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Logic of proofs $\mathsf{LP}$ , introduced by S. Artemov, originally designed for describing properties of formal proofs, now became a basis for the theory of knowledge with justification (cf. S. Artemov, Evidence-based common knowledge, Technical report TR–2004018, CUNY Ph.D. Program in Computer Science, 2005). So far, in epistemic systems with(More)
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 propositional logic of proofs LP revealed an explicit provability reading of modal logic S4 which provided an indented provability semantics for the propositional intuitionistic logic IPC and led to a new area, Justification Logic. In this paper, we find the first-order logic of proofs FOLP capable of realizing first-order modal logic S4 and, therefore,(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)