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Computational Interrpretations of Logics
Zbornik radova, Tome 12 (2009) no. 20, p. 159 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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The fundamental connection between logic and computation, known as the Curry-Howard correspondence or formulae-astypes and proofs-as-programs paradigm, relates logical and computational systems. We present an overview of computational interpretations of intuitionistic and classical logic: - intuitionistic natural deduction - A-calculus; - intuitionistic sequent calculus - A Gtz-calculus; - classical natural deduction - AJ.L-calculus; - classical sequent calculus - XJ.Lj:L-calculus. In this work we summarise the authors' contributions in this field. Fundamental properties of these calculi, such as confluence, normalisation properties, reduction strategies call-by-value and call-by-name, separability, reducibility method, A-models are in focus. These fundamental properties and their counterparts in logics, via the CurryHoward correspondence, are discussed. 
@article{ZR_2009_12_20_a4,
     author = {Silvia Ghilezan and Silvia Likavec},
     title = {Computational {Interrpretations} of {Logics}},
     journal = {Zbornik radova},
     pages = {159 },
     year = {2009},
     volume = {12},
     number = {20},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZR_2009_12_20_a4/}
}
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Silvia Ghilezan; Silvia Likavec. Computational Interrpretations of Logics. Zbornik radova, Tome 12 (2009) no. 20, p. 159 . http://geodesic.mathdoc.fr/item/ZR_2009_12_20_a4/