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Possibilistic Graphical Models [chapter]

C. Borgelt, J. Gebhardt, R. Kruse
2000 Computational Intelligence in Data Mining  
Graphical modeling is an important method to efficiently represent and analyze uncertain information in knowledge-based systems.  ...  In this paper we provide an overview on the state of the art of possibilistic networks w.r.t. to propagation and learning algorithms.  ...  Acknowledgments The concepts and methods of possibilistic graphical modeling presented in this paper were applied within the CEC-ESPRIT III BRA 6156 DRUMS II project (Defeasible Reasoning and Uncertainty  ... 
doi:10.1007/978-3-7091-2588-5_3 fatcat:qklssnkhj5hgnh4y7c364tcrqq

Logic-based subsumption architecture

Eyal Amir, Pedrito Maynard-Zhang
2004 Artificial Intelligence  
Our system combines the virtues of using the represent-and-reason paradigm and the behavioral-decomposition paradigm. It allows multiple goals to be serviced simultaneously and reactively.  ...  It also allows high-level tasks and is tolerant to different changes and elaborations of its knowledge in runtime. Finally, it allows us to give more commonsense knowledge to robots.  ...  The complete theory and an index of its symbols appear in Appendices B.1 and B.2. The goal-focused part represents the effects of robot motions in situation calculus.  ... 
doi:10.1016/j.artint.2003.07.001 fatcat:h3z7bayngfg7hc3wxbfsei5snq

Introduction to the manifold calculus of Goodwillie-Weiss [article]

Brian A. Munson
2010 arXiv   pre-print
Our perspective focuses on the role the derivatives of a functor F play in this theory, and the analogies with ordinary calculus.  ...  We present an introduction to the manifold calculus of functors, due to Goodwillie and Weiss.  ...  Let X : P({1, 2}) → Top be a covariant functor, and write X S in place of X (S). Let P 0 (2) be the subposet of nonempty subsets, and let P 1 (2) be the subposet of proper subsets.  ... 
arXiv:1005.1698v1 fatcat:tjfdwukhuzfmfbfgpp53tkivlm

Geometrical representations in the learning of two-variable functions

Maria Trigueros, Rafael Martínez-Planell
2009 Educational Studies in Mathematics  
This lack of research findings limits the understanding of how students learn the main ideas involved in the study of multivariable calculus.  ...  The portion of the project we report here concentrates on investigating the relationship between students' notion of subsets of Cartesian three-dimensional space and the understanding of graphs of twovariable  ...  We are thankful to Ed Dubinsky for his comments and suggestions.  ... 
doi:10.1007/s10649-009-9201-5 fatcat:26n2olvxovggxktcqodiedwk3m

Functorial String Diagrams for Reverse-Mode Automatic Differentiation [article]

Mario Alvarez-Picallo, Dan R. Ghica, David Sprunger, Fabio Zanasi
2021 arXiv   pre-print
We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure.  ...  Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness  ...  ACKNOWLEDGMENTS This material is based upon work supported by the Engineering and Physical Sciences Research Council (UK) under Grant EP/V001612/1 (Nominal String Diagrams).  ... 
arXiv:2107.13433v1 fatcat:2bnsqea5nvgxhhsakuwlhwq6oi

Polarimetric study of birefringent turbid media with three-dimensional optic axis orientation

Noé Ortega-Quijano, Félix Fanjul-Vélez, José Luis Arce-Diego
2013 Biomedical Optics Express  
We present a novel analytical method for characterizing the intrinsic retardance and the three-dimensional optic axis orientation of uniform and uniaxial turbid media.  ...  The results corroborate its capacity to successfully characterize 3D linear birefringence in a straightforward way.  ...  Although this critical issue is well-known, to the best of the Authors' knowledge the correspondence between the effective and intrinsic linear retardances has not been analytically stated before in the  ... 
doi:10.1364/boe.5.000287 pmid:24466494 pmcid:PMC3891339 fatcat:epnij3a23ba3fce3gwaqz2jtbe

D'Alembert: Between Newtonian Science and the Cartesian Inheritance

Agamenon R. E. Oliveira
2017 Advances in Historical Studies  
This paper is a tribute to the tercentenary of d'Alembert's birth. It studies the way how d'Alembert (  ...  Acknowledgements I am in debt with professor Michel Paty who sent to me many papers, documents and his D'Alembert's biography.  ...  Brazilian historians of sciences consider Paty one of the most important experts on D'Alembert's thought.  ... 
doi:10.4236/ahs.2017.64010 fatcat:2lwat4dukjb7has7cnfrxmnwcm

Book Review: Analytic functional calculus and spectral decompositions

Raúl E. Curto
1986 Bulletin of the American Mathematical Society  
a decomposition is unique with respect to the conditions (i) and (ii), and both D and N are indeed polynomials in T.  ...  Complaints about choice of content should be forestalled until the appearance of a second volume, due out in the near future and promising cohomology, semilattices, Lie semigroups, and other topics of  ...  is a compact, nonempty subset of the cartesian product of the individual spectra, that it is contained in any algebraic joint spectrum, and that itpossesses a rich functional calculus: if U is an open  ... 
doi:10.1090/s0273-0979-1986-15421-2 fatcat:tfs2p6zeqneflp4x4gkwox22gu

