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Computing Truth Values in the Topos of Infinite Peirce’s α-Existential Graphs

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  • Tohmé, Fernando
  • Caterina, Gianluca
  • Gangle, Rocco

Abstract

We present here an approach to the analysis of the truth values of Peirce’s α-graphs without the restriction of finite number of elements (cuts and characters) on the Sheet of Assertion. We show that the ensuing structure in which such graphs are objects constitutes a topos. While the computation of the truth value of a graph in the topos can be an infinite process, we show that using the concept of grossone (①) the subobject classifier of the topos allows to determine a truth value for each graph.

Suggested Citation

  • Tohmé, Fernando & Caterina, Gianluca & Gangle, Rocco, 2020. "Computing Truth Values in the Topos of Infinite Peirce’s α-Existential Graphs," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    • Handle: RePEc:eee:apmaco:v:385:y:2020:i:c:s0096300320302964
    DOI: 10.1016/j.amc.2020.125343
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    References listed on IDEAS

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    1. Cococcioni, Marco & Pappalardo, Massimo & Sergeyev, Yaroslav D., 2018. "Lexicographic multi-objective linear programming using grossone methodology: Theory and algorithm," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 298-311.
    2. Kauffman, Louis H., 2015. "Infinite computations and the generic finite," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 25-35.
    3. Caldarola, Fabio, 2018. "The Sierpinski curve viewed by numerical computations with infinities and infinitesimals," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 321-328.
    4. Sergeyev, Yaroslav D., 2007. "Blinking fractals and their quantitative analysis using infinite and infinitesimal numbers," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 50-75.
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