5 found
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  1. On an Intuitionistic Logic for Pragmatics.Gianluigi Bellin, Massimiliano Carrara & Daniele Chiffi - 2018 - Journal of Logic and Computation 50 (28):935–966..
    We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justi cations and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at the (...)
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  2.  43
    A system of natural deduction for GL.Gianluigi Bellin - 1985 - Theoria 51 (2):89-114.
  3.  28
    Errata Corrige to “Pragmatic and dialogic interpretation of bi-intuitionism. Part I”.Gianluigi Bellin, Massimiliano Carrara, Daniele Chiffi & Alessandro Menti - 2016 - Logic and Logical Philosophy 25 (2).
  4.  36
    (1 other version)Pragmatic and dialogic interpretations of bi-intuitionism. Part 1.Gianluigi Bellin, Massimiliano Carrara, Daniele Chiffi & Alessandro Menti - 2014 - Logic and Logical Philosophy 23 (4):449-480.
    We consider a “polarized” version of bi-intuitionistic logic [5, 2, 6, 4] as a logic of assertions and hypotheses and show that it supports a “rich proof theory” and an interesting categorical interpretation, unlike the standard approach of C. Rauszer’s Heyting-Brouwer logic [28, 29], whose categorical models are all partial orders by Crolard’s theorem [8]. We show that P.A. Melliès notion of chirality [21, 22] appears as the right mathematical representation of the mirror symmetry between the intuitionistic and co-intuitionistc sides (...)
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  5.  2
    On the Pi-calculus and Linear Logic.Gianluigi Bellin & P. J. Scott - 1992 - LFCS, Department of Computer Science, University of Edinburgh.
    "We detail Abramsky's 'proofs-as-processes" paradigm for interpreting classical linear logic (CCL) [11] into a 'synchronous' version of the [pi]-calculus recently proposed by Milner [24]. The translation is given at the abstract level of proof structures. We give a detailed treatment of information flow in proof-nets and show how to mirror various evaluation strategies for proof normalization. We also give Soundness and Completeness results for the process-calculus translations of various fragments of CLL. The paper also gives a self-contained introduction to some (...)
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