arXiv:2604.04344v1 Announce Type: new Abstract: We establish a computation-substrate-agnostic inference architecture in which domain is an explicit first-class computational parameter. This produces domain-scoped pruning that reduces per-query search space from O(N) to O(N/K), substrate-independent execution over symbolic, neural, vector, and hybrid substrates, and transparent inference chains where every step carries its evaluative context. The contribution is architectural, not logical. We formalize the computational theory across five dimensions: a five-layer architecture; three domain computation modes including chain indexing, path traversal as Kleisli composition, and vector-guided computation as a substrate transition; a substrate-agnostic interface with three operations Query, Extend, Bridge; reliability conditions C1 to C4 with three failure mode classes; and validation through a PHQ-9 clinical reasoning case study. The computational theory including operational semantics, complexity bounds, monad structure, substrate transitions, and boundary conditions is the contribution of this paper.

arXiv:2604.01770v2 Announce Type: replace Abstract: Knowledge graphs store large numbers of relations efficiently, but they remain weak at representing a quieter difficulty: the meaning of a concept often shifts with the domain in which it is used. A triple such as Apple, instance-of, Company may be acceptable in one setting while being misleading or unusable in another. In most current systems, domain information is attached as metadata, qualifiers, or graph-level organization. These mechanisms help with filtering and provenance, but they usually do not alter the formal status of the assertion itself. This paper argues that domain should be treated as part of knowledge representation rather than as supplementary annotation. It introduces the Domain-Contextualized Concept Graph (DCG), a framework in which domain is written into the relation and interpreted as a modal world constraint. In the DCG form (C, R at D, C'), the marker at D identifies the world in which the relation holds. Formally, the relation is interpreted through a domain-indexed necessity operator, so that truth, inference, and conflict checking are all scoped to the relevant world. This move has three consequences: ambiguous concepts can be disambiguated at the point of representation; invalid assertions can be challenged against their domain; cross-domain relations can be connected through explicit predicates. The paper develops this claim through a Kripke-style semantics, a compact predicate system, a Prolog implementation, and mappings to RDF, OWL, and relational databases. The contribution is a representational reinterpretation of domain itself. The central claim is that many practical failures in knowledge systems begin when domain is treated as external to the assertion. DCG addresses that by giving domain a structural and computable role inside the representation.