Provability interpretations of modal logic
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Publication:1235695
DOI10.1007/BF02757006zbMath0352.02019WikidataQ56057304 ScholiaQ56057304MaRDI QIDQ1235695
Publication date: 1976
Published in: Israel Journal of Mathematics (Search for Journal in Brave)
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Logic of proofs ⋮ Hyperdiagonalizable algebras ⋮ Provability algebras and proof-theoretic ordinals. I ⋮ On bimodal logics of provability ⋮ On modal logics of model-theoretic relations ⋮ On arithmetical completeness of the logic of proofs ⋮ Cut elimination for GLS using the terminability of its regress process ⋮ Effectively constructible fixed points in Sacchetti's modal logics of provability ⋮ On superintuitionistic logics as fragments of proof logic extensions ⋮ Franco Montagna's work on provability logic and many-valued logic ⋮ Free and projective bimodal symmetric Gödel algebras ⋮ A course on bimodal provability logic ⋮ Interpretability of various extensions of arithmetic ⋮ Cut-elimination for provability logic by terminating proof-search: formalised and deconstructed using Coq ⋮ A simple proof of arithmetical completeness for \(\Pi_ 1\)-conservativity logic ⋮ Liar-type paradoxes and the incompleteness phenomena ⋮ Generic generalized Rosser fixed points ⋮ Magari and \(\Delta\)-pseudo-Boolean algebras ⋮ A modal logic of consistency ⋮ The power of temporal proofs ⋮ Hard provability logics ⋮ Interpretability suprema in Peano arithmetic ⋮ Intuitionistic logic and modality via topology ⋮ The modal logic of Gödel sentences ⋮ On predicate provability logics and binumerations of fragments of Peano arithmetic ⋮ Syntactical models and fixed points for the basic logic of proofs ⋮ Intuitionistic diagonalizable algebras ⋮ Provability, truth, and modal logic ⋮ Rosser provability and normal modal logics ⋮ Lewis meets Brouwer: constructive strict implication ⋮ A proof theory for the logic of provability in true arithmetic ⋮ The omega-rule interpretation of transfinite provability logic ⋮ Definability and commonsense reasoning ⋮ Intermediate logics and the de Jongh property ⋮ Pretabular varieties of modal algebras ⋮ Transductions in arithmetic ⋮ A short note on essentially \(\Sigma_1\) sentences ⋮ Interpretations of the first-order theory of diagonalizable algebras in Peano arithmetic ⋮ The undecidability of the first-order theory of diagonalizable algebras ⋮ Omega-consistency and the diamond ⋮ A modal provability logic of explicit and implicit proofs ⋮ A propositional logic with explicit fixed points ⋮ Anderson and Belnap's invitation to sin ⋮ Definability theorems in normal extensions of the provability logic ⋮ Variations on a Montagovian theme ⋮ Mathematical modal logic: A view of its evolution ⋮ The decision problem of provability logic with only one atom ⋮ Continuum of normal extensions of the modal logic of provability with the interpolation property ⋮ The polytopologies of transfinite provability logic ⋮ Feasible operations on proofs: the logic of proofs for bounded arithmetic ⋮ Provability: The emergence of a mathematical modality ⋮ On the proof of Solovay's theorem ⋮ Rosser orderings and free variables ⋮ Predicate provability logic with non-modalized quantifiers ⋮ The de Jongh property for basic arithmetic ⋮ The disjunction property of intermediate propositional logics ⋮ Provability logic and the completeness principle ⋮ Sequent calculi for intuitionistic Gödel-Löb logic ⋮ Reflexive-insensitive logics, the boxdot translation, and the modal logic of generic absoluteness ⋮ Algebraization of quantifier logics, an introductory overview ⋮ Arithmetical completeness theorem for modal logic \(\mathsf{K}\) ⋮ Modal companions of intermediate propositional logics ⋮ On a strengthening of the non-isomorphism theorem for provability algebras ⋮ On the provability logic of bounded arithmetic ⋮ The analytical completeness of Dzhaparidze's polymodal logics ⋮ A generalized notion of weak interpretability and the corresponding modal logic ⋮ On products of posets and coproducts of KM-algebras ⋮ On the complexity of arithmetical interpretations of modal formulae ⋮ Arithmetical soundness and completeness for \(\Sigma_{2}\) numerations ⋮ Independent numerations of theories and recursive progressions ⋮ The logic of linear tolerance ⋮ Modal provability foundations for argumentation networks ⋮ Paraconsistent informational logic ⋮ The knower paradox in the light of provability interpretations of modal logic ⋮ On modal logic of deductive closure ⋮ Referential logic of proofs ⋮ Modal logics with several operators and probability interpretations ⋮ Uniform arithmetical completeness of modal provability logics ⋮ The \(\Sigma_1\)-provability logic of \(\mathsf{HA}\) ⋮ A simplified proof of arithmetical completeness theorem for provability logic GLP ⋮ Calculating self-referential statements. 