AQuARIUM:

A Hierarchically-Supported
Mono-Symbolic Language for Analogic Integration

Ron Cottam, Willy Ranson & Roger Vounckx

In press

NBU Series in Cognitive Science: Advances in Analogy Research:
Integration of Theory and Data from the Cognitive,
Computational and Neural Sciences , pp 408-409.
Edited by Keith Holyoak, Dedre Gentner and Boicho Kokinov
New Bulgarian University, Sofia, 1998, ISBN: 954-535-200-0

Abstract

            We propose a new contextually aware universal paradigm which can extend or replace formal logic, and which is capable of supporting hierarchical metastates and a description of the development of life and consciousness through evolutionary computation.

            In presupposing a coherent universe, we acknowledge the correlation of its constituent properties and processes, and accept that all of its regions must remain communicative to support coherence. Distinguishable forms then exist through the actions of one coherent set of processes. Successful survivalist processing of massive amounts of real-time data by living entities necessitates the availability of simplified but locally representative models of "reality" which are couched in terms familiar to the processor: the use of analogues.

            The selection of favourable analogues follows the same criteria and suffers from the same difficulties as does their successful linguistic transmission. We can integrate these two processes into a single format, that of a unified hierarchical symbolic language which displays only-partially-deterministic coupling between its formally represented parts. "AQuARIUM"** provides a framework for this symbolic language, which consists initially of only a single symbol. The symbol contains just enough information to invite questions as to its significance, without presenting sufficient detail for an intelligently inquisitive "selector" to be sure of the correctness of an initial guess as to its meaning. The nature of the resulting questions can then be used to evaluate the context into which more detailed description will be placed, rather than presupposing unilaterally a "correct" comprehensional context.

            Separate analogues emerge from "reality" as structures which correspond to the formulation of "locally sufficient" approximating metastatic representations of an otherwise partially disordered or chaotic region of the universal phase space. Consequently, an analogue is always to some extent defective in its detail, in that it must of necessity exhibit differences from its "real" counterpart. Internally, for an "originating" processor, the use of a selected analogue is relatively simple, given a good memory of which characteristics have been selected as, or determined to be, "correct" analogous details. However, the transfer of an analogue from one processor to another is fraught with dangers. The major difficulty in selecting a transferable analogue is to match the "representative" characteristics recognised by its creator to those which are interpreted by its receptor. For example, in likening the flow of "electrons" through a network of wires and switches, to the early-morning rush of commuters through tunnels and barriers in accessing the Metro, we should not assume that "electrons" carry briefcases with them, nor that first of all they kiss their wives goodbye before commencing the journey.

            Communication of an idea from one processor to another depends on an equivalence of both of their logic systems and their data environments, or alternatively on a successful manner of evaluating any differences between these and correcting for them. This always necessitates a two-directional process where ultimately it will be unimportant which of the two processors initiated the communication, but only whether this evaluation and correction has been successfully carried out. The implied correspondence to inter-processor cooperation is inherent to the framework provided by AQuARIUM.

            Ultimately, in a coherent universe, all analogues of all "realities" are equivalent when account is taken of their associated approximations, and they can consequently all be integrated into a descriptive language of this kind. The maintenance of universal coherence requires continuous communication between all stable metastatic entities, yet the natural presence of an Einsteinian communication restriction eliminates the possibility of instantaneous direct correlation in a causally coherent domain. Formally defined metastates cannot communicate directly with each other, and any communication which does occur must take place at least partially through the causal chaos represented by nonlocality. The complete range of possibilities between these two extremes can initially be modeled in AQuARIUM by a modified recursive form of Dempster-Schafer probability.


**AQuARIUM: "A Query and And Reflection Interaction Using MAGIC: Mathematical Algorithms Generating Interdependent Confidences"
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