On Two Models of Provability
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[1] Lev D. Beklemishev,et al. Reflection principles and provability algebras in formal arithmetic , 2005 .
[2] Giorgie Dzhaparidze,et al. The logic of linear tolerance , 1992 .
[3] Rostislav Yavorskiy. On the Logic of the Standard Proof Predicate , 2000, CSL.
[4] P. Bernays,et al. Grundlagen der Mathematik , 1934 .
[5] Sergei N. Artëmov. Evidence-Based Common Knowledge , 2005 .
[6] Stewart Shapiro,et al. Epistemic and Intuitionistic Arithmetic , 1985 .
[7] Vladimir Krupski,et al. Operational Logic of Proofs with Functionality Condition on Proof Predicate , 1997, LFCS.
[8] Albert Visser. Substitutions of Sigma10 - sentences: explorations between intuitionistic propositional logic and intuitionistic arithmetic , 2002, Ann. Pure Appl. Log..
[9] Vítezslav Svejdar. Modal Analysis of Generalized Rosser Sentences , 1983, J. Symb. Log..
[10] Sergei N. Artëmov,et al. Functionality in the Basic Logic of Proofs , 1993 .
[11] Sergei N. Artëmov. Kolmogorov and Gödel's approach to intuitionistic logic: current developments , 2004 .
[12] Michael Zakharyaschev,et al. Modal Logic , 1997, Oxford logic guides.
[13] Stewart Shapiro. Introduction-Intensional Mathematics and Constructive Mathematics , 1985 .
[14] Sergei N. Artëmov. Justified common knowledge , 2006, Theor. Comput. Sci..
[15] Konstantin N. Ignatiev,et al. On strong provability predicates and the associated modal logics , 1993, Journal of Symbolic Logic.
[16] Alessandra Carbone,et al. Much shorter proofs: A bimodal investigation , 1990, Math. Log. Q..
[17] Albert Visser,et al. Peano's Smart Children: A Provability Logical Study of Systems with Built-in Consistency , 1986, Notre Dame J. Formal Log..
[19] George Boolos,et al. Reflection principles and iterated consistency assertions , 1979, Journal of Symbolic Logic.
[20] W. Lenzen,et al. Knowledge, Belief, and Subjective Probability: Outlines of a Unified System of Epistemic/Doxastic Logic , 2003 .
[21] Daniel Maurice Raphaël Leivant. Logic and computational complexity : International Workshop LCC '94, Indianapolis, IN, USA, October 13-16, 1994 : selected papers , 1995 .
[22] Albert Visser,et al. Interpretability Logic , 1990 .
[23] Alessandro Berarducci,et al. The interpretability logic of Peano arithmetic , 1990, Journal of Symbolic Logic.
[24] Sergei N. Artëmov,et al. Logical Omniscience Via Proof Complexity , 2006, CSL.
[25] Per Lindström,et al. Provability logic—a short introduction , 2008 .
[26] B. Renne. Semantic Cut-elimination for Two Explicit Modal Logics , 2006 .
[27] S. Feferman. Arithmetization of metamathematics in a general setting , 1959 .
[28] Rostislav Yavorskiy,et al. Provability logics with quantifiers on proofs , 2001, Ann. Pure Appl. Log..
[29] A. Heyting,et al. Intuitionism: An introduction , 1956 .
[30] A. Kolmogoroff. Zur Deutung der intuitionistischen Logik , 1932 .
[31] Joost J. Joosten,et al. Modal matters in interpretability logics , 2004 .
[32] Sergei N. Artëmov,et al. On propositional quantifiers in provability logic , 1993, Notre Dame J. Formal Log..
[33] M. H. Lob,et al. Solution of a Problem of Leon Henkin , 1955, J. Symb. Log..
[34] Rohit Parikh. Knowledge and the Problem of Logical Omniscience , 1987, ISMIS.
[35] George Boolos,et al. Provability: the emergence of a mathematical modality , 1991, Stud Logica.
[36] V. Y. Shavrukov. Isomorphisms of diagonalizable algebras , 1996 .
[37] Franco Montagna,et al. The logic of π1-conservativity , 1990, Arch. Math. Log..
[38] Yoram Moses,et al. Resource-bounded Knowledge , 1988, TARK.
[39] Joost Johannes Joosten,et al. Interpretability formalized , 2004 .
[40] George Boolos,et al. Extremely undecidable sentences , 1982, Journal of Symbolic Logic.
