从IF到BI：一个依赖与分离的故事
From IF to BI: a tale of dependence and separation
摘要：
我们需要一个新的眼光在逻辑的信息依赖和独立的Hintikka和Sandu和Vaananen，和他们的组成语义由于霍奇斯。我们如何霍奇斯的语义可以被看作是一个特殊的情况下，一般建设，这提供了一个背景下，一个有用的完整性定理，就更广泛的一类模型。我们对逻辑的每个方面都有一些新的认识。我们表明，自然命题逻辑所携带的语义是捆绑的蕴涵由于Pym和O 'Hearn，它结合了直觉和乘法连接词的逻辑。这引入了几个新的连接词以前没有考虑在逻辑的信息依赖，但我们显示发挥了非常自然的作用，最显着的直觉含义。至于量词，我们表明，他们在霍奇斯语义的解释是被迫的，因为他们是下的图像通常的塔斯基语义的一般建设，这意味着他们是伴随着替代，因此唯一确定。至于依赖谓词，我们表明，这是从一个更简单的谓词，恒常性或依赖于没有定义。这就离不开直觉蕴涵的运用。然后将函数相关的Armstrong公理恢复为直觉蕴涵公理的标准集。我们还证明了Hodges风格的完全抽象结果，其中直觉蕴涵起着非常自然的作用。
英文摘要：
We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Vaananen, and their compositional semantics due to Hodges. We show how Hodges' semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics is the logic of Bunched Implications due to Pym and O'Hearn, which combines intuitionistic and multiplicative connectives. This introduces several new connectives not previously considered in logics of informational dependence, but which we show play a very natural role, most notably intuitionistic implication. As regards the quantifiers, we show that their interpretation in the Hodges semantics is forced, in that they are the image under the general construction of the usual Tarski semantics; this implies that they are adjoints to substitution, and hence uniquely determined. As for the dependence predicate, we show that this is definable from a simpler predicate, of constancy or dependence on nothing. This makes essential use of the intuitionistic implication. The Armstrong axioms for functional dependence are then recovered as a standard set of axioms for intuitionistic implication. We also prove a full abstraction result in the style of Hodges, in which the intuitionistic implication plays a very natural rôle.
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