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Single-Assumption Systems in Proof-Theoretic Semantics
Journal of Philosophical Logic ( IF 0.7 ) Pub Date : 2022-04-25 , DOI: 10.1007/s10992-022-09658-4
Leonardo Ceragioli 1
Affiliation  

Proof-theoretic semantics is an inferentialist theory of meaning, usually developed in a multiple-assumption and single-conclusion framework. In that framework, this theory seems unable to justify classical logic, so some authors have proposed a multiple-conclusion reformulation to accomplish this goal. In the first part of this paper, the debate originated by this proposal is briefly exposed and used to defend the diverging opinion that proof-theoretic semantics should always endorse a single-assumption and single-conclusion framework. In order to adopt this approach some of its criteria of validity, especially separability, need to be weakened. This choice is evaluated and defended. The main argument in this direction is based on the circular dependences of meaning between multiple assumptions and conjunctions, and between multiple conclusions and disjunctions. In the second part of this paper, some systems that suit the new requirements are proposed for both intuitionistic and classical logic. A proof that they are valid, according to the weakened criteria, is sketched.



中文翻译:

证明论语义中的单假设系统

证明论语义学是一种推理主义的意义理论,通常在多重假设和单一结论的框架中发展。在该框架下,该理论似乎无法证明经典逻辑的合理性,因此一些作者提出了多重结论重构来实现这一目标。在本文的第一部分,由该提案引发的辩论被简要暴露并用于捍卫不同的观点,即证明论语义应该始终支持单一假设和单一结论框架。为了采用这种方法,它的一些标准有效性,尤其是可分离性,需要削弱。这个选择被评估和辩护。这个方向的主要论点是基于多个假设和连词之间以及多个结论和析取之间的意义的循环依赖。在本文的第二部分,针对直觉逻辑和经典逻辑提出了一些适合新要求的系统。根据弱化的标准,它们是有效的证明被勾勒出来。

更新日期:2022-04-26
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