Caro Marcelo, Gostaria de explicitar melhor a posição de Perlovsky. Ele não está propondo que a solução do problema da complexidade computacional (CC) seja encontrada em um outro tipo de lógica formal. Ele propõe uma lógica não-formal, que chamou de "Lógica Dinâmica". Vejamos quais são os seus passos: (p. 27 de "Towards Physics of Mind") CC is still unsolved within logic....(but) incomputability of logic does not entail incomputability of the mind (because) Logic is not the basic mechanism of the mind." (p. 29) "Concept-models that our mind uses for understanding the world are in a constant need of adaptation. Knowledge is not just a static state; it is in a constant process of adaptation and learning. Without adaptation of concept-models we will not be able to understand the ever-changing surrounding world. We will not be able to orient ourselves or satisfy any of the bodily needs. Therefore, we have an inborn need, a drive, an instinct to improve our knowledge. I call it the knowledge instinct. Mathematically it is described as a maximization of a similarity measure between concept-models and the world (as it is sensed by sensory organs; also the very sensing is usually adapted and shaped during perception)." (pç. 32) " An important aspect of dynamic logic is matching vagueness or fuzziness of similarity measures to the uncertainty of models. Initially, parameter values are not known, and uncertainty of models is high; so is the fuzziness of the similarity measures. In the process of learning, models become more accurate, and the similarity measure more crisp, the value of the similarity increases." (p. 33) "To apply...dynamic logic...one needs to develop parametric adaptive models of expected patterns. The models and conditional partial similarities...(include) a uniform model for noise, Gaussian blobs for highly-fuzzy, poorly resolved patterns, and parabolic models... Thus, a problem that was not solvable due to CC becomes solvable using dynamic logic. During an adaptation process, initial fuzzy and uncertain models are associated with structures in the input signals, and fuzzy models become more definite and crisp with successive iterations. The type, shape, and number, of models are selected so that the internal representation within the system is similar to input signals: the...concept-models represent structure-objects in the signals."
Abraços Alfredo Pereira Jr. --------------------------------------------------- Caros. Se o 3o excluído fosse culpado da complexidade toda, então a lógica intuicionista seria menos complexa q a lógica clássica (NPTIME). Mas acontece de ser MAIS complexa (PSPACE). A busca pelo culpado da complexidade é o santo graal daqueles que buscam pela lógica que caracterizaria a class P, mas ela é bem elusica. []s Marcelo 2010/11/1 <[email protected]>: > 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 McCulloch?Pitts neuronal voltage input?output 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
