This paper is divided into three parts. In the first part, we review the historical background of a system of logic devised by Henry S. Leonard to allow for reasoning using existence as a predicate. In the second part, we consider various directions in which his logic could be further developed, syntactically, semantically, and as an adjunct to quantifier elimination and set theory. In the third and final part, we develop proofs of some underlying results of his logic, using modern notation but retaining his axioms and rules of inference.
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机译：本文分为三个部分。在第一部分中，我们回顾了亨利·伦纳德（Henry S. Leonard）设计的逻辑系统的历史背景，该逻辑系统允许使用存在作为谓词进行推理。在第二部分中，我们考虑了可以在语法上，语义上进一步发展他的逻辑的各种方向，并作为量词消除和集合理论的辅助手段。在第三部分（也是最后一部分）中，我们使用现代符号表示法，但保留其公理和推理规则，以证明其逻辑的一些基本结果。
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