Domain-constrained knowledge representation: A modal framework

Chao Li; Yuru Wang; Chunyi Zhao

cs.AIApr 2, 2026

Domain-constrained knowledge representation: A modal framework

Authors: Chao Li, Yuru Wang, Chunyi Zhao

Organizations: School of Information Science and Technology, Northeast Normal University · Centre of Educational Design and Learning, University of Otago

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.

Figures & tables

Approach	Layer	CDC’s Relationship
DBpedia / Freebase	Implementation	Provides data substrate
Wikidata	Implementation	Extends with domain-scoped reasoning
Upper ontologies	Formal semantics	More flexible philosophy
Domain ontologies	Specialized	Cross-domain integration layer
Conceptual spaces	Geometric theory	Cognitive inspiration
Frame semantics	Linguistic theory	Theoretical grounding

Table 1: Positioning CDC relative to existing approaches.

Use Case	Pattern	Example
Academic Research	Discipline@Theory	’Psychology@Behaviorism’
Education	Grade@Subject@Topic	’HighSchool@Chemistry@Organic’
Enterprise	Department@Project	’Engineering@ProductA@Testing’
Historical	Era@Region@Movement	’Renaissance@Italy@Humanism’
Technical Docs	Stack@Version@Context	’[email protected]@Mobile_Apps’
Personal Learning	Individual@Background	’Student_Li@CS_Major’

Table 2: Domain specification patterns by use case.

Panel of Figure 1 — Figure 1: Topology preservation across domain worlds. The six-node chain Responsibility $\to$ Care $\to$ Character $\to$ Discipline $\to$ Qualities $\to$ Impact is structurally invariant; only domain-specific content changes.

Dimension	Traditional KR	CDC
What a triple asserts	An unconditional fact	A modally constrained assertion $\Box_{D}R(C,C^{\prime})$
Role of domain	Absent or metadata	First-class constraint operator
Disambiguation	External multi-module pipeline	Structural property of representation
Reasoning scope	Global (all facts, all rules)	World-local (per domain)
Falsification	Not possible at representation layer	Inconsistent assertions rejected by $\Box_{D}$
Cross-domain reasoning	Manual ontology alignment	Modal possibility $\Diamond(D_{1}\wedge D_{2})$

Table 3: Comparison of traditional KR and CDC along key representational dimensions.

Relation	Transitive	Symmetric	Reflexive	Complexity
is_a	✓	$\times$	$\times$	$O(n^{2})$
part_of	✓	$\times$	$\times$	$O(n^{2})$
requires	✓	$\times$	$\times$	$O(n^{2})$
analogous_to	$\times$	✓	$\times$	$O(n^{2})$
fuses_with	$\times$	✓	$\times$	$O(n^{3})$

Table 4: Algebraic properties and complexity of CDC relations.

Representation	Triple Structure	Fields	Overhead vs. RDF
RDF Triple	$\langle s,p,o\rangle$	3	baseline
RDF Named Graph	$\langle s,p,o,g\rangle$	4	$+1$ graph URI
Wikidata Qualifier	$\langle s,p,o\rangle$ + qualifier list	$3+\text{var}$	$+N$ qualifier pairs
CDC	$\langle c,r,c^{\prime},d\rangle$	4	$+1$ domain string

Table 5: Per-triple storage comparison across representations.

Operation	RDF (no domain)	CDC
Simple lookup	$O(N)$ scan or $O(1)$ indexed	$O(N/K)$ scan or $O(1)$ indexed
Transitive closure	$O(N^{2})$ over all triples	$O((N/K)^{2})$ within one world
Cross-domain search	N/A (no formal mechanism)	$O(N/K_{1}\times N/K_{2})$ between two worlds

Table 6: Query complexity comparison between RDF and CDC.

Capability	RDF	Wikidata	CDC
Scope relation to domain	Via separate graphs (manual)	Via annotation (not structural)	Structural (part of tuple)
Reject inconsistent assertions	No	No	Yes ( $\Box_{D}$ constraint)
Transitive closure respects domain	Only if separate graphs	Requires custom extensions	Automatic
A priori disambiguation	No	No	Yes (pre-scoped at repr. time)
Cross-domain analogy	No formal mechanism	No formal mechanism	analogous_to@ $D_{1}{\leftrightarrow}D_{2}$
Storage overhead per triple	baseline	$+N$ qualifier pairs	$+1$ string field

Table 7: Capability comparison: RDF, Wikidata qualifiers, and CDC.

Property	RDF Named Graph	CDC (via mapping)
Statement grouping	✓	✓
SPARQL queryability	✓	✓
Inference scoping	$\times$ (manual GRAPH clauses)	✓(automatic)
Falsification	$\times$	✓( $\Box_{D}$ semantics)
Cross-graph reasoning	$\times$	✓( analogous_to , fuses_with )

Table 8: Properties preserved by the RDF Named Graph–CDC mapping.

Knowledge Representation

Knowledge representation studies how to encode facts, concepts, rules, context, and uncertainty so machines can interpret and reason over them.

