Publication Date:
2016-01-30
Description:
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.
Print ISSN:
0955-792X
Electronic ISSN:
1465-363X
Topics:
Computer Science
,
Mathematics
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