doi:10.1007/s00153-007-0045-3 fatcat:qf2zk7fh7fa5rmkboyj4pp46hi

Region Classification with Markov Field Aspect Models

Jakob Verbeek, Bill Triggs
2007 2007 IEEE Conference on Computer Vision and Pattern Recognition  
More advanced models attempt to improve the coherence of the labellings by introducing some form of inter-patch coupling: traditional spatial models such as MRF's provide crisper local labellings by exploiting  ...  We study two spatial models: one based on averaging over forests of minimal spanning trees linking neighboring image regions, the other on an efficient chain-based Expectation Propagation method for regular  ...  We now discuss two models that capture more of the spatial coherence of natural region labels.  ... 
doi:10.1109/cvpr.2007.383098 dblp:conf/cvpr/VerbeekT07 fatcat:4godgnmojzfvxfoj7aybpydfc4

Coinduction in Flow: The Later Modality in Fibrations

Henning Basold, Michael Wagner
2019 Conference on Algebra and Coalgebra in Computer Science  
Part of the framework are also various results that enable a wide range of applications: transportation of (co)limits, exponentials, fibred adjunctions and first-order connectives from the initial fibration  ...  Ultimately, we generalise the work of Birkedal et al. [16] on the topos of trees to arbitrary fibrations with the effect of much wider applicability to, for example, quantitative reasoning and probabilistic  ...  In this example, we show how the semantics of the modalities of the probabilistic modal µ-calculus (pLµ) can be modelled as liftings.  ... 
doi:10.4230/lipics.calco.2019.8 dblp:conf/calco/Basold19 fatcat:de4sngban5ggll2hp2ifba3shm

Extending qubit coherence by adaptive quantum environment learning [article]

Eleanor Scerri, Erik M. Gauger, Cristian Bonato
2019 arXiv   pre-print
, and hence an increase of the qubit coherence.  ...  In this work, we investigate how the back-action of the quantum measurements used in the learning process can be harnessed to extend qubit coherence.  ...  Due to to the exponential scaling of the Hilbert space, we restricted this simulation to a spin bath of 7 nuclear spins, although the same results can be obtained for larger environments, as we show in  ... 
arXiv:1911.12192v1 fatcat:pvjoqmvjbnbnle336lfuhs5oo4

A Tetrahedron-Based Heat Flux Signature for Cortical Thickness Morphometry Analysis [chapter]

Yonghui Fan, Gang Wang, Natasha Lepore, Yalin Wang
2018 Lecture Notes in Computer Science  
from Short-axis Cine MRI: Preserving the Temporal Coherence of Cardiac Motion 545 Cell Instance Tracking with Cosine Embeddings and Recurrent Hourglass Networks 551 Some Investigations on Robustness of  ...  in Placental Ultrasound Images via Layer Aggregation 281 Deep Reinforcement Learning for Vessel Centerline Tracing in Multi-modality 3D Volumes 282 Unsupervised Learning for Fast Probabilistic Diffeomorphic  ... 
doi:10.1007/978-3-030-00931-1_48 pmid:30338317 pmcid:PMC6191198 fatcat:dqhvpm5xzrdqhglrfftig3qejq

Towards a Complexity-through-Realisability Theory [article]

Thomas Seiller
2015 arXiv   pre-print
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational  ...  This paper provides the background, motivations and perspectives of this complexity-through-realisability theory to be developed, and illustrates it with recent results.  ...  However, the proposed proof method does not naturally appear as a natural proof in the sense of Razborov and Rudich [11] .  ... 
arXiv:1502.01257v2 fatcat:p5b36gxqizbohi3wfwk4unmj2e
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