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Logic of proofs LP introduced by S. Artemov in 1995 describes properties of proof predicate " t is a proof of F " in the propositional language extended by atoms of the form [[t]]F. Proof are represented by terms constructed by three elementary recursive operations on proofs. In order to make the language more expressive we introduce the additional storage… (More)

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 2F (x). Accordingly, if 2 stands for 'provable in arithmetic,' ∀x2F (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 2F… (More)

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