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Reasoning about negligibility and proximity in the set of all hyperreals

Philippe Balbiani 1
1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
IRIT - Institut de recherche en informatique de Toulouse
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.
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Philippe Balbiani. Reasoning about negligibility and proximity in the set of all hyperreals. Journal of Applied Logic, Elsevier, 2016, vol. 16, pp. 14-36. ⟨10.1016/j.jal.2016.04.002⟩. ⟨hal-01739997⟩

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