Hilbert空间作为不定承诺选择算子
Hilbert's epsilon as an Operator of Indefinite Committed Choice
摘要：
保罗·伯奈斯和大卫·希尔伯特谨慎地避免了对希尔伯特的ε算子的过度描述，只公理化了与他们的证明论研究相关的东西。从语义上讲，这使得ε运算符被低估了。与此同时，有几个建议的语义的选择操作符。在回顾了希尔伯特的算子语义的文献后，我们提出了一个新的语义，具有以下特点：我们避免了过度规范（如右唯一性），但承认不定选择，承诺选择和经典逻辑。此外，我们的语义的证明搜索支持最佳的，是自然的，在这个意义上，它不仅反映了一些情况下的指涉解释的不定冠词在自然语言，但也可能有助于语言哲学。最后，我们问的问题，我们的自由变量框架内的语义是否可以作为一个有用的规范和计算的话语在自然语言的范例。
英文摘要：
Paul Bernays and David Hilbert carefully avoided overspecification of Hilbert's epsilon-operator and axiomatized only what was relevant for their proof-theoretic investigations. Semantically, this left the epsilon-operator underspecified. In the meanwhile, there have been several suggestions for semantics of the epsilon as a choice operator. After reviewing the literature on semantics of Hilbert's epsilon operator, we propose a new semantics with the following features: We avoid overspecification (such as right-uniqueness), but admit indefinite choice, committed choice, and classical logics. Moreover, our semantics for the epsilon supports proof search optimally and is natural in the sense that it does not only mirror some cases of referential interpretation of indefinite articles in natural language, but may also contribute to philosophy of language. Finally, we ask the question whether our epsilon within our free-variable framework can serve as a paradigm useful in the specification and computation of semantics of discourses in natural language.
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