English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A famous result, conjectured by G\"odel in 1932 and proved by McKinsey andTarski in 1948, says that $\varphi$ is a theorem of intuitionisticpropositional logic IPC iff its G\"odel-translation $\varphi'$ is a theorem ofmodal logic S4. In this paper, we extend an intuitionistic version of modallogic S1+SP, introduced in our previous paper (S. Lewitzka, Algebraic semanticsfor a modal logic close to S1, J. Logic and Comp., doi:10.1093/logcom/exu067)to a classical modal logic L and prove the following: a propositional formula$\varphi$ is a theorem of IPC iff $\square\varphi$ is a theorem of L (actually,we show: $\Phi\vdash_{IPC}\varphi$ iff $\square\Phi\vdash_L\square\varphi$, forpropositional $\Phi,\varphi$). Thus, the map $\varphi\mapsto\square\varphi$ isan embedding of IPC into L, i.e. L contains a copy of IPC. Moreover, L is aconservative extension of classical propositional logic CPC. In this sense, Lis an amalgam of CPC and IPC. We show that L is sound and complete w.r.t. aclass of special Heyting algebras with a (non-normal) modal operator.

A modal logic amalgam of classical and intuitionistic propositional logic