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Reasoning about negligibility and proximity in the set of all hyperreals

Balbiani, Philippe Reasoning about negligibility and proximity in the set of all hyperreals. (2016) Journal of Applied Logic, 16. 14-36. ISSN 1570-8683

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Official URL: https://doi.org/10.1016/j.jal.2016.04.002

Abstract

We consider the binary relations of negligibility, comparability and proximity in the set of all hyperreals. Associating with negligibility, comparability and proximity the binary predicates N, C and P and the connectives [N], [C] and [P], we consider a first-order theory based on these predicates and a modal logic based on these connectives. We investigate the axiomatization/completeness and the decidability/complexity of this first-order theory and this modal logic.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at Journal of Applied Logic (ISSN : 1570-8683) website : https://www.sciencedirect.com/science/article/pii/S157086831630012X
HAL Id:hal-01739997
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
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Deposited On:07 Mar 2018 14:41

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