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Discovering the discovery of the hierarchy of formal languages

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Abstract

The hierarchy of formal languages is a mathematical representation of linguistic geometry (LG). LG is a type of game theory for a class of extensive discrete games called abstract board games (ABG), scalable to the level of real life defense systems. LG is a formal model of human reasoning about armed conflict, a mental reality “hard-wired” in the human brain. LG, an evolutionary product of millions of years of human warfare, must be a component of the primary language of the human brain (as introduced by Von Neumann). Experiences of development of LG must be instructive for solving another major puzzle, discovering the algorithm of discovery, yet another ancient component of the primary language. This paper reports results on discovering mental processes involved in the development of the hierarchy of formal languages. Those mental processes manifesting execution of the algorithm of discovery are called visual streams. This paper reveals the visual streams that were involved in the thought experiments led to the development of the formal theory of LG. Specifically, it demonstrates the streams involved in choosing the formal-linguistic representation of LG; the type of formal languages and grammars, the so-called controlled grammars; the construction of the grammars of shortest trajectories and the grammar of zones. This paper introduces a hypothesis of how we construct and focus visual streams.

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  1. STILMAN Advanced Strategies, Denver, CO, USA

    Boris Stilman

  2. University of Colorado Denver, Denver, CO, USA

    Boris Stilman

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  1. Boris Stilman
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Correspondence to Boris Stilman.

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Stilman, B. Discovering the discovery of the hierarchy of formal languages. Int. J. Mach. Learn. & Cyber. 5, 517–541 (2014). https://doi.org/10.1007/s13042-012-0146-0

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