Caros Colegas, recentemente apareceram teorias matemáticas da consciência, como no Abstract abaixo. Também destaco o paper "Towards a Physics of the Mind", de Leonid Perlovsky, artigo publicado no periódico "Physics of Life Reviews", que contém uma parte introdutória muito interessante, em que o autor identifica no Princípio do Terceiro Excluído a raiz do problema da hipercomplexidade combinatorial na Inteligência Artificial "forte". Também tem obtido destaque o trabalho de Balduzzi e Tononi "Qualia: the Geometry of Integrated Information" (vide entrevista com Tononi no New York Times: http://www.nytimes.com/2010/09/21/science/21consciousness.html?_r=2). Se alguém da lista tiver comentários a tecer sobre o assunto, ficarei grato. Abraços Alfredo Pereira Jr.
http://dx.doi.org/10.1016/j.jal.2009.05.002 Journal of Applied Logic 8(1):114-140, March 2010 Dynamics of mental activity Willard L. Miranker and Gregg J. Zuckerman Motivated by neuronal modeling, our development of the mathematical foundations of consciousness in [W. Miranker, G. Zuckerman, Mathematical Foundations of Consciousness, J. Appl. Logic (2009)] (M-Z) was characterized by an axiomatic theory for consciousness operators that acted on the collection of all sets. Consciousness itself was modeled as emanating from the action of such operators on the labeled decoration of a graph, the latter set theoretic construct given the characterization of experience. Since mental activity (conscious and unconscious) is a time dependent process, we herein develop a discrete time dependent version of the theory. Specification of the relevant mental dynamics illuminates and expands the development of the mathematical framework in (M-Z) upon which our study of consciousness rests. This framework is an abstraction of neural net modeling. We review the Aczel theory for decorating labeled graphs, in particular that theory's application to the (M-Z) foundations. The relevant neuronal modeling concepts and terminology are also reviewed. A number of examples are presented. Then an extension of our considerations from graphs to multigraphs is made, since the latter represent a more accurate model of neuronal circuit connectivity. The dynamics are crafted for non-well-founded constructs by development of a hierarchy of systems, starting with the McCullochPitts neuronal voltage inputoutput relations and building to a dynamics for the cognitive notions of memes and themata; these latter corresponding to aspects of decorations of labeled graphs associated with neural networks. We conclude with a summary and discussion of the semantics of the cognitive features of our development: memes, themata, qualia, consciousness operators, awareness field. Keywords: Awareness field; Anti-foundation axiom; Consciousness; M-Z Theory; Mental dynamics; Neural networks; Non-well-founded sets _______________________________________________ Logica-l mailing list [email protected] http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l
