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Graphical representation of covariant-contravariant modal formulae

Luca Aceto, Ignacio Fábregas, David de Frutos-Escrig, Anna Ingólfsdóttir, Miguel Palomino
2011 Electronic Proceedings in Theoretical Computer Science  
We show in this paper that the formulae from the covariant-contravariant modal logic that admit a "graphical" representation by means of processes, modulo the covariant-contravariant simulation preorder  ...  In order to obtain the desired graphical representation result, we first restrict ourselves to the case of covariant-contravariant systems without bivariant actions.  ...  Reflection and Preservation of Properties in Coalgebraic (bi)Simulations  ... 
doi:10.4204/eptcs.64.1 fatcat:tughygyofjappe325d3jtfpibq

A categorical interpretation of C.S. Peirce's propositional logic Alpha

Geraldine Brady, Todd H. Trimble
2000 Journal of Pure and Applied Algebra  
Peirce's graphical system Alpha for propositional logic is given a geometric representation in terms of isotopy classes of planar diagrams, and surgery rules on these diagrams called illative transformations  ...  The geometric and algebraic representations are extended to give multi-sorted analogues of Alpha. An interpretation of Alpha is given in terms of linear logic and the theory of closed categories.  ...  Acknowledgements It is our pleasure to acknowledge the help of Stuart Kurtz, who with the ÿrst author initiated a mathematical study of existential graphs [11] .  ... 
doi:10.1016/s0022-4049(98)00179-0 fatcat:kbroc2py4bhbvhmu3d66nfzykq

High-order spectral/hp element discretisation for reaction–diffusion problems on surfaces: Application to cardiac electrophysiology

Chris D. Cantwell, Sergey Yakovlev, Robert M. Kirby, Nicholas S. Peters, Spencer J. Sherwin
2014 Journal of Computational Physics  
polynomial order, while retaining geometric flexibility in the representation of the domain.  ...  models can be significantly reduced through the surface representation and use of high-order methods.  ...  S.Y. and R.M.K. are supported by the Department of Energy (DOE NETL DE-EE0004449). We acknowledge the support of the Imperial College High Performance Computing Service.  ... 
doi:10.1016/j.jcp.2013.10.019 pmid:24748685 pmcid:PMC3991332 fatcat:zint4dq3andu3ogz4tk2becguu

Density Matrices with Metric for Derivational Ambiguity [article]

Adriana D. Correia, Michael Moortgat, Henk T. C. Stoof
2020 arXiv   pre-print
of lexical and derivational forms of ambiguity controlled at the level of the interpretation.  ...  Ambiguous word meanings, in this work, are represented as mixed states, and the compositional interpretation of phrases out of their constituent parts takes the form of a strongly monoidal functor sending  ...  Acknowledgements A.D.C. thanks discussions with Sanjaye Ramgoolam and Martha Lewis that contributed to the duality concepts included in the journal version of this paper.  ... 
arXiv:1908.07347v3 fatcat:yv5q6tedxjcs5lhebjzny5b674

Tensor Glyph Warping: Visualizing Metric Tensor Fields using Riemannian Exponential Maps [chapter]

Anders Brun, Hans Knutsson
2009 Mathematics and Visualization  
These glyphs capture the appearance of the tensors relative to the coordinate system of the human observer.  ...  In this chapter we first derive the well-known metric sphere glyph from the geodesic equations, where the tensor field to be visualized is regarded as the metric of a manifold.  ...  Acknowledgments We thank Magnus Herberthson for valuable discussions on tensors and manifolds and Carl-Fredrik Westin for discussions on the application of these glyphs to Diffusion Tensor MRI data.  ... 
doi:10.1007/978-3-540-88378-4_7 fatcat:o3okmfytbbeijij4m5xwiqa4dy

A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics

Jean-Marie Clarisse, Stéphane Jaouen, Pierre-Arnaud Raviart
2004 Journal of Computational Physics  
This method relying on a description of the perturbed flow in terms of linear Lagrangian perturbations is an outgrowth of an unpublished work by the author [11] and of the Godunov-type method for multi-material  ...  The principle of a discrete formulation of the geometric conservation law [46] for the motion perturbation is introduced, granting mass conservation at the perturbation level.  ...  (X i ), 1 ≤ i ≤ 3, are the vector covariant components, and η 1 , η 2 , η 3 the contravariant vector basis.  ... 
doi:10.1016/j.jcp.2004.01.003 fatcat:ygclxu2fpbgbpmx4b5rvtk33e4

Induction and recursion on datatypes [chapter]

Henk Doornbos, Roland Backhouse
1995 Lecture Notes in Computer Science  
All relations go from a covariant set A to a contravariant set X, in the sense that a morphism from R to R ′ consists of two maps f : A −→ A ′ , g : X ′ −→ X, satisfying f (a)R ′ x = aRg(x).  ...  In the last two decades, all these research areas have seen an interest in the development of two-dimensional modal systems, i.e. formalisms in which the truth of formulas of the language is evaluated  ...  The use of this algebra is illustrated by derivations of a shortest path, a hamiltonian circuits, and a sorting algorithm. All derivations are formal, understandable and concise.  ... 
doi:10.1007/3-540-60117-1_14 fatcat:namzjvik6vapne363qzzvaqdlu

