Computational value analysis has largely treated values as instances of predefined universal taxonomies, making it difficult to discover culturally specific value dimensions not fully represented in existing schemes. We formulate value analysis as an open-ended discovery problem grounded in the argumentative contexts in which values are expressed. To this end, we propose an LLM-assisted framework that discovers human value dimensions directly from text without relying on predefined taxonomies. It extracts Premise-Conclusion-Stance (P-C-S) argumentative edges under explicit argument tree constraints, expands each edge into structured value-semantic descriptions spanning goal, principle, tradeoff, and perspective dimensions, and induces coherent value clusters via co-association consensus clustering over the embedding representations. We evaluate the framework across ten languages using external label alignment, internal structural stability metrics, and human judgment. Results show that the framework is robust and transferable, with the induced value structures achieving low hallucination and strong alignment with human judgments while revealing culturally distinctive value orientations that both align with and meaningfully complement established psychological frameworks. By shifting computational value analysis from taxonomy-driven classification toward open-ended discovery, our framework offers a new approach to cross-cultural value research, with implications for culturally aware AI alignment.