A Meta-Logic of Inference Rules: Syntax

TL;DR

This paper introduces a meta-language for analyzing multiple-conclusion inference rules that include asserted and rejected propositions, addressing the impact of rejected propositions and reverse substitution on structurality.

Contribution

It proposes a new framework for handling rejected propositions and reverse substitution within the meta-language for inference rules.

Findings

Defined a new concept of structurality accommodating rejected propositions

Extended the meta-language to include multiple-conclusion inference rules

Analyzed the implications of rejected propositions on rule structurality

Abstract

This work was intended to be an attempt to introduce the meta-language for working with multiple-conclusion inference rules that admit asserted propositions along with the rejected propositions. The presence of rejected propositions, and especially the presence of the rule of reverse substitution, requires certain change the definition of structurality.