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Complexity of the Lambek Calculus with One Division and a Negative-Polarity Modality for Weakeningстатья
Статья опубликована в журнале из списка Web of Science и/или Scopus
- Авторы: Pentus A.E., Pentus M.R.
- Журнал: Journal of Mathematical Sciences
- Том: 269
- Номер: 4
- Год издания: 2023
- Издательство: Plenum Publishers
- Местоположение издательства: United States
- Первая страница: 544
- Последняя страница: 557
- DOI: 10.1007/s10958-023-06299-z
- Аннотация: In this paper, we consider a variant of the Lambek calculus allowing empty antecedents. This variant uses two connectives: the left division and a unary modality that occurs only with negative polarity and allows weakening in antecedents of sequents. We define the notion of a proof net for this calculus, which is similar to those for the ordinary Lambek calculus and multiplicative linear logic. We prove that a sequent is derivable in the calculus under consideration if and only if there exists a proof net for it. We present a polynomial-time algorithm for deciding whether an arbitrary given sequent is derivable in this calculus.
- Добавил в систему: Пентус Мати Рейнович