Errata Corrige to “Pragmatic and dialogic interpretation of bi-intuitionism. Part I”

Gianluigi Bellin, Massimiliano Carrara, Daniele Chiffi, Alessandro Menti



The goal of [3] is to sketch the construction of a syntactic categorical model of the bi-intuitionistic logic of assertions and hypotheses AH, axiomatized in a sequent calculus AH-G1, and to show that such a model has a chirality-like structure inspired by the notion of dialogue chirality by P-A. Melliès [8]. A chirality consists of a pair of adjoint functors L R, with L: A → B, R: B → A, and of a functor (.)* : A → Bop(0,1) satisfying certain conditions. The definition of the logic AH in [3] needs to be modified so that our categories A and B are actually dual. With this modification, a more complex structure emerges.


bi-intuitionism; categorical proof theory; justificationism; meaning-as-use; speech-acts theory

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Bellin, G., “Assertions, hypotheses, conjectures, expectations: Rough-sets semantics and proof-theory”, pp. 193–241 in Advances in Natural Deduction. A Celebration of Dag Prawitz’s Work, L.C. Pereira, E. H. Haeusler, and V. de Paiva (eds.), series “Trends in Logic”, vol. 39, Springer Science + Business Media Dordrecht 2014. DOI: 10.1007/978-94-007-7548-0_10

Bellin, G., and C. Biasi, “Towards a logic for pragmatics. Assertions and conjectures”, Journal of Logic and Computation, 14, 4 (2004): 473–506. DOI: 10.1093/logcom/14.4.473

Bellin, G., M. Carrara, D. Chiffi, and A. Menti, “Pragmatic and dialogic interpretations of bi-intuitionism. Part I”, Logic and Logical Philosophy, 23, 4 (2014), 449–480. DOI: 10.12775/LLP.2014.011

Biasi, C., and F. Aschieri, “A term assignment for polarized bi-intuitionistic logic and its strong normalization”, Fundamenta Informaticae, 84, 2 (2008): 185–205.

Crolard, T., “Subtractive logic”, Theoretical Computer Science, 254, 1–2 (2001): 151–185. DOI: 10.1016/S0304-3975(99)00124-3

Drobyshevich, S., “On classical behavior of intuitionistic modalities”, Logic and Logical Philosophy, 24 (2015): 79–106. DOI: 10.12775/LLP.2014.019

Melliès, P-A., “Dialogue categories and chiralities”, manuscript (available at the author’s web page Link).

Melliès, P.-A., “A micrological study of negation”, manuscript (available at the author’s web page Link)

Print ISSN: 1425-3305
Online ISSN: 2300-9802

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