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

• Authors: Bellin Gianluigi , Carrara Massimiliano , Chiffi Daniele , Menti Alessandro
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

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

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2016
• Volume: 25
• Issue: 2
• Pages: 225-233

Dates

online

2015-04-18

Contributors

author

Bellin Gianluigi

• Dipartimento di Informatica, Università di Verona, Strada Le Grazie, 37134 Verona, Italy

author

Carrara Massimiliano

• FISPPA Department, University of Padua, Padova, Italy

author

Chiffi Daniele

• LEMBS, University of Padua, Padua, Italy

author

Menti Alessandro

• Dipartimento di Informatica, Università di Verona, Strada Le Grazie, 37134 Verona, Italy

References

• 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 https://www.irif.fr/~mellies/tensorial-logic/2-dialogue-categories-and-chiralities.pdf).
• Melliès, P.-A., “A micrological study of negation”, manuscript (available at the author’s web page https://www.irif.fr/~mellies/tensorial-logic/4-micrological-study-of-negation.pdf)

Identifiers

DOI

10.12775/LLP.2015.005