Compositionality and String Diagrams for Game Theory [article]

Jules Hedges, Evguenia Shprits, Viktor Winschel, Philipp Zahn
2016 arXiv   pre-print
We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games.  ...  We apply this language to the game theoretical setting and show examples how to use it for some economic games where we highlight the compositional nature of our higher-order game theory.  ...  By translating into this setting a large set of powerful tools of software design and verification can be applied: automated equilibrium checking, predicate testing, modal logics, type and category theory  ... 
arXiv:1604.06061v1 fatcat:kdgsbheltfekfmxcux65s5iuve

An algebraic theory of normal forms

Silvio Ghilardi
1995 Annals of Pure and Applied Logic  
of modal algebras, whereas for the other cases we give only the final results.  ...  . * There is a general theorem by Lawvere of existence of left adjoints for algebraic functors which applies to our case.  ...  This is obviously contravariant; the covariant power set functor on the other hand, when applied to arrows gives direct image as a result. where the function I? is so defined: I?  ... 
doi:10.1016/0168-0072(93)e0084-2 fatcat:cdebx4wvybdu7psf5fzct5kcoy

The Institutional Approach [article]

Robert E. Kent
2018 arXiv   pre-print
The institutional approach incorporates locally the lattice of theories idea of Sowa from the theory of knowledge representation.  ...  Institutions unite the lattice approach of Formal Concept Analysis of Ganter and Wille with the distributed logic of Information Flow of Barwise and Seligman.  ...  A contravariant passage is a (covariant) passage from the opposite of a contextsame action, but change of perspective.  ... 
arXiv:1810.08074v1 fatcat:alk7cvbyazc3fczmd22hu4drpy

Latent Variable Models [chapter]

Christopher M. Bishop
1998 Learning in Graphical Models  
The structure of such probabilistic models can be made particularly transparent by giving them a graphical representation, usually in terms of a directed acyclic graph, or Bayesian network.  ...  We show how a particular form of linear latent variable model can be used to provide a probabilistic formulation of the well-known technique of principal components analysis (PCA).  ...  of differential geometry in which raised indices denote contravariant components and lowered indices denote covariant components, with an implicit summation over pairs of repeated covariant-contravariant  ... 
doi:10.1007/978-94-011-5014-9_13 fatcat:vsxwdao3gnbthn6psg6uuba5na

Modal Process Rewrite Systems [chapter]

Nikola Beneš, Jan Křetínský
2012 Lecture Notes in Computer Science  
We consider modal transition systems with infinite state space generated by finite sets of rules.  ...  In particular, we extend process rewrite systems to the modal setting and investigate decidability of the modal refinement relation between systems from various subclasses.  ...  The graphical representability of a variant of alternating simulation called covariant-contravariant simulation has been recently studied in [AFdFE + 11].  ... 
doi:10.1007/978-3-642-32943-2_9 fatcat:cctit65bwbcadctxkuz6l5fvhm

On Refinements of Boolean and Parametric Modal Transition Systems [chapter]

Jan Křetínský, Salomon Sickert
2013 Lecture Notes in Computer Science  
We consider the extensions of modal transition systems (MTS), namely Boolean MTS and parametric MTS and we investigate the refinement problems over both classes.  ...  Firstly, we reduce the problem of modal refinement over both classes to a problem solvable by a QBF solver and provide experimental results showing our technique scales well.  ...  The graphical representability of a variant of alternating simulation called covariant-contravariant simulation has been recently studied in [AFdFE + 11].  ... 
doi:10.1007/978-3-642-39718-9_13 fatcat:3hvqc64bcbbknfzwry3vbeuaqu

On Refinements of Boolean and Parametric Modal Transition Systems [article]

Jan Křetínský, Salomon Sickert
2013 arXiv   pre-print
We consider the extensions of modal transition systems (MTS), namely Boolean MTS and parametric MTS and we investigate the refinement problems over both classes.  ...  Firstly, we reduce the problem of modal refinement over both classes to a problem solvable by a QBF solver and provide experimental results showing our technique scales well.  ...  The graphical representability of a variant of alternating simulation called covariant-contravariant simulation has been recently studied in [AFdFE + 11].  ... 
arXiv:1304.5278v1 fatcat:ofe4fda5ynebbdw6gfmv4ozknm

Local Local Reasoning: A BI-Hyperdoctrine for Full Ground Store [chapter]

Miriam Polzer, Sergey Goncharov
2020 Lecture Notes in Computer Science  
Modelling and reasoning about dynamic memory allocation is one of the well-established strands of theoretical computer science, which is particularly well-known as a source of notorious challenges in semantics  ...  We capitalize on recent progress on categorical semantics of full ground store, in terms of a full ground store monad, to build a corresponding semantics of a higher order logic over the corresponding  ...  The contravariant action of H is given by projection and the covariant action is induced by functoriality of rangepSq. pr p : Sq pHpw´, ρ 1 : w1 Ñ w2 qpη P Hpw´, w1 qqq " rangepSqpρ 1 qppr p : Sq ηq pr  ... 
doi:10.1007/978-3-030-45231-5_28 fatcat:d2deva7z7fdk5gy2rgjuo7ux6e
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