论文标题
直觉量化词的时间解释：单一案例
Temporal interpretation of intuitionistic quantifiers: Monadic case
论文作者
论文摘要
在最近的一篇论文中，我们表明直觉量化器承认以下时间解释：“将来永远”（以$ \ forall $）和“过去的某个时候”（对于$ \ for $ \ coments $）。在本文中，我们研究了直觉谓词逻辑的Monadic碎片$ \ sf MIPC $。众所周知，$ \ sf MIPC $被完全忠实地翻译成谓词$ \ sf s4 $（Gödeltranslation）的Monadic片段$ \ sf ms4 $。我们引入了$ \ sf s4 $的新时态扩展，该扩展由$ \ sf ts4 $表示，并将$ \ sf mipc $的替代完整和忠实的翻译提供为$ \ sf ts4 $，从而产生上述Monadic Intuitionistic量化器的时间解释。我们通过证明$ \ sf ms4 $和$ \ sf ts4 $都可以完全忠实地转换为$ \ sf ms4 $的时态扩展，我们用$ \ sf ms4.t $表示，我们可以将这种新翻译与Gödel翻译进行比较，并将其分解为$ \ sf ts4 $。这是通过利用介绍的新逻辑的代数和关系语义来完成的。作为副产品，我们证明了$ \ sf ms4.t $的有限模型属性（FMP），并证明所涉及的其他逻辑的FMP可以是由于所考虑的翻译的充实和忠诚而得出的。
In a recent paper we showed that intuitionistic quantifiers admit the following temporal interpretation: "always in the future" (for $\forall$) and "sometime in the past" (for $\exists$). In this paper we study this interpretation for the monadic fragment $\sf MIPC$ of the intuitionistic predicate logic. It is well known that $\sf MIPC$ is translated fully and faithfully into the monadic fragment $\sf MS4$ of the predicate $\sf S4$ (Gödel translation). We introduce a new tense extension of $\sf S4$, denoted by $\sf TS4$, and provide an alternative full and faithful translation of $\sf MIPC$ into $\sf TS4$, which yields the temporal interpretation of monadic intuitionistic quantifiers mentioned above. We compare this new translation with the Gödel translation by showing that both $\sf MS4$ and $\sf TS4$ can be translated fully and faithfully into a tense extension of $\sf MS4$, which we denote by $\sf MS4.t$. This is done by utilizing the algebraic and relational semantics for the new logics introduced. As a byproduct, we prove the finite model property (fmp) for $\sf MS4.t$ and show that the fmp for the other logics involved can be derived as a consequence of the fullness and faithfulness of the translations considered.
