可解释性逻辑标记技术的理论与应用

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2022-07-07 DOI:10.1002/malq.202200015

Evan Goris, Marta Bílková, Joost J. Joosten, Luka Mikec

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引用次数: 1

摘要

关系语义中关键后继[5]的概念一直是可解释性逻辑中大多数经典模态完备性证明的核心。在本文中，我们将使用一个更一般的概念，即保证后继的概念。这将使关于普通和广义Veltman语义的完备性证明更简明地公式化。由于它们有趣的理论性质，我们将花一些空间来研究一种特殊的保证标签，即所谓的完整标签和极大标签。在对保证性进行一般处理之后，我们将应用它来得到一类受限帧的模态逻辑ILP $\mathsf {ILP}$ w.r.t.广义语义的完备性结果。

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Theory and application of labelling techniques for interpretability logics

The notion of a critical successor [5] in relational semantics has been central to most classic modal completeness proofs in interpretability logics. In this paper we shall work with a more general notion, that of an assuring successor. This will enable more concisely formulated completeness proofs, both with respect to ordinary and generalised Veltman semantics. Due to their interesting theoretical properties, we will devote some space to the study of a particular kind of assuring labels, the so-called full labels and maximal labels. After a general treatment of assuringness, we shall apply it to obtain a completeness result for the modal logic $ILP$ w.r.t. generalised semantics for a restricted class of frames.

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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.