Modeling Knowledge and Decision-Making with the Conditional Reasoning Framework

Representing and reasoning with complex, uncertain, context-dependent, and value-laden knowledge remains a fundamental challenge in Artificial Intelligence (AI) and Knowledge Representation (KR). Existing frameworks often struggle to integrate diverse knowledge types, make underlying assumptions explicit, handle normative constraints, or provide robust justifications for inferences. This preprint introduces the Conditional Reasoning Framework (CRF) and its Orthogonal Knowledge Graph (OKG) as a novel computational and conceptual architecture designed to address these limitations. The CRF operationalizes conditional necessity through a quantifiable, counterfactual test derived from a generalization of J.L. Mackie's INUS condition, enabling context-dependent reasoning within the graph-based OKG. Its design is grounded in the novel Theory of Minimal Axiom Systems (TOMAS), which posits that meaningful representation requires at least two orthogonal (conceptually independent) foundational axioms; TOMAS provides a philosophical justification for the CRF's emphasis on axiom orthogonality and explicit context (W). Furthermore, the framework incorporates expectation calculus for handling uncertainty and integrates the "ought implies can" principle as a fundamental constraint for normative reasoning. By offering a principled method for structuring knowledge, analyzing dependencies (including diagnosing model limitations by identifying failures of expected necessary conditions), and integrating descriptive and prescriptive information, the CRF/OKG provides a promising foundation for developing more robust, transparent, and ethically-aware AI systems.