## Binding modalitiesстатья

Статья опубликована в высокорейтинговом журнале

Информация о цитировании статьи получена из Scopus, Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 28 июня 2016 г.
• Авторы:
• Журнал: Journal of Logic and Computation
• Том: 26
• Номер: 1
• Год издания: 2016
• Издательство: Oxford University Press
• Местоположение издательства: United Kingdom
• Первая страница: 451
• Последняя страница: 461
• DOI: 10.1093/logcom/ext017
• Аннотация: The standard first-order reading of modality does not bind individual variables, i.e. if x is free in F(x), then x remains free in □F(x). Accordingly, if □ stands for ‘provable in arithmetic,’ ∀x□F(x) states that F(n) is provable for any given value of n = 0,1,2,...; this corresponds to a de re reading of modality. The other, de dicto meaning of □F(x), suggesting that F(x) is derivable as a formula with a free variable x, is not directly represented by a modality, though, semantically, it could be approximated by compound constructions, e.g. □∀xF(x). We introduce the first-order logic FOS4* in which modalities can bind individual variables and, in particular, can directly represent both de re and de dicto modalities. FOS4* extends first-order S4 and is the natural forgetful projection of the first-order logic of proofs FOLP. The same method of introducing binding modalities obviously works for other modal logics as well.
• Добавил в систему: Золин Евгений Евгеньевич

### Работа с статьей

 [1] Artemov S. N., Yavorskaya T. Binding modalities // Journal of Logic and Computation. — 2016. — Vol. 26, no. 1. — P. 451–461. The standard first-order reading of modality does not bind individual variables, i.e. if x is free in F(x), then x remains free in □F(x). Accordingly, if □ stands for ‘provable in arithmetic,’ ∀x□F(x) states that F(n) is provable for any given value of n = 0,1,2,...; this corresponds to a de re reading of modality. The other, de dicto meaning of □F(x), suggesting that F(x) is derivable as a formula with a free variable x, is not directly represented by a modality, though, semantically, it could be approximated by compound constructions, e.g. □∀xF(x). We introduce the first-order logic FOS4* in which modalities can bind individual variables and, in particular, can directly represent both de re and de dicto modalities. FOS4* extends first-order S4 and is the natural forgetful projection of the first-order logic of proofs FOLP. The same method of introducing binding modalities obviously works for other modal logics as well. [ DOI ]