Hierarchies of probabilistic models of navigation: the Bayesian Map and the Abstraction operator

J. Diard, P. Bessiere, E. Mazer
2004 IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004  
In the resulting hierarchy, localization in the high level model is based on probabilistic competition of the lower level models.  ...  Hierarchies of probabilistic models of navigation: the Bayesian Map and the Abstraction operator.  ...  In our Bayesian Map formalism, we will constraint what maps are used for (the questions), but not how the knowledge necessary for using the map is structured (the decomposition). III.  ... 
doi:10.1109/robot.2004.1308866 dblp:conf/icra/DiardBM04a fatcat:gv7wvjxxrfcl5gmisnk2v234ki

Local Parallel Model Checking for the Alternation-Free μ-Calculus [chapter]

Benedikt Bollig, Martin Leucker, Michael Weber
2002 Lecture Notes in Computer Science  
For practical applications, however, it suffices to restrict the µ-calculus to the alternationfree fragment, denoted by L 1 µ , in which nesting of minimal and maximal fixedpoint operators is prohibited  ...  It allows the formulation of many safety as well as liveness properties and subsumes the logic CTL [10], which is employed in many practical verification tools.  ...  The model-checking game of T and ϕ has as the board the Cartesian product S × Q of the set of states and ϕ's positions.  ... 
doi:10.1007/3-540-46017-9_11 fatcat:b2ugpg52ofggbk4fgfo24xr3s4

Applying Universal Algebra to Lambda Calculus

G. Manzonetto, A. Salibra
2008 Journal of Logic and Computation  
From one side we survey the knowledge we have acquired these last ten years about the lattice of all λ-theories (= equational extensions of untyped λ-calculus) and the models of lambda calculus via universal  ...  We show that the indecomposable semantics (i.e., the semantics of lambda calculus given in terms of models of lambda calculus, which are directly indecomposable as combinatory algebras) includes the continuous  ...  These elements define a direct decomposition of the algebra as the Cartesian product of two other algebras, just like idempotent elements in rings.  ... 
doi:10.1093/logcom/exn085 fatcat:muo26iplxbe2diepxtlnnutdxi

Surmounting the Cartesian Cut Through Philosophy, Physics, Logic, Cybernetics, and Geometry: Self-reference, Torsion, the Klein Bottle, the Time Operator, Multivalued Logics and Quantum Mechanics

Diego L. Rapoport
2009 Foundations of physics  
We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation, generates the  ...  Thus, from a primitive distinction in the vacuum plane and the axioms of the calculus of distinction, we can derive by incorporating paradox, the world conception succintly described above.  ...  Larry Horwitz, for his example of integrity in the persue of knowledge, his warm and kind support and encouragement. To Prof. Martin Land and Prof.  ... 
doi:10.1007/s10701-009-9334-5 fatcat:s5t4f2t3bzcofozjkivjdoshyu

Guaranteed robust nonlinear minimax estimation

L. Jaulin, E. Walter
2002 IEEE Transactions on Automatic Control  
By combining tools of interval analysis and constraint propagation, it becomes possible to compute the corresponding minimax estimates in an approximate but guaranteed way, even when the model output is  ...  Minimax parameter estimation aims at characterizing the set of all values of the parameter vector that minimize the largest absolute deviation between experimental data and corresponding model outputs.  ...  Consider, for instance, the situation ofFigure 3, where the Cartesian domains to be considered are boxes.  ... 
doi:10.1109/tac.2002.804479 fatcat:hydmbfftizc2fd2i3wzsnnk4fi

Co-Algebraic Models for Quantitative Spatial Logics

Vincenzo Ciancia, Gian Luigi Ferrari
2007 Electronical Notes in Theoretical Computer Science  
The evaluation of a formula yields a value in a suitable multi-valued algebraic structure, giving a measure of the satisfaction of a requirement, induced by the decomposition of a system into subsystems  ...  We introduce a class of coalgebraic models and a family of modal logics that support the specification of spatial properties of distributed applications.  ...  Acknowledgement The authors wish to thank Alberto Lluch-Lafuente for helpful comments.  ... 
doi:10.1016/j.entcs.2007.07.004 fatcat:y6iguaqgnfg3hflaacsqhc2fzy

On an intuitionistic logic for pragmatics

Gianluigi Bellin, Massimiliano Carrara, Daniele Chiffi
2015 Journal of Logic and Computation  
Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations  ...  Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, defined as a hypothesis that in some situation the truth of p is epistemically necessary.  ...  Informally, they could be explained by saying that implication has to hold in all possible worlds "in the future of our knowledge" and subtraction in some world "in the past of our knowledge".  ... 
doi:10.1093/logcom/exv036 fatcat:kiqprtcp6vfrhnutwqpyadmpyy
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