不确定性的命题类型理论

IF 0.6 3区数学 Q2 LOGIC

Studia Logica Pub Date : 2024-05-03 DOI:10.1007/s11225-024-10099-0

Víctor Aranda, Manuel Martins, María Manzano

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引用次数: 0

摘要

本文的目的是定义一个部分命题类型理论。我们的系统在双重意义上是部分的：（命题）类型的层次结构包含部分函数，语言的某些表达（包括公式）可能是未定义的。我们对未定义值的具体解释是克莱因的强不确定性逻辑。我们提出了新系统的语义，并证明层次结构中任何域的每个元素在对象语言中都有一个名称。最后，我们提供了一个证明系统和一个（构造性）完备性证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Propositional Type Theory of Indeterminacy

The aim of this paper is to define a partial Propositional Type Theory. Our system is partial in a double sense: the hierarchy of (propositional) types contains partial functions and some expressions of the language, including formulas, may be undefined. The specific interpretation we give to the undefined value is that of Kleene’s strong logic of indeterminacy. We present a semantics for the new system and prove that every element of any domain of the hierarchy has a name in the object language. Finally, we provide a proof system and a (constructive) proof of completeness.

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来源期刊

Studia Logica MATHEMATICS-LOGIC

CiteScore

1.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The leading idea of Lvov-Warsaw School of Logic, Philosophy and Mathematics was to investigate philosophical problems by means of rigorous methods of mathematics. Evidence of the great success the School experienced is the fact that it has become generally recognized as Polish Style Logic. Today Polish Style Logic is no longer exclusively a Polish speciality. It is represented by numerous logicians, mathematicians and philosophers from research centers all over the world.