I deal with two approaches to proof-theoretic semantics: one based on argument structures and justifications, which I call reducibility semantics, and one based on consequence among (sets of) formulas over atomic bases, called base semantics. The latter splits in turn into a standard reading, and a variant of it put forward by Sandqvist. I prove some results which, when suitable conditions are met, permit one to shift from one approach to the other, and I draw some of the consequences of these results relative to the issue of completeness of (recursive) logical systems with respect to proof-theoretic notions of validity. This will lead me to focus on a notion of base-completeness, which I will discuss with reference to known completeness results for intuitionistic logic. The general interest of the proposed approach stems from the fact that reducibility semantics can be understood as a labelling of base semantics with proof-objects typed on (sets of) formulas for which a base semantics consequence relation holds, and which witness this very fact. Vice versa, base semantics can be understood as a type-abstraction of a reducibility semantics consequence relation obtained by removing the witness of the fact that this relation holds, and by just focusing on the input and output type of the relevant proof-object.

翻译：本文探讨两种证明论语义学方法：一种基于论证结构与证成，我称之为可归约性语义学；另一种基于原子基上（集合）公式间的后承关系，称为基语义学。后者进一步分为标准解读及其变体，后者由Sandqvist提出。我证明了一些结果，这些结果在满足适当条件时允许从一种方法转换到另一种方法，并针对逻辑系统相对于证明论有效性概念的（递归）完备性问题，推导出这些结果的部分推论。这将引导我聚焦于基完备性概念，并参照直觉主义逻辑的已知完备性结果进行讨论。所提方法的普遍意义在于，可归约性语义学可理解为对基语义学的标注，其中证明对象以（集合）公式为类型，这些公式满足基语义学的后承关系，且证明对象本身即为该关系的见证。反之，基语义学可理解为可归约性语义学后承关系的类型抽象，通过移除该关系成立的见证，仅关注相关证明对象的输入与输出类型而实现。