On the Semantics of Intensionality
On the Semantics of Intensionality
复制标题
论内涵性语义
DOI：
10.1007/978-3-662-54458-7_32
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
G. A. Kavvos
中科院分区：
文献类型：
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作者：
G. A. Kavvos
在本文中，我们提出了一个范畴理论的内涵。我们首先回顾内涵的概念，并讨论它与逻辑和计算机科学的相关性。事实证明，1-范畴理论并不是研究外延和内涵相互作用的最合适的工具。因此，我们考虑\v{C}ubri\'{c}，Dybjer和Scott的P-范畴，它们是仅在部分等价关系（PER）下的范畴。在这种情况下，我们引入了一个新的P-范畴结构，即暴露。暴露非常接近函子，除了它们不保留P-范畴的PER。受模态逻辑范畴语义学的启发，我们开始发展他们的理论。我们的主要例子表明，暴露是一个抽象的行为良好的内涵设备，如哥德尔编号。其结果是一个统一的框架，在这个框架中，Kleene，Godel，Tarski和Rice的经典结果找到了简洁，清晰的公式，并且在他们的证明中涉及的每个逻辑设备或假设都可以用相同的代数方式表示。
In this paper we propose a categorical theory of intensionality. We first revisit the notion of intensionality, and discuss we its relevance to logic and computer science. It turns out that 1-category theory is not the most appropriate vehicle for studying the interplay of extension and intension. We are thus led to consider the P-categories of \v{C}ubri\'{c}, Dybjer and Scott, which are categories only up to a partial equivalence relation (PER). In this setting, we introduce a new P-categorical construct, that of exposures. Exposures are very nearly functors, except that they do not preserve the PERs of the P-category. Inspired by the categorical semantics of modal logic, we begin to develop their theory. Our leading examples demonstrate that an exposure is an abstraction of well-behaved intensional devices, such as G\"odel numberings. The outcome is a unifying framework in which classic results of Kleene, G\"odel, Tarski and Rice find concise, clear formulations, and where each logical device or assumption involved in their proofs can be expressed in the same algebraic manner.
脱敏谷氨酸受体塑造虎蝾螈视网膜神经节细胞的兴奋性突触输入。
DOI：
10.1523/jneurosci.15-09-06189.1995
发表时间：
1995
期刊：
The Journal of neuroscience : the official journal of the Society for Neuroscience.
影响因子：
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作者：
Lukasiewicz,PD;Lawrence,JE;Valentino,TL
通讯作者：
Valentino,TL