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The sequential approach ⋮ The modal logic of reverse mathematics ⋮ Modal tableau calculi and interpolation ⋮ Provability logics for natural Turing progressions of arithmetical theories ⋮ Logical equations and admissible rules of inference with parameters in modal provability logics ⋮ The logic of arithmetical hierarchy ⋮ The provability logics of recursively enumerable theories extending Peano arithmetic at arbitrary theories extending Peano arithmetic ⋮ Syntactical results on the arithmetical completeness of modal logic ⋮ On inclusions between quantified provability logics ⋮ Proof Theory in Philosophy of Mathematics ⋮ Kleene's Amazing Second Recursion Theorem ⋮ VALENTINI’S CUT-ELIMINATION FOR PROVABILITY LOGIC RESOLVED ⋮ On strong provability predicates and the associated modal logics ⋮ On modal systems having arithmetical interpretations ⋮ The Henkin Sentence ⋮ Kripke Models Built from Models of Arithmetic ⋮ European Summer Meeting of the Association for Symbolic Logic ⋮ THE ∀∃ THEORY OF PEANO Σ1 SENTENCES ⋮ THE SET-THEORETIC MULTIVERSE ⋮ SOLOVAY-TYPE THEOREMS FOR CIRCULAR DEFINITIONS ⋮ On the degrees of unsolvability of modal predicate logics of provability ⋮ Infinitary combinatorics and modal logic ⋮ European Summer Meeting of the Association for Symbolic Logic (Logic Colloquium '88), Padova, 1988 ⋮ Finite Kripke models and predicate logics of provability ⋮ Provability in finite subtheories of PA and relative interpretability: a modal investigation ⋮ Provability multilattice logic ⋮ Arithmetical completeness theorems for monotonic modal logics ⋮ An Arithmetically Complete Predicate Modal Logic ⋮ Modal completeness of sublogics of the interpretability logic IL ⋮ Partitioning Kripke frames of finite height ⋮ Extensions of Solovay's system \(\mathbf{S}\) without independent sets of axioms ⋮ Mechanising Gödel-Löb provability logic in HOL light ⋮ Some observations on the FGH theorem ⋮ An (almost) fuzzy logic of action and preferences, its quasi-model interpretations, and the problem of its decidability ⋮ Polynomially and superexponentially shorter proofs in fragments of arithmetic ⋮ The degree of the set of sentences of predicate provability logic that are true under every interpretation ⋮ Theory and application of labelling techniques for interpretability logics ⋮ ANOTHER LOOK AT THE SECOND INCOMPLETENESS THEOREM ⋮ Admissible rules for six intuitionistic modal logics ⋮ DISJUNCTION AND EXISTENCE PROPERTIES IN MODAL ARITHMETIC ⋮ AN ESCAPE FROM VARDANYAN’S THEOREM ⋮ Solutions to the knower paradox in the light of Haack's criteria ⋮ Linear $ \mathrm{GLP}$-algebras and their elementary theories ⋮ Bisimulations between generalized Veltman models and Veltman models ⋮ Undecidability in diagonalizable algebras ⋮ Provability logic: models within models in Peano arithmetic ⋮ Forcing, Multiverse and Realism ⋮ INTERPRETABILITY LOGICS AND GENERALISED VELTMAN SEMANTICS ⋮ Coinduction in Flow: The Later Modality in Fibrations ⋮ CAN MODALITIES SAVE NAIVE SET THEORY? ⋮ Explicit Provability and Constructive Semantics ⋮ Peano Corto and Peano Basso: A Study of Local Induction in the Context of Weak Theories ⋮ Derived topologies on ordinals and stationary reflection ⋮ The complexity of the modal predicate logic of “true in every transitive model of ZF” ⋮ ARITHMETICAL INTERPRETATIONS AND KRIPKE FRAMES OF PREDICATE MODAL LOGIC OF PROVABILITY ⋮ Fixed point algebras ⋮ The principles of interpretability ⋮ Arithmetical interpretations of dynamic logic ⋮ Sentences implying their own provability ⋮ The modal logic of forcing ⋮ Machine Checking Proof Theory: An Application of Logic to Logic ⋮ THE -PROVABILITY LOGIC OF ⋮ Interpretability over peano arithmetic ⋮ The single-conclusion proof logic and inference rules specification ⋮ Logic of proofs and provability ⋮ Provability logics with quantifiers on proofs ⋮ PROVABILITY LOGICS RELATIVE TO A FIXED EXTENSION OF PEANO ARITHMETIC ⋮ The interpretability logic of Peano arithmetic ⋮ 1999 European Summer Meeting of the Association for Symbolic Logic ⋮ Symmetric Logic of Proofs ⋮ The Context of Inference ⋮ CURRENT RESEARCH ON GÖDEL’S INCOMPLETENESS THEOREMS ⋮ NON–WELL-FOUNDED DERIVATIONS IN THE GÖDEL-LÖB PROVABILITY LOGIC ⋮ Reflection principles and iterated consistency assertions ⋮ Kleene’s Amazing Second Recursion Theorem ⋮ The modalized Heyting calculus: a conservative modal extension of the Intuitionistic Logic ★ ⋮ On the proof theory of the modal logic for arithmetic provability ⋮ COMPLETE ADDITIVITY AND MODAL INCOMPLETENESS ⋮ THE MODAL LOGICS OF KRIPKE–FEFERMAN TRUTH ⋮ Constructive Modalities with Provability Smack ⋮ Topological Interpretations of Provability Logic ⋮ Extremely undecidable sentences ⋮ MÜNCHHAUSEN PROVABILITY ⋮ Modal Logics that Bound the Circumference of Transitive Frames ⋮ European Summer Meeting of the Association for Symbolic Logic, Uppsala 1991 ⋮ Meeting of the Association for Symbolic Logic Florence, Italy 1982 ⋮ On the nonexistence of certain normal forms in the logic of provability ⋮ Irrelevance and relevance of Gödel’s theorems to artificial intelligence ⋮ MONADIC INTUITIONISTIC AND MODAL LOGICS ADMITTING PROVABILITY INTERPRETATIONS
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