[41] Rineke Verbrugge,et al. On the Provability Logic of Bounded Arithmetic , 1993, Ann. Pure Appl. Log..
[42] Jean Gallier,et al. Ann. Pure Appl. Logic , 1997 .
[43] K. Gödel,et al. Kurt Gödel : collected works , 1986 .
[44] Leo Esakia,et al. Intuitionistic logic and modality via topology , 2004, Ann. Pure Appl. Log..
[45] A. Visser. Propositional combinations of Σ-sentences in Heyting's Arithmetic , 1994 .
[46] Лев Дмитриевич Беклемишев,et al. Схемы рефлексии и алгебры доказуемости в формальной арифметике@@@Reflection principles and provability algebras in formal arithmetic , 2005 .
[47] Sergei N. Artëmov. ON MODAL LOGICS AXIOMATIZING PROVABILITY , 1986 .
[48] Tatiana Yavorskaya,et al. Logic of proofs and provability , 2001, Ann. Pure Appl. Log..
[49] M. Fitting. Semantics and Tableaus for LPS4 , 2004 .
[50] Sergei N. Artëmov,et al. The Basic Logic of Proofs , 1992, CSL.
[51] Franco Montagna,et al. The undecidability of the first-order theory of diagonalizable algebras , 1980 .
[52] Franco Montagna,et al. The predicate modal logic of provability , 1984, Notre Dame J. Formal Log..
[53] Artur S. d'Avila Garcez,et al. We Will Show Them! Essays in Honour of Dov Gabbay, Volume One , 2005, We Will Show Them!.
[54] Claudio Bernardi,et al. The uniqueness of the fixed-point in every diagonalizable algebra , 1976 .
[55] Robert Goldblatt,et al. Arithmetical necessity, provability and intuitionistic logic , 2008 .
[56] Vincent F. Hendricks,et al. Active Agents , 2003, J. Log. Lang. Inf..
[57] John Myhill,et al. Some Remarks on the Notion of Proof , 1960 .
[58] Sergei N. Artëmov,et al. Logic of knowledge with justifications from the provability perspective. , 2004 .
[59] T. Carlson,et al. Modal logics with several operators and provability interpretations , 1986 .
[60] D.H.J. de Jongh,et al. The logic of the provability , 1998 .
[61] Michael Zakharyaschev,et al. Modal companions of intermediate propositional logics , 1992, Stud Logica.
[62] Roman Kuznets,et al. Making knowledge explicit: How hard it is , 2006, Theor. Comput. Sci..
[63] R. Yavorsky. Provability logics with quantifiers on proofs , 2001 .
[64] Nikolai V. Krupski. Typing in reflective combinatory logic , 2006, Ann. Pure Appl. Log..
[65] A. Heyting. Die intuitionistische Grundlegung der Mathematik , 1931 .
[66] Albert Visser,et al. Rules and Arithmetics , 1998, Notre Dame J. Formal Log..
[67] Melvin Fitting,et al. A Logic of Explicit Knowledge , 2004 .
[68] Robert Saxon Milnikel. Derivability in certain subsystems of the Logic of Proofs is Pi2p-complete , 2007, Ann. Pure Appl. Log..
[69] Lev D. Beklemishev,et al. Parameter Free Induction and Provably Total Computable Functions , 1999, Theor. Comput. Sci..
[70] Giorgi Japaridze. From truth to computability I , 2006, Theor. Comput. Sci..
[71] Andrzej Grzegorczyk. Some relational systems and the associated topological spaces , 1967 .
[72] V. Yu. Shavrukov,et al. On Rosser's Provability Predicate , 1991, Math. Log. Q..
[73] Ronald Fagin,et al. Reasoning about knowledge , 1995 .
[74] Sergei N. Artëmov. Kolmogorov's Logic of Problems and a Provability Interpretation of Intuitionistic Logic , 1990, TARK.
[75] G. Boolos,et al. Self-Reference and Modal Logic , 1985 .
[76] Tatiana Yavorskaya. Provability Logic with Operations on Proofs , 1997, LFCS.
[77] Lev D. Beklemishev. The Worm principle , 2003 .
[78] Alexei Yu. Muravitsky,et al. On superintuitionistic logics as fragments of proof logic extensions , 1986, Stud Logica.
[79] Natalia Rubtsova. Evidence Reconstruction of Epistemic Modal Logic S5 , 2006, CSR.
