TY - JOUR
AU - Drobyshevich, Sergey
PY - 2014/08/16
Y2 - 2022/01/19
TI - On classical behavior of intuitionistic modalities
JF - Logic and Logical Philosophy
JA - LLP
VL - 24
IS - 1
SE - Articles
DO - 10.12775/LLP.2014.019
UR - https://apcz.umk.pl/LLP/article/view/LLP.2014.019
SP - 79–104
AB - We study connections between four types of modal operators – necessity, possibility, un-necessity and impossibility – over intuitionitstic logic in terms of compositions of these modal operators with intuitionistic negation. We investigate which basic compositions, i.e. compositions of the form ¬δ, δ¬ or ¬δ¬, yield modal operators of the same type over intuitionistic logic as over classical logic. We say that such compositions behave classically. We study which modal properties correspond to each basic compositions behaving classically over intuitionistic logic and also prove that KC constitutes the smallest superintuitionistic logic over which all basic compositions behave classically.
ER -