文章基本信息

标题：Information Flow in Logics in the Vicinity of BB
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作者：Andrew Tedder
期刊名称：Australasian Journal of Logic
印刷版ISSN：1448-5052
电子版ISSN：1448-5052
出版年度：2021
卷号：18
期号：1
页码：1-24
DOI：10.26686/ajl.v18i1.6288
出版社：Philosophy Department, University of Melbourne
摘要：Situation theory in general, and channel theory in particular, have been used to provide motivational accounts of the ternary relation semantics of relevant, substructural, and various non-classical logics. Among the constraints imposed by channel-theory, one must posit a certain existence criterion for situations which result from the composites of multiple channels (this is used in modeling information flow). In logics obeying a certain associativity condition, it is relatively straightforward to show that a certain such condition is met, but the problem is trickier in non-associative logics. Following Tedder (2017), where it was shown that the conjunction-conditional fragment of the logic B admits the existence of composite channels, I present a generalised version of the previous argument, appropriate to logics with disjunction, using the neighbourhood ternary relation semantic framework. I close by suggesting that the logic BB (∧I) , which falls in between Lavers’ system BB and the standard ‘minimal’ relevant logic B , satisfies the conditions for the general argument to go through.
其他摘要：Situation theory, and channel theory in particular, have been used to provide motivational accounts of the ternary relation semantics of relevant, substructural, and various non-classical logics. Among the constraints imposed by channel-theory, we must posit a certain existence criterion for situations which result from the composites of multiple channels (this is used in modeling information flow). In associative non-classical logics, it is relatively easy to show that a certain such condition is met, but the problem is trickier in non-associative logics. Following Tedder (2017), where it was shown that the conjunction-conditional fragment of the logic B admits the existence of composite channels, I present a generalised ver- sion of the previous argument, appropriate to logics with disjunction, in the neighbourhood ternary relation semantic framework. I close by suggesting that the logic BB (^I), which falls between Lavers' system BB and B , satisfies the conditions for the general argument to go through (and prove that it satisfies all but one of those conditions).