[80] Lev D. Beklemishev,et al. Bimodal logics for extensions of arithmetical theories , 1996, Journal of Symbolic Logic.
[81] Franco Montagna,et al. The logic ofII1-conservativity continued , 1992, Arch. Math. Log..
[82] Laurence Bonjour,et al. The coherence theory of empirical knowledge , 1976 .
[83] Dov M. Gabbay,et al. Chapter 13 – Labelled Deductive Systems , 2003 .
[84] Sergei N. Artëmov. Logic of Proofs , 1994, Ann. Pure Appl. Log..
[85] Dr. A. Visser. A Modal Analysis of some Principles of the Provability Logic of Heyting Arithmetic , 1999 .
[86] Sergei N. Artëmov. Operations on Proofs that can be Specified by Means of Modal Logic , 1999, Advances in Modal Logic.
[87] Sergei N. Artëmov. Nonarithmeticity of truth predicate logics of provability , 1985 .
[88] Robert L. Constable,et al. Chapter X - Types in Logic, Mathematics and Programming , 1998 .
[89] Sergei N. Artëmov. Explicit provability and constructive semantics , 2001, Bull. Symb. Log..
[90] Lev D. Beklemishev,et al. On Bimodal Logics of Provability , 1994, Ann. Pure Appl. Log..
[91] Artemov. NON-ARITHMETICAL BEHAVIOR OF TRUTH PREDICATE LOGICS OF PROVABILITY , 1985 .
[92] Alessandra Carbone,et al. Rosser Orderings in Bimodal Logics , 1989, Math. Log. Q..
[93] G. Boolos. The Unprovability of Consistency: An Essay in Modal Logic , 1979 .
[94] Franco Montagna,et al. Much Shorter Proofs , 1989, Math. Log. Q..
[95] Sergei N. Artemovy. Operational Modal Logic , 1995 .
[96] C. Smorynski. The Incompleteness Theorems , 1977 .
[97] Sergei N. Artëmov. Existential Semantics for Modal Logic , 2005, We Will Show Them!.
[98] Richard Spencer-Smith,et al. Modal Logic , 2007 .
[99] Franco Montagna,et al. Interpretations of the first-order theory of diagonalizable algebras in peano arithmetic , 1980 .
[100] Wilfrid Hodges,et al. Logic: from foundations to applications: European logic colloquium , 1996 .
[101] Vladimir Krupski,et al. Referential logic of proofs , 2006, Theor. Comput. Sci..
[102] George Boolos. On Deciding the Truth of Certain Statements Involving the Notion of Consistency , 1976, J. Symb. Log..
[103] A. Macintyre,et al. Gödel's diagonalization technique and related properties of theories , 1973 .
[104] Nikolai K. Vereshchagin,et al. Provability, complexity, grammars , 1999, American Mathematical Society translations series 2.
[105] Sergei N. Artëmov,et al. On epistemic logic with justification , 2005, TARK.
[106] S. C. Kleene,et al. Introduction to Metamathematics , 1952 .
[107] Sergei N. Artëmov,et al. The Logic of the Gödel Proof Predicate , 1993, Kurt Gödel Colloquium.
[108] Nikolai V. Krupski,et al. On the complexity of the reflected logic of proofs , 2006, Theor. Comput. Sci..
[109] Melvin Fitting,et al. The logic of proofs, semantically , 2005, Ann. Pure Appl. Log..
[110] Albert Visser,et al. Embeddings of Heyting algebras , 1993 .
[111] Albert Visser,et al. An Overview of Interpretability Logic , 1997, Advances in Modal Logic.
[112] Samuel R. Buss,et al. The Modal Logic of Pure Provability , 1990, Notre Dame J. Formal Log..
[113] C. McCarty. CONSTRUCTIVISM IN MATHEMATICS , 2009 .
[114] Lev D. Beklemishev,et al. Proof-theoretic analysis by iterated reflection , 2003, Arch. Math. Log..
[115] J.F.A.K. van Benthem. Modal Frame Correspondence Generalized , 2005 .
[116] Alvin I. Goldman,et al. A Causal Theory of Knowing , 1967 .
[117] Tatiana Yavorskaya,et al. Operations on proofs and labels , 2007, J. Appl. Non Class. Logics.
[118] Evan Goris. Logic of Proofs for Bounded Arithmetic , 2006, CSR.
[119] L. Henkin. Review: J. C. C. McKinsey, Alfred Tarski, Some Theorems About the Sentential Calculi of Lewis and Heyting , 1948 .
