A logic of hypothetical conjunction

A logic of hypothetical conjunction
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假设合取逻辑

DOI:
10.1093/logcom/exz018
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发表时间:
2019
影响因子:
0.7
通讯作者:
Collinson M
Collinson M
中科院分区:
计算机科学4区
文献类型:
--
作者:
Collinson M

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考虑了一个二进制连接词,它可以作为许多条件逻辑中条件连接词的匹配连接词来读取。阅读这个连接词最自然的方式通常是作为一个连词,然而,假设地,被认为是在假设下可以获得的一种状态。连接词可以被赋予一个内涵语义,扩展了在可能世界上使用二元关系的命题索引族的条件逻辑的标准语义。该语义由支持条件语义和新连接的操作之间的伴随关系决定。假设性连接词的语义包含了由三元关系语义支持的与子结构和相关逻辑相关的融合连接词的语义,因此包含了许多其他形式的连接词。讨论了假设连接连接的一些应用,包括在计算机科学应用中使用的资源推理的广义形式。
A binary connective that can be read as a matching conjunction for conditional connectives found in many conditional logics is considered. The most natural way to read this connective is often as a conjunctionand yet, hypothetically, considered to hold of a state of affairs that could be obtained under the hypothesis. The connective can be given an intensional semantics extending a standard semantics of conditional logic that uses propositionally indexed families of binary relations on possible worlds. This semantics is determined by an adjoint relationship between the operations supporting the semantics of the conditional and the new conjunction. The semantics of the hypothetical conjunction connective subsumes the semantics, supported by a ternary relation semantics, of the fusion connective that arises in connection with substructural and relevant logics, and therefore subsumes a number of other forms of conjunction. A number of applications of the hypothetical conjunction connective are discussed, including generalized forms of resource reasoning used in computer science applications.
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