A bilateral Hilbert-style investigation of 2-intuitionistic logic

Результат исследования: Научные публикации в периодических изданияхстатья

Аннотация

We develop a bilateral Hilbert-style calculus for 2-intuitionistic logic of Heinrich Wansing. This calculus is defined over signed formulas of two types: formulas signed with plus correspond to assertions, while formulas signed with minus correspond to rejections. In this way, the provided system is a Hilbert-style calculus, which does take rejection seriously by considering it a primitive notion on par with assertion. We show that this presentation is not trivial and provide two equivalent axiomatizations obtained by extending intuitionistic and dual intuitionistic logics, respectively. Finally, we show that 2-intuitionistic logic is in some sense definitionally equivalent to a variant of Nelson's logic with constructible falsity.

Язык оригиналаанглийский
Страницы (с-по)665-692
Число страниц28
ЖурналJournal of logic and computation
Том29
Номер выпуска5
DOI
СостояниеОпубликовано - 1 сен 2019

Цитировать