R. Goldblatt Arithmetical necessity, provability and intuitionistic logic, Theoria, v. 44, pp. 38-- 46, 1978. Home/Search Document Not in Database Summary Related Articles Check |
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Theoremhood Preserving Maps Characterising Cut Elimination.. - Demri, Goré (2001) (Correct)
....as K4 plus the axiom schema 2(2p Grz is defined as S4 plus the axiom schema 2(2(p 2p. The logic Grz can also be axiomatised as S4 plus the axiom schema 2(2(p p [GHH97] which came to light in investigations of the connection between intuitionistic and modal logic (see e.g. [Gol78]) We write L [resp. L F] to denote the extension of L [resp. LF] obtained by adding the axiom schemata 2 (p (2 p 2 q) q 23 q q 2 3q That is, there is a finite sequence 1 , #n such that #n = # and for any # 1, n , either # i is an ....
R. Goldblatt. Arithmetical necessity, provability and intuitionistic logic. Theoria, 44:38--46, 1978. 32
Explicit Provability and Constructive Semantics - Artemov (2000) (1 citation) (Correct)
....semantics (Kleene, 1945, 51] 4. Beth models (1956, 22] 5. Dialectica Interpretation (Godel, 1958, 40] 6. Curry Howard isomorphism (1958, 32] 7. Medvedev s logic of problems (1962, 71] 8. Kripke models (1965, 59] 9. Kuznetsov Muravitsky Goldblatt interpretation (1976, [42], 63] 10. Categorical semantics (Goldblatt, 1979, 43] Those interpretations have shown to be extremely fruitful for understanding intuitionistic logic though none of them qualifies as a BHK semantics. Interpretations 1 5, 7, 8, 10 are not related to provability. In particular, Kleene ....
....and Vardanyan [102] who demonstrated that the first order logic of formal provability was not axiomatizable. The issue of provability semantics for S4 was addressed by Lemmon [65] Myhill [77] 78] Kripke [58] Montague [76] Novikov [79] Mints [73] Kuznetsov and Muravitsky [63] Goldblatt [42], Boolos [25] 26] Shapiro [88] 89] Buss [29] Artemov [5] and many others. However, there were no adequate Godelian provability semantics for S4 found 5 . Moreover, in [76] the problem was announced hopeless. In this paper we give a complete solution to the problem of provability ....
R. Goldblatt, Arithmetical necessity, provability and intuitionistic logic, Theoria, vol. 44 (1978), pp. 38--46.
Speaking About Transitive Frames in Propositional Languages - Suzuki, Wolter.. (1998) (1 citation) (Correct)
....proof interpretation. Thus S4 can be regarded as a logic of informal provability, even in a very precise sense, as has been recently shown by Artemov [3] An embedding of Int into the logic of formal provability (in Peano arithmetic) GL was constructed by Boolos [7] Goldblatt [14] and Kuznetsov and Muravitskij [16] Here we need the map T which first takes the Godel translation T of an L formula and then to simulate reflexivity in irreflexive frames for GL replaces every 2 in T by 2 = 2 . T alone is not able to embed Int into GL; for instance, T(p ....
R.I. Goldblatt. Arithmetical necessity, provability and intuitionistic logic. Theoria, 44:38--46, 1978.
On Epistemic Logic with Justification - Sergei Artemov Elena (Correct)
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R. Goldblatt Arithmetical necessity, provability and intuitionistic logic, Theoria, v. 44, pp. 38-- 46, 1978.
The Modal Logic of Pure Provability - Samuel Buss Department (1990) (6 citations) (Correct)
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Rob Goldblatt. Arithmetical necessity, provability and intuitionistic logic. Theoria, 44:38--46, 1978.
Explicit Provability And Constructive Semantics - Artemov (2001) (1 citation) (Correct)
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R. Goldblatt, Arithmetical necessity, provability and intuitionistic logic, Theoria, vol. 44 (1978), pp. 38--46.
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