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  1. Sergei N. Artemov (2012). The Ontology of Justifications in the Logical Setting. Studia Logica 100 (1-2):17-30.
    Justification Logic provides an axiomatic description of justifications and delegates the question of their nature to semantics. In this note, we address the conceptual issue of the logical type of justifications: we argue that justifications in the logical setting are naturally interpreted as sets of formulas which leads to a class of epistemic models that we call modular models . We show that Fitting models for Justification Logic naturally encode modular models and can be regarded as convenient pre-models of the (...)
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  2. Sergei N. Artemov (2001). Explicit Provability and Constructive Semantics. Bulletin of Symbolic Logic 7 (1):1-36.
    In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which (...)
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  3. Sergei N. Artemov (1999). Realization of Intuitionistic Logic by Proof Polynomials. Journal of Applied Non-Classical Logics 9 (2-3):285-301.
    ABSTRACT In 1933 Gödel introduced an axiomatic system, currently known as S4, for a logic of an absolute provability, i.e. not depending on the formalism chosen ([God 33]). The problem of finding a fair provability model for S4 was left open. The famous formal provability predicate which first appeared in the Gödel Incompleteness Theorem does not do this job: the logic of formal provability is not compatible with S4. As was discovered in [Art 95], this defect of the formal provability (...)
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  4. Sergei N. Artemov & Lev D. Beklemishev (1993). On Propositional Quantifiers in Provability Logic. Notre Dame Journal of Formal Logic 34 (3):401-419.