Modélisation des Systèmes Complexes

                                                                        Prochaine réunion lundi 23 mai 2016    

Conservatoire National des Arts et Métiers (CNAM)
2, rue Conté Paris 3 ième, salle 31-2-87,

Zeno Toffano       Centrale Supélec, Gif sur Yvette

Symbolique quantique pour la logique

We propose a matrix model for two- and many-valued logic using families of observables in Hilbert space, the eigenvalues give the truth values of logical propositions where the atomic input proposition cases are represented by the respective eigenvectors. For binary logic using the truth values {0,1} logical observables are pairwise commuting projectors. For the truth values {+1,-1} the operator system is formally equivalent to that of a composite quantum spin 1/2 system, the logical observables being isometries belonging to the Pauli group. Also in this approach Fuzzy logic arises naturally when considering non-eigenvectors. The fuzzy membership function is obtained by the quantum mean value of the logical projector observable and turns out to be a probability measure in agreement with recent quantum cognition models. The analogy of many-valued logic with quantum angular momentum is then established. Logical observables for three-value logic are formulated as functions of the Lz observable of the orbital angular momentum l= 1. The representatitve 3-valued 2-argument logical obserrvables for the Min and Max connectives are explicitly obtained.

                        Atelier au colloque de la World Organisation of Systems and Cybernetics,
                        25 au 27 janvier 2017, Rome (Italie).    

Quantum modelling for complex systems

The formalism of quantum mechanics offers a general framework to consider a variety of areas outside of the natural remit of physics, as economics, organisations and social interaction, psychology, artificial intelligence, human language, cognition, information retrieval, biology, political science. The application areas addressed typically operate at a macroscopic scale. They may share many key properties with quantum systems including: non-commutativity of measurement, Indeterminacy, non-separability, contextuality, proposals to test temporal nonlocality in perception and cognition, study of non-commutative structures in learning behavior.
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                                                                                                à   duboisf - at - cnam - dot - fr

                                                                        Réunion suivante en cours de conception    

Animation : François Dubois, duboisf - at - cnam - dot - fr

mise à jour : 13 mai 2016