On connexivity in modal and conditional contexts

Paper

Abstract

We define and axiomatize three new logics based on the connexive logic

, the modal logic

and the conditional logics

and

. These logics display strong connexivity properties and are connected to one another, since

is the reflexive extension of

and

is faithfully embeddable into both

and

in a multitude of natural ways. We argue that all the three logics provide (albeit in different ways) natural expansions of

to their respective languages that preserve and further develop several core properties of

, especially its connexivity profile.