One proof-theoretic approach to equality in quantificational logic treats equality as a logical connective: in particular, term equality can be given both left and right introduction rules in a sequent calculus proof system. We present a particular example of this approach to equality in a first-order logic setting in which there are no predicate symbols (apart from equality). After we illustrate some interesting applications of this logic, we show that provability in this logic is undecidable.

中文翻译：

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当相等是逻辑连接时证明搜索的不可判定性

量化逻辑中对等式的一种证明理论方法将等式视为逻辑连接词：特别是，可以在连续微积分证明系统中同时给出左右引入规则。我们在没有谓词符号（除相等之外）的一阶逻辑设置中展示了这种方法的特定示例。在我们说明了这个逻辑的一些有趣的应用之后，我们证明了这个逻辑中的可证明性是不可判定的。