论文标题
从不一致到不兼容
From inconsistency to incompatibility
论文作者
论文摘要
本文的目的是将正式不一致的逻辑（$ \ textbf {lfi} $ s）概括为处理不兼容概念的系统，该系统通过二元连接表示。基本思想是，拥有两个不兼容的公式来扣除扣除额，并且作为一种特殊情况，当$ \ textbf {lfi} $ s的意义上，公式变得一致（在$ \ textbf {lfi} $ s）上，当它与自己的否定不兼容时。我们展示了这种概念如何以非平凡的方式扩展到一致性，并为许多简单的$ \ textbf {lfi} $呈现保守的翻译，以介绍一些最基本的不兼容性逻辑，以确切的方式的证据是什么不合时宜地将一致性的概述概述为一致性。我们基于有限的非确定性矩阵为新逻辑以及决策程序提供语义。正如这里所证明的那样，根据blok-pigozzi不可用的代数也不可以代数，也无法通过有限的nmatrices来表征这些系统，这是合理的。最后，我们将逻辑与其他侧重于治疗不兼容的系统进行了比较，特别是由Brandom率先开发的逻辑，并由Peregrin进一步开发。
The aim of this article is to generalize logics of formal inconsistency ($\textbf{LFI}$s) to systems dealing with the concept of incompatibility, expressed by means of a binary connective. The basic idea is that having two incompatible formulas to hold trivializes a deduction, and as a special case, a formula becomes consistent (in the sense of $\textbf{LFI}$s) when it is incompatible with its own negation. We show how this notion extends that of consistency in a non-trivial way, presenting conservative translations for many simple $\textbf{LFI}$s into some of the most basic logics of incompatibility, what evidences in a precise way how the notion of incompatibility generalizes that of consistency. We provide semantics for the new logics, as well as decision procedures, based on restricted non-deterministic matrices. The use of non-deterministic semantics with restrictions is justified by the fact that, as proved here, these systems are not algebraizable according to Blok-Pigozzi nor are they characterizable by finite Nmatrices. Finally, we briefly compare our logics to other systems focused on treating incompatibility, specially those pioneered by Brandom and further developed by Peregrin.
