Intuitionistic $j$-Do-Calculus in Topos Causal Models

תקציר מקורי באנגליתarXiv:2510.17944v2 Announce Type: replace-cross Abstract: In this paper, we generalize Pearl's do-calculus to an Intuitionistic setting called $j$-stable causal inference inside a topos of sheaves. Our framework is an elaboration of the recently proposed framework of Topos Causal Models (TCMs), where causal interventions are defined as subobjects. We generalize the original setting of TCM using the Lawvere-Tierney topology on a topos, defined by a modal operator $j$ on the subobject classifier $\Omega$. We introduce $j$-do-calculus, where we replace global truth with local truth defined by Kripke-Joyal semantics, and formalize causal reasoning as structure-preserving morphisms that are stable along $j$-covers. $j$-do-calculus is a sound rule system whose premises and conclusions are formul