We investigate how very large populations are able to reach a global consensus, out of local "microscopic" interaction rules, in the framework of a recently introduced class of models of semiotic dynamics, the so-called Naming Game. We compare in particular the convergence mechanism for interacting agents embedded in a low-dimensional lattice with respect to the mean-field case. We highlight that in low-dimensions consensus is reached through a coarsening process which requires less cognitive effort of the agents, with respect to the mean-field case, but takes longer to complete. In 1-d the dynamics of the boundaries is mapped onto a truncated Markov process from which we analytically computed the diffusion coefficient. More generally we show that the convergence process requires a memory per agent scaling as N and lasts a time N^{1+2/d} in dimension d<5 (d=4 being the upper critical dimension), while in mean-field both memory and time scale as N^{3/2}, for a population of N agents. We present analytical and numerical evidences supporting this picture.

If one isolated species (corporation) is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species (corporations) can be expressed by a coupled system of two discrete logistic equations. As three basic relationships between two species are present in Nature, namely symbiosis, predator-prey and competition, three different models are obtained. Each model is a cubic two-dimensional discrete logistic-type equation with its own dynamical properties: stationary regime, periodicit y, quasi-periodicity and chaos. We also propose that these models could be useful for thinking in the different interactions happening in the economic world, as for instance for the competition and the collaboration between corporations. Furthermore, these models could be considered as the basic ingr edients to construct more complex interactions in the ecological and economic networks.

Aggregated phenomena in social sciences and economi cs are highly dependent on the way individuals interact. To help understanding the interplay betwe en socio-economic activities and underlying social networks, this paper studies a sequential prisoner's dilemma with binary choice. It proposes an analytical and computational insight about the role of endogenous networks in emergence and sustainability of cooperation and exhibits an alternative to the choice and refusal mechanism that is often proposed to explain cooperation. The study fo cuses on heterogeneous equilibriums and emergence of cooperation from an all-defector state that are the two stylized facts that this model successfully reconstructs.

Object Analysis, from this paper point of view, is just a continuity to the already well defined Object Oriented Programming and modeling techniques, with a difference, that is, we will be looking for automated methods realizing the analysis of the object, and eventually construct an object model of a given environment -or a signal. From one hand the "Object" concept define a central point for Object's Data storage, and the functions, interfacing it to the external world, and on the other hand, the "Object" concept, threw its hierarchy, is an actual investment of "similarities" between different object forms, known as polymorphisms . Object programming has been used, with a great success, in computer science. But the thinking process, or the analysis process, generating these models, is of course nothing but intelligence; our intelligence, with its inherent complexity. In our search for an automated object-analysis capable algorithms -or machines, image processing, and more generally signal processing, are the most capable in what we know in science. To this date, image-processing science, coupled to the information processing science, do provide us with different analysis technique of the signal that can be categorized into these categories: 1.

The axiom scheme of Extensionality states that whenever two predicates or relations are coextensive they must have the same propertie s: XY ( null x(Xnull x Ynull x) Z (ZX ZY)) (1) Historically Extensionality has always been problematic, the main problem being that in many areas of application, though not perhaps in t he foundations of mathematics, the statement is simply false. This was reco gnized by Whitehead and Russell in Principia Mathematica [32], where intensional functions such as ' A believes that p ' or'it is a strange coincidence that p ' are discussed at length. However, in the introduction to the second edition ( 1927) of the Prin-cipia Whitehead and Russell (influenced by Wittgenstein's Tractatus) already entertain the possibility that "all functions of functions are extensional". Thirteen years later, in Church's [6] canonical formulation of t he Theory of Types, it is observed that axioms of Extensionality should be adopt ed "[i]n order to obtain classical real number theory (analysis)", a wording that does not seem to rule out the option of not adopting them. Church's formula tion of type theory was completely syntactic and axioms could be adopted or d ropped at will, The Journal of Symbolic Logic, to appear.

In vector quantization the number of vectors used to construct the codebook is always an undefined problem, there is always a compromise between the number of vectors and the quantity of information lost during the compression. In this text we present a minimum of Entropy principle that gives solution to this compromise and represents an Entropy point of view of signal compression in general. Also we present a new adaptive Object Quantization technique that is the same for the compression and the perception.

