一句话:研究在无限字与无限树上加入基于 Baire 范畴和 Lebesgue 测度的“几乎所有”量词的一元二阶逻辑扩展。
本文研究一元二阶逻辑(MSO)在无限字与无限树上的扩展。作者引入广义的“几乎所有”量词,并分别用拓扑学中的 Baire 范畴和测度论中的 Lebesgue 测度来解释其语义。该工作考察这种带测度/范畴量词的 MSO 变体在无限结构上的表达能力和语义行为。摘要未给出具体定理、判定性或复杂度结果,因此核心贡献在于提出并系统研究这一逻辑扩展框架。
We investigate the extension of Monadic Second Order logic, interpreted over infinite words and trees, with generalized "for almost all" quantifiers interpreted using the notions of Baire category and Lebesgue measure.
@article{paperbot415,
title = {Monadic Second Order Logic with Measure and Category Quantifiers},
author = {Matteo Mio and Michał Skrzypczak and Henryk Michalewski},
journal = {Logical Methods in Computer Science},
volume = {Volume 14, Issue 2},
number = {Automata and logic},
year = {2018},
doi = {10.23638/lmcs-14(2:2)2018}
}