How the Undeducible Becomes Derivable: A Formal Framework for Artificial Intuition

Purpose: the purpose of this paper is to provide a formal framework for modeling intuition as a logically definable inferential phenomenon. Methodology: the study employs a formal and conceptual methodology grounded in non-relational modal semantics, specifically Resolution Matrix Semantics (RMS). Indeterminate truth values in RMS are reinterpreted as superposed logical states rather than as epistemic uncertainty. Each admissible semantic resolution generates a component logic, which is treated as a basis state in a logical state space. Logical validity is formalized using operator-based semantics, and acceptance of conclusions is governed by a collapse rule based on semantic support. The framework is developed through formal definitions and inference rules and is illustrated using modal and deontic examples. Philosophical analysis is used to assess the implications of the framework for Gödel’s incompleteness theorem and the Penrose argument. Findings: the paper demonstrates the existence of emergent inferences: formulas that are accepted in a superposed logical state despite being derivable in none of the component logics individually. These inferences are formally defined as instances of artificial intuition. The results show that intuition can be modeled as an interference effect between incompatible logics followed by a collapse to a stable conclusion. The framework further shows that Gödelian incompleteness applies only to monological formal systems and does not constrain poly-logical superposed reasoning. In normative applications, the approach provides a non-trivial resolution of conflicting obligations without logical explosion. Unique Contribution to Theory, Practice and Policy: the study contributes to theory by introducing quantum-inspired poly-logic as a novel formal framework that extends classical and non-classical logics beyond monological reasoning and provides a precise definition of intuition as emergent inference. In practice, the framework offers a principled architecture for artificial intelligence systems capable of creative, context-sensitive, and conflict-stabilizing reasoning. At the policy level, the approach provides a formal basis for managing normative and ethical conflicts in complex decision-making environments, supporting pluralistic and non-explosive reasoning under inconsistency.