On the Costs of Nonclassical Logic
On the Costs of Nonclassical Logic
复制标题
论非经典逻辑的成本
DOI：
10.1007/s10992-017-9424-3
复制
发表时间：
2017
影响因子：
1.5
通讯作者：
Carlo Nicolai
中科院分区：
文献类型：
--
作者：
V. Halbach;Carlo Nicolai
语义悖论的解决通常涉及对语义词汇的经典逻辑的限制。在本文中，我们在一个模型案例中研究了这些限制的代价。特别地，我们确定了两个捕捉相同真理概念的真理系统：（一个变体）用经典逻辑表述的Feferman的KF系统（符号逻辑杂志，56,1 - 49,1991），以及（一个变体）用基本De Morgan逻辑表述的Halbach和Horsten的PKF系统（符号逻辑杂志，71,677 - 712,2006）。已知经典系统比非经典系统强得多。我们通过证明PKF的真值理论原理不能被指责来评估这种不对称的原因：归纳限于非语义词汇的PKF实际上与限制版本的KF证明为真相一致。
Solutions to semantic paradoxes often involve restrictions of classical logic for semantic vocabulary. In the paper we investigate the costs of these restrictions in a model case. In particular, we fix two systems of truth capturing the same conception of truth: (a variant) of the system KF of Feferman (The Journal of Symbolic Logic, 56, 1–49, 1991) formulated in classical logic, and (a variant of) the system PKF of Halbach and Horsten (The Journal of Symbolic Logic, 71, 677–712, 2006), formulated in basic De Morgan logic. The classical system is known to be much stronger than the nonclassical one. We assess the reasons for this asymmetry by showing that the truth theoretic principles of PKF cannot be blamed: PKF with induction restricted to non-semantic vocabulary coincides in fact with what the restricted version of KF proves true.