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A Note on Strong Axiomatization of Gödel Justification Logic
Studia Logica ( IF 0.7 ) Pub Date : 2019-08-01 , DOI: 10.1007/s11225-019-09871-4
Nicholas Pischke

Justification Logics are special kinds of modal logics which provide a framework for reasoning about epistemic justification. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators "$t:$", indexed over $t$ by a corresponding set of justification terms, which thus explicitly encode the justification for the necessity assertion in the syntax. With these operators, one can therefore not only reason about modal effects on propositions but also about dynamics inside the justifications themselves. We replace this classical boolean base with G\"odel logic, one of the three most prominent fuzzy logics, i.e. special instances of many-valued logics, taking values in the unit interval $[0,1]$, which are intended to model inference under vagueness. We extend the canonical possible-world semantics for Justification Logic to this fuzzy realm by considering fuzzy accessibility- and evaluation-functions evaluated over the minimum t-norm and establish strong completeness theorems for various fuzzy analogies of prominent extensions for basic Justification Logic.

中文翻译:

关于哥德尔证明逻辑的强公理化的注记

证成逻辑是一种特殊的模态逻辑,它提供了一个关于认知证成的推理框架。为此,他们通过一系列必要性样式的模态运算符“$t:$”扩展了经典的布尔命题逻辑,通过一组相应的证明项在 $t$ 上进行索引,从而明确地编码了必要性断言的证明句法。有了这些算子,人们不仅可以推理对命题的模态效应,还可以推理论证本身内部的动态。我们将这个经典的布尔基替换为 G\"odel 逻辑,这是三个最突出的模糊逻辑之一,即多值逻辑的特殊实例,取单位区间 $[0,1]$ 中的值,旨在建模模糊下的推理。
更新日期:2019-08-01
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