Incompatibility and Inference as Bases of Logic

0506960 - FLÚ 2020 RIV GB eng C - Conference Paper (international conference)
Peregrin, Jaroslav
Incompatibility and Inference as Bases of Logic.
The Logica Yearbook 2015. London: College Publications, 2016 - (Arazim, P.; Dančák, M.), s. 157-162. ISBN 978-1-84890-213-8.
[Logica 2015. Hejnice (CZ), 15.06.2015-19.06.2015]
R&D Projects: GA ČR(CZ) GA13-21076S
Institutional support: RVO:67985955
Keywords : inference * incompatibility * classical logic * intuitionist logic
OECD category: Philosophy, History and Philosophy of science and technology

That logic can be based merely either on the concept of inference, or on that of incompatibility has been already shown. The question is whether such austere foundations predetermine the kind of logic we reach in such a way. In this paper we show that in the case of logic based on inference the natural outcome is intuitionist logic, while we can reach also classical logic (if we sacrifice naturalness). However, in case of logic based on incompatibility the outcome is not really optional: the resulting logic is classical and there is no obvious way how to reach intuitionist logic.
Permanent Link: http://hdl.handle.net/11104/0298078