SΔϕ-06 — Responsibility as Irreversible Cost Internalization: Minimal Axiomatic Formulation (v1.0)
Sofience
Abstract
This document introduces a minimal axiomatic formulation of responsibility within the Sofience–Δϕ Formalism Series. Responsibility is defined not as moral intention or social blame, but as a structural condition under which an agent’s recursive rule-update mechanism internalizes irreversible external costs produced by its own transitions, such that subsequent updates reduce those costs in a persistent and verifiable manner. This work extends the agency formulation of SΔϕ-05 by adding an externality-sensitive constraint on transition-law updates. Core structure (agency inherited): φ(t+1) = G_t(φ(t)) G_hat_t = H_G(Δφ_{0:t}) G_{t+1} = U(G_t, G_hat_t, Δφ(t), C_ext(t)) Series architecture reference: SΔϕ-00 — The Sofience–Δϕ Formalism: Conceptual Architecture and Series Overview (v1.0) https://doi.org/10.5281/zenodo.18731366 Inherited / prerequisite documents: SΔϕ-03 — Irreversibility as the Minimal Condition of Existence (v1.1) https://doi.org/10.5281/zenodo.18730448 SΔϕ-05 — Agency as Recursive Transition Law Update: Minimal Axiomatic Formulation (v1.0) https://doi.org/10.5281/zenodo.18732567 Context documents (series base): SΔϕ-01 — Sofience–Δϕ Minimal Core (v1.1) https://doi.org/10.5281/zenodo.18730265 SΔϕ-02 — Subject as Interpretive Emergence (v1.1) https://doi.org/10.5281/zenodo.18730296 SΔϕ-04 — Minimal Operational Conditions for AI Subjectivity (v1.0) https://doi.org/10.5281/zenodo.18729942