We present TruthSplit, an interactive system for multi-perspective argument analysis. Existing argumentation tools typically analyze properties of the argument itself, such as structure, quality, stance, or persuasiveness, while leaving perspective-specific background knowledge implicit. TruthSplit addresses this gap by supporting an exploratory analysis of how the same claim can lead to different conclusions when interpreted through worldview-specific values, assumptions, and conceptual definitions. We refer to this perspective-dependent analysis as conditional validity.Given an input argumentative text, TruthSplit extracts claims and premises, applies a three-layer natural language inference (NLI) approach to assess both logical and worldview-specific normative consistency, and conditions large language model (LLM) reasoning on structured worldview profiles that encode core values and decision principles. The system then generates perspective-specific interpretations, identifies value conflicts and assumption gaps, and visualizes divergence through interactive analytical interfaces.