文章基本信息

标题：Many-dimensional Modal Logic of Tense and Temporal Interval and its Decidability
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作者：Suguru Yoshioka ; Satoshi Tojo
期刊名称：人工知能学会論文誌
印刷版ISSN：1346-0714
电子版ISSN：1346-8030
出版年度：2006
卷号：21
期号：3
页码：257-265
DOI：10.1527/tjsai.21.257
出版社：The Japanese Society for Artificial Intelligence
摘要：Linear tense logics are widely accepted for structural temporal representation, where the basic K_T has two modal operators G and H, each of which represents the future and the past, respectively. On the other hand, the temporal interval relations arranged by Allen have long been the standard of natural language semantics, though it still lacks the modal-logical foundation. Van Benthem proposed ∉^up and ∉_down in regard to the accessibility to overlapping intervals and subintervals, respectively; however, the logical feature of the modality has not well studied. In this study, we propose a many-dimensional logic including the conventional tense logic, together with such interval accessibility. And, we show that our logic provide a formal apparatus for a precise aspectual classification. Lastly, we introduce the sequent system for our logic. We show the subformula property holds in our system, and thus would be able to show the decidability.
关键词：aspectual classification ; interval logic ; many-dimensional modal logic ; sequent system ; temporal logic