A reasoned argument or tarka is essential for a wholesome vāda that aims at establishing the truth. A strong tarka constitutes of a number of elements including an anumāna based on a valid hetu. Several scholars, such as Dharmakīrti, Vasubandhu and Dignāga, have worked on theories for the establishment of a valid hetu to distinguish it from an invalid one. This paper aims to interpret Dignāga’s hetu-cakra, called the wheel of grounds, from a modern philosophical perspective by deconstructing it into a simple probabilistic mathematical model. The objective is to understand how and why a vāda based on a probabilistically weaker hetu can degrade into a Jalpa or vitaṇḍā. To do so, the paper maps the concept of ‘Bounded Rationality’ onto the hetu-cakra. Bounded Rationality, an idea coined by the management thinker Herbert Simon, is often employed in understanding decision-making processes of rational agents. In the context of this paper, the concept would state that the prativādin and ālocaka (debater) may not hold unbounded information to back their pratijnā (proposition). The paper argues that within the probabilistically deconstructed hetu-cakra model, most people argue in the ‘Zone of Bounded Rationality’, and thus, the probability of a debate degrading into Jalpa or vitaṇḍā is high.

中文翻译：

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迪尼亚加的赫图·卡克拉的数学模型

对于旨在建立真相的有益健康的论证，合理的论证或“ tarka”必不可少。坚硬的柏油由许多元素组成，包括基于有效hetu的anumāna。Dharmakīrti，Vasubandhu和Dignāga等几位学者研究了建立有效hetu的理论，以区别于无效的hetu。本文旨在通过将其分解为简单的概率数学模型，从现代哲学的角度来解释狄加纳加的“地轮”。目的是了解基于概率较弱的hetu的vāda如何以及为什么会退化为Jalpa或vitaṇḍā。为此，本文将“有限理性”的概念映射到了hetu-cakra上。管理思想家赫伯特·西蒙（Herbert Simon）提出的有限理性 通常用于理解理性主体的决策过程。在本文的上下文中，该概念将说明prativādin和ālocaka（战斗员）可能没有掌握无穷信息来支持其pratijnā（命题）。该论文认为，在概率解构的hetu-cakra模型中，大多数人都在“有限理性区”中争论，因此，辩论降级为Jalpa或vitaṇḍā的可能性很高。