Wednesday, 3. April 2019, 10:30, Sala Riunioni (2nd floor).
Satoru Niki (Japan Advanced Institute of Science and Technology)
Empirical Negation and Beth Semantics
The negation in intuitionistic logic has a ‘future-oriented’ character, as elucidated by the valuation in Kripke models. Its application in mathematical contexts has been validated by the success of constructive mathematics. Its applicability in non-mathematical contexts, in contrast, is argued to have some problems. The existence of a different, ‘empirical’ notion of negation within the framework of intuitionistic logic has been discussed by Heyting, Dummett and others. De (2013) proposed empirical negation as falsity at the bottom root of a Kripke model, and De and Omori (2014) gave the axiomatisation of this logic.
In this talk, I will discuss how the choice of semantics in formulating empirical negation affects the logic one obtains, with Beth semantics as a particular example. This is followed by an examination of arithmetic with empirical negation.