K. Godel, 1933, \Eine Interpretation des intuitionistischen Aussagenkalkuls", Ergebnisse eines matematischen Kolloquiums 4, pp.34-40. Home/Search Document Not in Database Summary Related Articles Check |
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Simulating Polyadic Modal Logics by Monadic Ones - Goguadze, Piazza, Venema (1 citation) (Correct)
....simulations can and have been used to derive results about (families of) L 1 logics from results about L 2 logics, and vice versa. Obviously, the more properties a simulation preserves or re ects, the more useful it is. G odel s translation of intuitionistic logic in Grzegorczyk s logic, cf. [4], provides a wellknown early example of a simulation. Important results in modal logic were obtained by Thomason in the early seventies, cf. 16, 17] Thomason showed how polymodal logics (that is, normal modal logics in a language with a number of diamonds or unary modalities) can be simulated by ....
K. Godel. Eine Interpretation des intuitionistischen Aussagenkalkuls. Ergebnisse eines mathematischen Kolloquiums, 6:39-40, 1933.
Simulating Polyadic Modal Logics by Monadic Ones - Goguadze, Piazza, Venema (2001) (1 citation) (Correct)
....simulations can and have been used to derive results about (families of) L 1 logics from results about L 2 logics, and vice versa. Obviously, the more properties a simulation preserves or re ects, the more useful it is. G odel s translation of intuitionistic logic in Grzegorczyk s logic, cf. [4], provides a wellknown early example of a simulation. Important results in modal logic were obtained by Thomason in the early seventies, cf. 16, 17] Thomason showed how polymodal logics (that is, normal modal logics in a language with a number of diamonds or unary modalities) can be simulated by ....
K. Godel. Eine Interpretation des intuitionistischen Aussagenkalkuls. Ergebnisse eines mathematischen Kolloquiums, 6:39-40, 1933. 45
A Pragmatic Interpretation Of Substructural Logics - Bellin, Pozza (Correct)
....a formal pragmatics: it characterizes the notion of justi cation of pragmatics sentences, as inductively de ned relations between illocutionary acts. ii) Suppose the language of L P is extended as in Example (ii) above, but with the axioms of the modal system S4. Then one could follow G odel [9], McKinsey and Tarski [11] and interpret 2 as there is a proof that is true ; thus we obtain the following modal translation of the assertive fragment of L P into its radical 3 We thank Giovanni Sambin for suggesting this example. A PRAGMATIC INTERPRETATION OF SUBSTRUCTURAL LOGICS 19 part ....
K. Godel. Eine Interpretation des Intuitionistischen Aussagenkalkuls, Ergebnisse eines Mathematischen Kolloquiums IV, 1933, pp. 39-40.
Explicit Provability and Constructive Semantics - Artemov (2000) (1 citation) (Correct)
....supplied with the adequate provability semantics, decidability and normalization theorems. We give solutions to the problem of the intended semantics for Godel s provability calculus S4 and to the problem of BHK semantics for intuitionistic propositional logic Int along the lines of Godel s papers [39], 41] These and other applications suggest that LP fills a certain gap in the foundations of proof theory. 1 Neither Heyting s paper [49] nor Kolmogorov s [52] contains the well known extra condition on the disjunction: a proof of a disjunction should also specify which one of the disjuncts it ....
....Int (also known as IPC) on the basis of the usual mathematical notion of proof (problem solution) and thus to provide a definition of Int within classical mathematics independent of intuitionistic assumptions. In this paper we follow the Kolmogorov Godel approach. In agreement with Godel s papers [39] and [41] we adopt the following natural requirements for provability semantics: 1. BHK proofs should correspond to proofs in some formal theory T T F , there is a BHK proof of F; and the predicate p is a BHK proof of F should be decidable 2. A BHK semantics should be non circular. In ....
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K. G odel, Eine Interpretation des intuitionistischen Aussagenkalkuls, Ergebnisse Math. Colloq., vol. 4 (1933), pp. 39--40.
A Polynomial Translation of Propositional S4 into Propositional.. - Egly (Correct)
....purely proof theoretical means, i.e. by proof transformations between di erent cut free sequent calculi. Consequently, this approach yields e ective translation procedures. 1 Introduction Embeddings of logics into other logics have a long tradition in the area of mathematical logic (see, e.g. [7, 11, 13, 10] for some classical references) Some embeddings are practically motivated, some others are of theoretical interest. The embedding of the modal logic S4 into the modal logic T (see, e.g. 2, 6] is an example for the former, because, due to the transitivity of the S4 accessibility relation, usual ....
....from theorem provers for classical ( rst order) logic by extending the latter with suitable theory uni cation procedures [12, 17] In this paper, we present a translation of the modal propositional logic S4 into propositional intuitionistic logic. The reverse embedding is well investigated [7, 11, 13, 10, 16]; see [15] for a discussion of the di erent approaches. It was used to relate the intended informal meaning of intuitionistic logic (the Brouwer HeytingKolmogorov semantics) which understands intuitionistic truth as provability to classical provability. Several variants of the embedding of ....
K. Godel. Eine Interpretation des intuitionistischen Aussagenkalkuls. In Ergebnisse eines Mathematischen Kolloquiums, volume 4, pages 39-40. 1933. English translation in [5], pp 300-303.
S5 is a Paraconsistent Logic and so is Classical First-Order Logic - Beziau (2000) (Correct)
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K. Godel, 1933, \Eine Interpretation des intuitionistischen Aussagenkalkuls", Ergebnisse eines matematischen Kolloquiums 4, pp.34-40.
Monotonic Modal Logics - Hansen (2003) (Correct)
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K. Godel. Eine Interpretation des intuitionistischen Aussagenkalkuls. Ergebnisse eines mathematischen Kolloquiums, 6:39-40, 1933.
Paraconsistent Logic from a Modal Viewpoint - Beziau (Correct)
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K. Godel, 1933, \Eine Interpretation des intuitionistischen Aussagenkalk uls", Ergebnisse eines matematischen Kolloquiums , 4, pp.34-40.
Explicit Provability And Constructive Semantics - Artemov (2001) (1 citation) (Correct)
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K. G odel, Eine Interpretation des intuitionistischen Aussagenkalkuls, Ergebnisse Math. Colloq., vol. 4 (1933), pp. 39--40.
Uniform Provability Realization of Intuitionistic Logic, Modality .. - Artemov (1999) (Correct)
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K. Godel, Eine Interpretation des intuitionistischen Aussagenkalkuls, Ergebnisse Math. Colloq., Bd. 4, S. 39-40, 1933.
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