[120] Sergei N. Artëmov,et al. Introducing Justification into Epistemic Logic , 2005, J. Log. Comput..
[121] Albert Visser. Löb's Logic Meets the µ-Calculus , 2005, Processes, Terms and Cycles.
[122] С.Н. Артемов,et al. Подход Колмогорова и Гeделя к интуиционистской логике и работы последнего десятилетия в этом направлении@@@Kolmogorov and Gödel's approach to intuitionistic logic: current developments , 2004 .
[123] Lev D. Beklemishev,et al. ON THE CLASSIFICATION OF PROPOSITIONAL PROVABILITY LOGICS , 1990 .
[124] John Myhill. Intensional Set Theory , 1985 .
[125] Giorgie Dzhaparidze,et al. A Generalized Notion of Weak Interpretability and the Corresponding Modal Logic , 1993, Ann. Pure Appl. Log..
[126] Giorgi Japaridze,et al. Introduction to computability logic , 2003, Ann. Pure Appl. Log..
[127] J. Girard,et al. Proofs and types , 1989 .
[128] J. Barkley Rosser,et al. Extensions of some theorems of Gödel and Church , 1936, Journal of Symbolic Logic.
[129] W. van der Hoek,et al. Epistemic logic for AI and computer science , 1995, Cambridge tracts in theoretical computer science.
[130] Rohit Parikh,et al. Logical Omniscience , 1994, LCC.
[131] Vladimir Krupski,et al. The single-conclusion proof logic and inference rules specification , 2001, Ann. Pure Appl. Log..
[132] Tatiana Yavorskaya. Negative Operations on Proofs and Labels , 2005, J. Log. Comput..
[133] R. Solovay. Provability interpretations of modal logic , 1976 .
[134] Harvey M. Friedman,et al. One hundred and two problems in mathematical logic , 1975, Journal of Symbolic Logic.
[135] Konstantin N. Ignatiev. The Provability Logic for sigma1-Interpolability , 1993, Ann. Pure Appl. Log..
[136] E. Pacuit. A Note on Some Explicit Modal Logics , 2005 .
[137] Roman Kuznets. On the Complexity of Explicit Modal Logics , 2000, CSL.
[138] Albert Visser,et al. The provability logics of recursively enumerable theories extending peano arithmetic at arbitrary theories extending peano arithmetic , 1984, J. Philos. Log..
[139] Rosalie Iemhoff,et al. On the admissible rules of intuitionistic propositional logic , 2001, Journal of Symbolic Logic.
[140] Elena Nogina. Logic of Proofs with the Strong Provability Operator , 1994 .
[141] A. Visser,et al. Evaluation, provably deductive equivalence in Heyting's arithmetic of substitution instances of propositional formulas , 1985 .
[142] Sergei N. Artëmov,et al. The basic intuitionistic logic of proofs , 2007, J. Symb. Log..
[143] Keith Lehrer,et al. Knowledge: Undefeated Justified True Belief , 1969 .
[144] Rosalie Iemhoff,et al. Provability logic and admissible rules , 2001 .
[145] Rosalie Iemhoff,et al. A Modal Analysis of Some Principles of the Provability Logic of Heyting Artihmetic , 1998, Advances in Modal Logic.
[146] R. Magari,et al. Representation and duality theory for diagonalizable algebras , 1975 .
[147] Franco Montagna,et al. An Operational Logic of Proofs with Positive and Negative Information , 1999, Stud Logica.
[148] Sergei N. Artëmov. Numerically correct provability logics , 1987 .
[149] Sergei N. Artëmov,et al. On First Order Logic of Proofs , 2001 .
[150] Alexey Mkrtychev,et al. Models for the Logic of Proofs , 1997, LFCS.
[151] Petr Hájek,et al. Metamathematics of First-Order Arithmetic , 1993, Perspectives in mathematical logic.
[152] V. Yu. Shavrukov. A Smart Child of Peano's , 1994, Notre Dame J. Formal Log..
[153] Alfred Tarski,et al. Some theorems about the sentential calculi of Lewis and Heyting , 1948, The Journal of Symbolic Logic.
[154] E. J. Lemmon,et al. New foundations for Lewis modal systems , 1957, Journal of Symbolic Logic.
[155] Edmund L. Gettier. Is Justified True Belief Knowledge? , 1963, Arguing About Knowledge.