保守翻译的普遍性
The ubiquity of conservative translations
摘要：
我们研究的概念之间的保守翻译的逻辑介绍费托萨和D'Ottaviano。我们表明，经典命题逻辑（CPC）是普遍的，在这个意义上说，每一个有限的后果关系在一个可数集的公式可以保守地转换成CPC。如果结果关系是可判定的，则转换是可计算的。更一般地说，我们可以采取，而不是CPC广泛的一类逻辑（扩展的某个片段的完整的Lambek演算FL），包括大多数非经典逻辑在文献中研究，因此在某种意义上说，（几乎）任何两个合理的演绎系统可以保守地翻译成对方。我们还给出了一些反例，特别是次协调逻辑LP不是普适的。
英文摘要：
We study the notion of conservative translation between logics introduced by Feitosa and D'Ottaviano. We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set of formulas can be conservatively translated into CPC. The translation is computable if the consequence relation is decidable. More generally, we show that one can take instead of CPC a broad class of logics (extensions of a certain fragment of full Lambek calculus FL) including most nonclassical logics studied in the literature, hence in a sense, (almost) any two reasonable deductive systems can be conservatively translated into each other. We also provide some counterexamples, in particular the paraconsistent logic LP is not universal.
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