We consider methods for aggregating preferences that are base d on the resolution of discrete optimization problems. For a review and references see Cook and Kress (1992), and Belkin and Levin (1990), and also David (1988) and Van B lokland-Vogelesang (1991). Some algorithmic aspects can be found in Barth elemy (1989) and Litvak (1982). The preferences are represented by arbitra ry binary relations (possibly weighted) or incomplete paired comparison matrices. The o utcome of an aggregation method is a set of "optimal" rankings (linear or weak ord ers) of the alternatives. Namely, a ranking is said to be optimal if it provides an ex tremum of some chosen objective function that expresses the connectio n (or proximity) between an arbitrary ranking and the original preferences.

The scores can be used in themselv es or serve as the basis for ranking or choice. For the present, only a few scoring pro cedures are endowed with their axiomatic characterizations. At the same time, a large num ber of ingenious procedures are advocated and used in such disciplines as manageme nt science, operations research, psychometrics, applied statistics, processing of spor t tournaments, graph theory, etc. Very few social choice papers deal with them. The aim of this pa per is to take one circumspect step toward an axiomatic framework for comparin g the merits of these elaborate procedures. As a result, we would like to isolate a family of s coring procedures that comprises a majority of'reasonable' procedures (so that th e further axioms could be imposed on this family). Two main approaches are applicable. The first one is to express the desired properties axiomatically, the second is to gather the ex isting procedures and specify their common algebraic form.

Preface This is a companion paper to Conscious Intelligent Systems Part 1 by the same author (1), which discusses a possible evolutionary path for consciousness and intelligence from simple systems to human level consciousness and intelligence. Man has long been held to be a thinking animal, his thought processes have been held to be the reason for his superiority over the animals. The grand aim of AI has always been to make an entity that can think. Turing took up this very question in his paper (2) on whether machines can think. On the more prosaic roads that real AI has been forced to follow, such grand questions have almost died down. Another major trigger for the demise has been Searle's Chinese Room (3) parody . With this rather cunning device, Searle set the cat among the pigeons and has helped induce self-doubt in the best of AI theorists. One of the major triggers towards Searle's views was language, whether syntax suffices for semantics and therefore understanding. From our evolutionary learning system perspective, which we discuss in Part I of this discussion, we see that all these processes are tied together, the processes of consciousness, intelligence, mind, thought, and language. In a bid to show the interconnectedness of these factors, we take up the question of understanding and its communication. Similar to our treatment of the subject of consciousness based intelligent systems in Part 1, here we treat understanding from first principles. Understanding In the real world when we use the term understanding, it has two main attributes; one is the capacity to infer, the other is the capacity to recognize or discern. In computing and AI contexts the word understanding is arguably tilted more in favor of inference than perception or cognition, in normal life and in the natural kingdom the reverse is true. This is primarily because AI's aims and present status look elemental when compared to the entities of the natural world. The other reason is that AI entities find it easier to infer than cognize, which is in itself a reflection of their design sources and its aims. For the purposes of this discussion the term understanding implies the natural version, a mix of cognition and inference. If we start from first principles, it is clear that for a rule to emerge out of a set of raw data, an inferential process has to run on it. This process could be a formal inferential process or a process that is driven by the needs of economy or efficiency. Rules need not always rise out of intentional activity, for instance the interaction of water flowing from an open tap into a pot already full of water can create a set of rules that disallow further water entry, limit mixing and regulate overflow, many natural rules rise from interactions like these.

Did natural consciousness and intelligent systems arise out of a path that was co-evolutionary to evolution? Can we explain human self-consciousness as having risen out of such an evolutionary path? If so how could it have been? In this first part of a two-part paper (titled IXI), we take a learning system perspective to the problem of consciousness and intelligent systems, an approach that may look unseasonable in this age of fMRI's and high tech neuroscience. We posit conscious intelligent systems in natural environments and wonder how natural factors influence their design paths. Such a perspective allows us to explain seamlessly a variety of natural factors, factors ranging from the rise and presence of the human mind, man's sense of I, his self-consciousness and his looping thought processes to factors like reproduction, incubation, extinction, sleep, the richness of natural behavior, etc. It even allows us to speculate on a possible human evolution scenario and other natural phenomena.