A version of intuitionistic type theory is extended with opposite types, allowing a different formalization of negation and obtaining a paraconsistent type theory ($\textsf{PTT} $). The rules for opposite types in $\textsf{PTT} $ are based on the rules of the so-called constructible falsity. A propositions-as-types correspondence between the many-sorted paraconsistent logic $\textsf{PL}_\textsf{S} $ (a many-sorted extension of López-Escobar’s refutability calculus presented in natural deduction format) and $\textsf{PTT} $ is proven. Moreover, a translation of $\textsf{PTT} $ into intuitionistic type theory is presented and some properties of $\textsf{PTT} $ are discussed.

中文翻译：

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具有对立类型的类型论：一种平行一致的类型论

直觉主义类型理论的一个版本被扩展为相反的类型，允许不同的否定形式化并获得一个平行一致的类型理论（$\textsf{PTT} $）。$\textsf{PTT} $ 中相反类型的规则是基于所谓的可构造虚假的规则。命题作为类型对应于多排序的平行一致逻辑 $\textsf{PL}_\textsf{S} $（López-Escobar 可反驳性演算的多排序扩展，以自然演绎格式呈现）和 $\textsf{ PTT} $ 被证明。此外，还提出了将$\textsf{PTT} $ 翻译成直觉类型理论并讨论了$\textsf{PTT} $ 的一些性质。