In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with multiple sequent arrows satisfying some specific conditions, which we will lay out in this paper. We will unfold our ideas with the help of a case study in logical tetralateralism and present an extension of Almukdad and Nelson’s propositional constructive four-valued logic by unary operations of meaningfulness and nonsensicality. We will argue that in sequent calculi with multiple sequent arrows it is possible to maintain certain features that are desirable if we assume an understanding of the meaning of connectives in the spirit of proof-theoretic semantics. The use of multiple sequent arrows will be justified by the presence of congruentiality-breaking unary connectives.

在本文中，我们将在证明论语义的背景下考虑双边主义的现有概念，并根据我们对双边主义的理解提出逻辑多边主义的扩展。这种方法与之前以该名称提出的方法不同，因为我们不认为多重言语行为是这种理论的核心，而是多重后果关系。我们认为，为了实现这一目标，最有益的证明理论实现是使用满足某些特定条件的多个顺序箭头的顺序演算，我们将在本文中对此进行阐述。我们将借助逻辑四边主义的案例研究来展开我们的想法，并通过有意义和无意义的一元运算来扩展 Almukdad 和 Nelson 的命题构造性四值逻辑。我们将论证，在具有多个连续箭头的连续演算中，如果我们假设本着证明理论语义的精神理解连接词的含义，则可以保持某些所需的特征。多个连续箭头的使用将通过破坏同余性的一元连接词的存在来证明是合理的。