以拓扑理论为视角，从卢卡谢维奇逻辑的角度看热带化问题

arXiv - MATH - Logic Pub Date : 2024-09-13 DOI:arxiv-2409.08682

Antonio Di Nola, Giacomo Lenzi, Brunella Gerla

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引用次数: 0

摘要

本文的主要目的是证明{\L}ukasiewicz逻辑、语义和热带结构等主题是富有成果的。这给{\L}ukasiewicz逻辑带来了topos理论的视角。我们提出了在V(C)中对MV-代数进行函数化的方法。我们进一步考虑了一种基于完备MV-词组的逻辑，它的真值是布尔值的扰动，我们展示了这种逻辑如何展示与非交换几何的点在扇形上相连的模型。

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Tropicalization through the lens of Łukasiewicz logic, with a topos theoretic perspective

The main aim of this paper is to show that the topics of {\L}ukasiewicz logic, semirings and tropical structures fruitfully meet. This gives rise to a topos theoretic perspective to {\L}ukasiewicz logic. A functorial tropicalization of MV-algebras in the variety V(C) is proposed. We further consider a logic based on perfect MV-algebras and having truth values that are perturbations of boolean values, and we show how this logic can exhibit models functorially connected with points of a non-commutative geometry.

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arXiv - MATH - Logic

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