Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
131 tokens/sec
GPT-4o
10 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Glivenko's theorem, finite height, and local tabularity (1806.06899v2)

Published 18 Jun 2018 in math.LO

Abstract: Glivenko's theorem states that a formula is derivable in classical propositional logic $\mathrm{CL}$ iff under the double negation it is derivable in intuitionistic propositional logic $\mathrm{IL}$: $\mathrm{CL}\vdash\varphi$ iff $\mathrm{IL}\vdash\neg\neg\varphi$. Its analog for the modal logics $\mathrm{S5}$ and $\mathrm{S4}$ states that $\mathrm{S5}\vdash \varphi$ iff $\mathrm{S4} \vdash \neg \Box \neg \Box \varphi$. In Kripke semantics, $\mathrm{IL}$ is the logic of partial orders, and $\mathrm{CL}$ is the logic of partial orders of height 1. Likewise, $\mathrm{S4}$ is the logic of preorders, and $\mathrm{S5}$ is the logic of equivalence relations, which are preorders of height 1. In this paper we generalize Glivenko's translation for logics of arbitrary finite height.

Summary

We haven't generated a summary for this paper yet.