Computational Realization of Representational Scientific Discovery

Abstract

A formally complete bounded representational space may contain every candidate expression permitted by a specified encoding, but explicit enumeration of such a space rapidly becomes computationally infeasible. This paper examines the computational and technological requirements for turning representational scientific discovery into an executable search methodology. The central distinction is between the complete formal domain S(Σ, L) and an effective search space Seff(Q, K, D, C) determined by the scientific question, available knowledge, empirical data, representation, and search constraints. Practical discovery is formulated as selective navigation of this effective domain rather than materialization of the complete representational space. The resulting architecture combines constraint-first search, candidate generation and ranking, consequence derivation, simulation, empirical evaluation, experimental design, and iterative feedback. Its central computational tension is between search-space reduction and target preservation: increasingly aggressive reduction improves tractability but increases the risk of excluding scientifically valuable unknown candidates. Existing technologies—including symbolic computation, automated reasoning, constraint solving, symbolic regression, scientific machine learning, numerical simulation, information retrieval, and automated experimentation—provide partial realizations of individual components, but not a demonstrated general-purpose system for open-ended scientific theory discovery. The remaining challenges include scientifically adequate representation, semantic integration, scalable constraint propagation, consequence derivation, uncertainty handling, novelty preservation, long-horizon coherence, and integration of theoretical search with empirical feedback. The framework therefore shifts the implementation problem from exhaustive generation to constrained, adaptive, and empirically testable search. It also suggests an incremental research program based on retrospective rediscovery, measurable search-space reduction, target-retention tests, restricted open problems, and progressively more demanding closed-loop scientific search.