Abstract
Each closed (i.e. variable free) formula of interpretability logic is equivalent in ILF to a closed formula of the provability logic G, thus to a Boolean combination of formulas of the form □n⊥.
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S. N. Artemov, Aritmetičeski polnyje teorii (Arithmetically complete modal theories), Semiotika i Informatika 14 (1980), pp. 115–133. (Translation in AMS Transl (2), vol. 135, 1987, pp. 39–54.)
S. N. Artemov, Priloženia modal'noj logiki i teorii dokazatel'stv, in Neklassičeskije logiki i ich primenenije, Moskva, 1982, pp. 3–22.
G. Boolos, On deciding the truth of certain statements involving the notion of consistency, Journal of Symbolic Logic 41 (1976), pp. 33–35.
R. Magari, The diagonalizable algebras, Bull. Unione Mat. Ital. 66-B (1975), pp. 117–125.
A. Visser, Interpretability logic, Logic Group Preprint Series no. 40, Department of Philosophy, University of Utrecht, Utrecht, to appear in Proceedings of the Heyting Conference, Chaika, Bulgaria, 1988.
A. Visser, An inside view of EXP, or: The closed fragment of the provability logic of (IΔ0+Ω1), Logic Group Preprint Series no. 43, Department of Philosophy, University of Utrecht, Utrecht, 1989.
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Hájek, P., Švejdar, V. A note on the normal form of closed formulas of interpretability logic. Stud Logica 50, 25–28 (1991). https://doi.org/10.1007/BF00370384
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DOI: https://doi.org/10.1007/BF00370384