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Дата последнего поиска статьи во внешних источниках: 28 июня 2016 г.
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.