Geodesic
On symbolic models for Single-Conclusion Logic of Proofs
Sbornik. Mathematics, Tome 202 (2011) no. 5, pp. 683-695

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In this paper we define symbolic models for Single-Conclusion Logics of Proofs. We prove the soundness and completeness of these logics with respect to the corresponding classes of symbolic models. We apply the semantic methods developed in this paper to justify the use of terms of single-conclusion logic of proofs as notation for derivations in this logic. Bibliography: 17 titles.
Keywords: formal derivation, proof predicate, single-conclusion logic of proofs, Mkrtychev models, internalization property. 
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     author = {V. N. Krupski},
     title = {On symbolic models for {Single-Conclusion} {Logic} of {Proofs}},
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V. N. Krupski. On symbolic models for Single-Conclusion Logic of Proofs. Sbornik. Mathematics, Tome 202 (2011) no. 5, pp. 683-695. http://geodesic.mathdoc.fr/item/SM_2011_202_5_a3/