Unified inverse correspondence for LE-logics

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-07-09 DOI:10.1016/j.apal.2025.103635

Alessandra Palmigiano , Mattia Panettiere

引用次数: 0

Abstract

We generalize Kracht's theory of internal describability from classical modal logic to the family of all logics canonically associated with varieties of normal lattice expansions (LE algebras). We work in the purely algebraic setting of perfect LEs; the formulas playing the role of Kracht's formulas in this generalized setting pertain to a first order language whose atoms are special inequalities between terms of perfect algebras. Via duality, formulas in this language can be equivalently translated into first order conditions in the frame correspondence languages of several types of relational semantics for LE-logics.

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le逻辑的统一逆对应

我们将Kracht的内可描述性理论从经典模态逻辑推广到与各种正规格展开（LE代数）正规相关的所有逻辑族。我们研究的是纯代数的完备最小二乘；在这个广义集合中扮演Kracht公式角色的公式属于一阶语言，它的原子是完全代数项之间的特殊不等式。通过对偶性，该语言中的公式可以等效地转换为le逻辑中几种关系语义的框架对应语言中的一阶条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.