3 papers
cs.LO2026
A Proof-Theoretic Study of Modal Logic
Hirohiko Kushida
This paper proposes a basic proof theoretic framework for major modal logics: {\sf S5} and some of its subsystems. The framework is based on a version of hypersequent calculus, and…
cs.LO2026
Cut-Elimination for the Bimodal Logic GR
Hirohiko Kushida
In this paper, we present a hypersequent calculus for bimodal logic GR, where the two modalities represent the arithmetic provability predicates of Goedel and Rosser, respectively.…
cs.LO2019
On the Constructive Truth and Falsity in Peano Arithmetic
Hirohiko Kushida
Recently, Artemov [4] offered the notion of constructive consistency for Peano Arithmetic and generalized it to constructive truth and falsity in the spirit of Brouwer-Heyting-Kolm…