模态包含逻辑及其变体的公理化

IF 0.4 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2025-01-27 DOI:10.1007/s00153-024-00957-y

Aleksi Anttila, Matilda Häggblom, Fan Yang

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引用次数: 0

摘要

我们提供了模态包含逻辑的一个完整的公理化——包含原子扩展的基于团队的模态逻辑。我们回顾并改进了逻辑的一个表达完备性和范式定理，定义了一个自然演绎证明系统，并用范式证明了公理化的完备性。模态逻辑的另外两个扩展具有与模态包含逻辑相同的表达能力，也提供了完全公化：一个扩展了一个might算子，另一个扩展了一个might算子的单世界变体。

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Axiomatizing modal inclusion logic and its variants

We provide a complete axiomatization of modal inclusion logic—team-based modal logic extended with inclusion atoms. We review and refine an expressive completeness and normal form theorem for the logic, define a natural deduction proof system, and use the normal form to prove completeness of the axiomatization. Complete axiomatizations are also provided for two other extensions of modal logic with the same expressive power as modal inclusion logic: one augmented with a might operator and the other with a single-world variant of the might operator.

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来源期刊

Archive for Mathematical Logic MATHEMATICS-LOGIC

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.