论文标题
Beth逻辑KR中的可确定性
Beth Definability in the Logic KR
论文作者
论文摘要
当且仅当代数类别中的每个代数类别中的每个表达式都是过滤时，beth可确定性属性具有可代数可逻辑的逻辑。使用这项技术，厄克特（Urquhart）在1999年表明，贝斯（Beth）的可辩率属性失败了，包括T，E和R在包括T，E和R的广泛类别。但是，这些逻辑的反例并未扩展到超级相关逻辑KR的代数对应物，即所谓的布尔型单体。在提出了Urquhart的建议之后，我们使用Freese构建的模块化晶格，以表明不必在广泛的关系代数中汇出了典范。该类包括布尔单型，因此Beth Distability属性因KR而失败。
The Beth Definability Property holds for an algebraizable logic if and only if every epimorphism in the corresponding category of algebras is surjective. Using this technique, Urquhart in 1999 showed that the Beth Definability Property fails for a wide class of relevant logics, including T, E, and R. However, the counterexample for those logics does not extend to the algebraic counterpart of the super relevant logic KR, the so-called Boolean monoids. Following a suggestion of Urquhart, we use modular lattices constructed by Freese to show that epimorphisms need not be surjective in a wide class of relation algebras. This class includes the Boolean monoids, and thus the Beth Definability Property fails for KR.
