On connexivity in modal and conditional contexts

TL;DR

This paper introduces three new connexive modal and conditional logics that extend the base connexive logic , exploring their properties, interrelations, and natural expansions while preserving core connexivity features.

Contribution

The paper defines and axiomatizes three novel connexive modal and conditional logics, analyzing their properties, relationships, and extensions, advancing the understanding of connexivity in modal and conditional contexts.

Findings

 is extended to three new logics with strong connexivity properties.

K is embeddable into CK and CK_R in natural ways.

The new logics preserve and develop core properties of , especially connexivity.

Abstract

We define and axiomatize three new logics based on the connexive logic $\mathsf{C}$, the modal logic $\mathsf{CnK}$ and the conditional logics $\mathsf{CnCK}$ and $\mathsf{CnCK}_R$. These logics display strong connexivity properties and are connected to one another, since $\mathsf{CnCK}_R$ is the reflexive extension of $\mathsf{CnCK}$ and $\mathsf{CnK}$ is faithfully embeddable into both $\mathsf{CnCK}$ and $\mathsf{CnCK}_R$ in a multitude of natural ways. We argue that all the three logics provide (albeit in different ways) natural expansions of $\mathsf{C}$ to their respective languages that preserve and further develop several core properties of $\mathsf{C}$, especially its connexivity profile.