Translating Metainferences Into Formulae

• DOI: 10.26686/ajl.v18i7.6801
• Publication Date: 2022-03-10T02:24:21Z
• Authors: Ariel Jonathan Roffé; Federico Pailos
• Keywords: Soundness; Tautology (logic); Sequent; Completeness (order theory); Base (topology)

In this paper, we present a way to translate the metainferences of mixed metainferential system into formulae an extended-language system, called its associated σ-system. To do this, σ-system will contain new operators (one for each standard), σ operators, which represent notions "belonging (given) standard". We first prove, in model-theoretic way, that these translations preserve (in)validity. That is, metainference is valid base if and only translation tautology corresponding then use results obtain other key advantages. Most interestingly, provide recipe building unlabeled sequent calculi σ-systems. exemplify with useful logics ST family, prove soundness completeness it, indirectly gives us calculus all those systems. Finally, respond some possible objections show how our σ-framework can shed light on “obeying” discussion within contexts