RPL的有效性及其在连续逻辑中的应用
Effectiveness in RPL, with Applications to Continuous Logic
摘要：
本文介绍了有理Pavelka逻辑（RationalPavelka逻辑的一种推广）和连续逻辑的可计算模型论的基础，并证明了模型论中某些定理的有效形式。我们展示了如何减少连续逻辑理性Pavelka逻辑。我们还定义了概念的可计算性和可判定性的模型的逻辑与可计算的，但不可数的，一组真假值，证明程度的公式w.r.t.线性理论是可计算的，并利用这一点进行有效的亨金建设。因此，对于连续逻辑中任何有效给定的相容线性理论，我们有效地产生了它的可判定模型。这是最好的可能，因为我们表明，连续逻辑的可计算模型论是经典逻辑的可计算模型论的扩展。我们的结论是，注意到一个可分离分类和可计算公理化理论（如概率空间或$L^p$巴拿赫格）的唯一可分离模型是可判定的。
英文摘要：
In this paper, we introduce a foundation for computable model theory of rational Pavelka logic (an extension of Łukasiewicz logic) and continuous logic, and prove effective versions of some theorems in model theory. We show how to reduce continuous logic to rational Pavelka logic. We also define notions of computability and decidability of a model for logics with computable, but uncountable, set of truth values; show that provability degree of a formula w.r.t. a linear theory is computable, and use this to carry out an effective Henkin construction. Therefore, for any effectively given consistent linear theory in continuous logic, we effectively produce its decidable model. This is the best possible, since we show that the computable model theory of continuous logic is an extension of computable model theory of classical logic. We conclude with noting that the unique separable model of a separably categorical and computably axiomatizable theory (such as that of a probability space or an $L^p$ Banach lattice) is decidable.
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