arXiv:2607.09729cs.AIcs.LO2026-07

提出首个无需排除矛盾假设的逻辑扩张方法,避免知识体系崩溃。

AGM-like Paraconsistent Partial Meet Abductive Expansion Operation

论文配图:AGM-like Paraconsistent Partial Meet Abductive Expansion Operation
图 1 · 摘自论文原文
  • 基于可容忍矛盾的逻辑框架,构建新型归纳推理扩张机制。
  • 在保持认知一致性前提下,可处理相互矛盾的解释假设。
  • 适合研究信念修正与非经典逻辑的学者参考。

1996年,Maurice Pagnucco首次提出类AGM归纳扩张操作。本文在此基础上,借鉴Atocha Aliseda的分类体系,提出一种新的真值矛盾容忍型类AGM归纳扩张操作——AGMpabd,该操作可在不导致认知状态荒谬化的前提下吸收矛盾解释假设,并建立其公理体系与传递性关系的局部满足构造。该形式化发展得益于近期提出的双真值对偶逻辑RCbr(一种LFI,即形式不一致逻辑),其具备自扩展性(满足替换性质),特别适用于信念修正场景。本工作为两篇论文中的第一篇:虽然所提操作具备多项创新特征,但尚未赋予矛盾否定与一致性算子重要的认知角色;这一增强将在第二篇论文中通过新系统AGMcircabd实现。据作者所知,这是AGM文献中首个此类操作。

原文摘要 · Abstract (English)

In his 1996 doctoral thesis, Maurice Pagnucco created the first AGM-like abductive expansion operation. Taking his operation as a basis, as well as a taxonomy -- inspired by Atocha Aliseda -- responsible for highlighting and formalizing the main components of abductive reasoning, the main aim of this paper is to present a new paraconsistent AGM-like abductive expansion operation -- capable of assimilating contradictory explanatory hypotheses without trivialization and the consequent absurd epistemic state -- with its postulates and its transitively relational partial meet construction. To a large extent, the formal development presented in this paper was only made possible by the recent creation of the paraconsistent logic RCbr, an LFI (Logics of Formal Inconsistencies) that establishes properties especially relevant to belief revision contexts, in particular, the ability to be self-extensional -- i.e., to satisfy the replacement property. This is the first of two papers: the paraconsistent abductive expansion operation announced here -- which is part of a new system called AGMpabd -- despite bringing many interesting features, does not assign any relevant epistemic role to the paraconsistent operators of negation and consistency. Only in a second paper will an analogous paraconsistent abductive expansion operation -- which is part of another new system, AGMcircabd -- be enhanced in this direction. Nevertheless, to the best of my knowledge, the operation developed in this paper is the first of its kind in the AGM literature.

逻辑推理信念修正矛盾容忍

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