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An Open Logic Approach to EPM
1  Politecnico di Milano, Italy

Abstract: Recently, Elementary Pragmatic Model (EPM) intrinsic Self-Reflexive Functional Logical Closure contributed to find an original solution to the dreadful double-bind problem in classic information and algorithmic theory. EPM is a high didactic versatile tool and new application areas are envisaged continuosly. In turn, this new awareness has allowed to enlarge our panorama for neurocognitive system behaviour understanding, and to develop information conservation and regeneration systems in a numeric self-reflexive/reflective evolutive reference framework. Unfortunately, a logically closed model cannot cope with ontological uncertainty by itself; it needs a complementary logical aperture operational support extension. We apply to EPM our Anticipatory Learning System (ALS) approach. In this way, it is possible to use two coupled irreducible information management subsystems, based on the following ideal coupled irreducible asymptotic dichotomy: "Information Reliable Predictability" and "Information Reliable Unpredictability" subsystems. To behave realistically, overall system must guarantee both Logical Closure and Logical Aperture, both fed by environmental "noise" (better... from what human beings call "noise"). So, a natural operating point can emerge as a new Trans-disciplinary Reality Level, out of the Interaction of Two Complementary Irreducible Information Management Subsystems. Building on this idea, it is possible to create an Evolutive Elementary Pragmatic Model (E2PM) able to profit by both classic EPM intrinsic Self-Reflexive Functional Logical Closure and new numeric Self-Reflective Functional Logical Aperture. EPM can be thought as a reliable starting subsystem to initialize a process of continuous self-organizing and self-logic learning refinement. Through the hypercube geometric algebra, we propose a notation that goes beyond a format distinction and constructed with the purpose to facilitate inferences either on a diagrammatic representation, or a lexical one. The latter particularly allows operations on complex propositions within hypercube with more than three dimensions, mentally difficult to imagine.
Keywords: EPM; machine learning; system theory; elementary pragmatic model; cybernetics; general systems theory