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  1. (2 other versions)Semantical Considerations on Modal Logic.Saul Kripke - 1963 - Acta Philosophica Fennica 16:83-94.
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  • Logic of proofs.Sergei Artëmov - 1994 - Annals of Pure and Applied Logic 67 (1-3):29-59.
    In this paper individual proofs are integrated into provability logic. Systems of axioms for a logic with operators “A is provable” and “p is a proof of A” are introduced, provided with Kripke semantics and decision procedure. Completeness theorems with respect to the arithmetical interpretation are proved.
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  • (1 other version)Modal logic.Yde Venema - 2000 - Philosophical Review 109 (2):286-289.
    Modern modal logic originated as a branch of philosophical logic in which the concepts of necessity and possibility were investigated by means of a pair of dual operators that are added to a propositional or first-order language. The field owes much of its flavor and success to the introduction in the 1950s of the “possible-worlds” semantics in which the modal operators are interpreted via some “accessibility relation” connecting possible worlds. In subsequent years, modal logic has received attention as an attractive (...)
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  • (2 other versions)The Unprovability of Consistency. An Essay in Modal Logic.C. Smoryński - 1979 - Journal of Symbolic Logic 46 (4):871-873.
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  • Per Martin-Löf. Intuitionistic type theory. Studies in proof theory. Bibliopolis, Naples1984, ix + 91 pp. [REVIEW]W. A. Howard - 1986 - Journal of Symbolic Logic 51 (4):1075-1076.
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  • Epistemic arithmetic is a conservative extension of intuitionistic arithmetic.Nicolas D. Goodman - 1984 - Journal of Symbolic Logic 49 (1):192-203.
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  • (1 other version)Foundations of Constructive Mathematics.Michael J. Beeson - 1987 - Studia Logica 46 (4):398-399.
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  • Arithmetical necessity, provability and intuitionistic logic.Rob Goldblatt - 1978 - Theoria 44 (1):38-46.
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  • The intended interpretation of intuitionistic logic.Scott Weinstein - 1983 - Journal of Philosophical Logic 12 (2):261 - 270.
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  • (1 other version)Some theorems about the sentential calculi of Lewis and Heyting.J. C. C. McKinsey & Alfred Tarski - 1948 - Journal of Symbolic Logic 13 (1):1-15.
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  • On modal systems having arithmetical interpretations.Arnon Avron - 1984 - Journal of Symbolic Logic 49 (3):935-942.
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  • On first-order theories with provability operator.Sergei Artëmov & Franco Montagna - 1994 - Journal of Symbolic Logic 59 (4):1139-1153.
    In this paper the modal operator "x is provable in Peano Arithmetic" is incorporated into first-order theories. A provability extension of a theory is defined. Presburger Arithmetic of addition, Skolem Arithmetic of multiplication, and some first order theories of partial consistency statements are shown to remain decidable after natural provability extensions. It is also shown that natural provability extensions of a decidable theory may be undecidable.
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  • Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
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  • Combinatory Logic.Haskell B. Curry, J. Roger Hindley & Jonathan P. Seldin - 1977 - Journal of Symbolic Logic 42 (1):109-110.
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  • Epistemic and intuitionistic formal systems.R. C. Flagg & H. Friedman - 1986 - Annals of Pure and Applied Logic 32:53-60.
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  • (1 other version)On weak completeness of intuitionistic predicate logic.G. Kreisel - 1962 - Journal of Symbolic Logic 27 (2):139-158.
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  • (1 other version)On the interpretation of intuitionistic number theory.S. C. Kleene - 1945 - Journal of Symbolic Logic 10 (4):109-124.
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  • (2 other versions)The Mathematics of Metamathematics.Donald Monk - 1963 - Journal of Symbolic Logic 32 (2):274-275.
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  • Über eine bisher noch nicht benützte erweiterung Des finiten standpunktes.Von Kurt Gödel - 1958 - Dialectica 12 (3‐4):280-287.
    ZusammenfassungP. Bernays hat darauf hingewiesen, dass man, um die Widerspruchs freiheit der klassischen Zahlentheorie zu beweisen, den Hilbertschen flniter Standpunkt dadurch erweitern muss, dass man neben den auf Symbole sich beziehenden kombinatorischen Begriffen gewisse abstrakte Begriffe zulässt, Die abstrakten Begriffe, die bisher für diesen Zweck verwendet wurden, sinc die der konstruktiven Ordinalzahltheorie und die der intuitionistischer. Logik. Es wird gezeigt, dass man statt deesen den Begriff einer berechenbaren Funktion endlichen einfachen Typs über den natürlichen Zahler benutzen kann, wobei keine anderen (...)
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  • Die intuitionistische grundlegung der mathematik.Arend Heyting - 1931 - Erkenntnis 2 (1):106-115.
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  • Some remarks on the notion of proof.John Myhill - 1960 - Journal of Philosophy 57 (14):461-471.
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  • The Logic of Provability.Philip Scowcroft - 1995 - Philosophical Review 104 (4):627.
    This is a book that every enthusiast for Gödel’s proofs of his incompleteness theorems will want to own. It gives an up-to-date account of connections between systems of modal logic and results on provability in formal systems for arithmetic, analysis, and set theory.
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  • (1 other version)New foundations for Lewis modal systems.E. J. Lemmon - 1957 - Journal of Symbolic Logic 22 (2):176-186.
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  • A. S. Troelstra and H. Schwichtenberg. Basic proof theory. Second edition of jsl lxiii 1605. Cambridge tracts in theoretical computer science, no. 43. cambridge university press, cambridge, new York, etc., 2000, XII + 417 pp. [REVIEW]Roy Dyckhoff - 2001 - Bulletin of Symbolic Logic 7 (2):280-280.
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  • (1 other version)Tools and Techniques in Modal Logic.Guram Bezhanishvili - 2001 - Bulletin of Symbolic Logic 7 (2):278-279.
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  • The modal logic of pure provability.Samuel R. Buss - 1990 - Notre Dame Journal of Formal Logic 31 (2):225-231.
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  • Kolmogorov and mathematical logic.Vladimir A. Uspensky - 1992 - Journal of Symbolic Logic 57 (2):385-412.
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  • Knowledge and Belief: An Introduction to the Logic of the Two Notions.Alan R. White - 1965 - Philosophical Quarterly 15 (60):268.
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  • The single-conclusion proof logic and inference rules specification.Vladimir N. Krupski - 2001 - Annals of Pure and Applied Logic 113 (1-3):181-206.
    The logic of single-conclusion proofs () is introduced. It combines the verification property of proofs with the single valuedness of proof predicate and describes the operations on proofs induced by modus ponens rule and proof checking. It is proved that is decidable, sound and complete with respect to arithmetical proof interpretations based on single-valued proof predicates. The application to arithmetical inference rules specification and -admissibility testing is considered. We show that the provability in gives the complete admissibility test for the (...)
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  • Mathematische Grundlagenforschung, Intuitionismus, Beweistheorie.R. Carnap - 1935 - Erkenntnis 5 (1):288-289.
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