See all 126 papers

Jun 13, 2026

Provenance-Enhanced Statements in Knowledge Graphs

Provenance-enhanced statements of the form "according to

X

\varphi

" are pervasive in contemporary knowledge graphs, especially in domains where graph content primarily represents claims, interpretations, and hypotheses (capta) rather than observer-independent facts (data). Current provenance models can record who asserted what, but they typically treat provenance as semantically neutral, leaving underspecified how attributed claims relate to factual commitment, to one another, and to reasoning. In this paper we introduce DEC, a framework that interprets provenance predicates as indicators of epistemic stance and groups provenance-homogeneous sets of statements into cognitive worlds. Drawing on cognitive modal logics (doxastic, epistemic, and conjectural), DEC characterizes locality, rationality, and controlled permeation between cognitive worlds and a distinguished factual core ("reality"), thereby enabling principled reasoning over attributed content without collapsing disagreements into inconsistencies. We formalize a DEC interpretation for RDF datasets that is conservative over RDF~1.2 semantics, clarify the role of intensionality and identity (including the Superman paradox), and illustrate the approach on common Semantic Web representations (named graphs, quoted triples/RDF-star, and reification). Finally, we describe our prototype DEC reasoner implemented as a Fuseki dataset module, supporting controlled factualisation and explicit detection of disagreements and delusions.

Fabio Vitali, Valentina Pasqual

University of Bologna, Italy

Logical Reasoning Data Provenance Knowledge Representation Graph Reasoning Knowledge Graphs Epistemic Logic

Ask PDF

Apr 13, 2026

Reasoning as Data: Representation-Computation Unity and Its Implementation in a Domain-Algebraic Inference Engine

Every existing knowledge system separates storage from computation. We show this separation is unnecessary and eliminate it. In a standard triple is_a(Apple, Company), domain context lives in the query or the programmer's mind. In a CDC four-tuple is_a(Apple, Company, @Business), domain becomes a structural field embedded in predicate arity. Any system respecting arity automatically performs domain-scoped inference without external rules. We call this representation-computation unity (RCU). From the four-tuple structure, three inference mechanisms emerge: domain-scoped closure, typed inheritance, and write-time falsification via cycle detection per domain fiber. We establish RCU formally via four theorems. RCU is implementable. We present a working symbolic engine (2400 lines Python+Prolog) resolving four engineering issues: rule-data separation, shared-fiber handling, read-only meta-layer design, and intersective convergence. A central result: CDC domain-constrained inference is distinct from Prolog with a domain argument. Two case studies validate the engine. ICD-11 classification (1247 entities, 3 axes) shows fibers resolve multiple inheritance. CBT clinical reasoning shows generalization to temporal reasoning with session turn as ordered domain index. Multi-constraint queries realize CSP arc-consistency with complexity O(m (N/K)^2), confirming the domain lattice's sparsity governs performance. When domain is structural, data computes itself.

Chao Li, Yuru Wang

Northeast Normal University

Symbolic Reasoning

Ask PDF

Feb 23, 2026

Denotational Semantics for ODRL: Knowledge-Based Constraint Conflict Detection

ODRL's six set-based operators -- isA, isPartOf, hasPart, isAnyOf, isAllOf, isNoneOf -- depend on external domain knowledge that the W3C specification leaves unspecified. Without it, every cross-dataspace policy comparison defaults to Unknown. We present a denotational semantics that maps each ODRL constraint to the set of knowledge-base concepts satisfying it. Conflict detection reduces to denotation intersection under a three-valued verdict -- Conflict, Compatible, or Unknown -- that is sound under incomplete knowledge. The framework covers all three ODRL composition modes (and, or, xone) and all three semantic domains arising in practice: taxonomic (class subsumption), mereological (part-whole containment), and nominal (identity). For cross-dataspace interoperability, we define order-preserving alignments between knowledge bases and prove two guarantees: conflicts are preserved across different KB standards, and unmapped concepts degrade gracefully to Unknown -- never to false conflicts. A runtime soundness theorem ensures that design-time verdicts hold for all execution contexts. The encoding stays within the decidable EPR fragment of first-order logic. We validate it with 154 benchmarks across six knowledge base families (GeoNames, ISO 3166, W3C DPV, a GDPR-derived taxonomy, BCP 47, and ISO 639-3) and four structural KBs targeting adversarial edge cases. Both the Vampire theorem prover and the Z3 SMT solver agree on all 154 verdicts. A key finding is that exclusive composition (xone) requires strictly stronger KB axioms than conjunction or disjunction: open-world semantics blocks exclusivity even when positive evidence appears to satisfy exactly one branch.

Daham Mustafa, Diego Collarana, Yixin Peng +4

RWTH Aachen University, Germany · Fraunhofer FIT, Sankt Augustin, Germany · University of Galway, Ireland

Policy Evaluation Knowledge Representation Constraint Satisfaction

Ask PDF

Abstract

Knowledge Representation

Explore similar work

Provenance-Enhanced Statements in Knowledge Graphs

Reasoning as Data: Representation-Computation Unity and Its Implementation in a Domain-Algebraic Inference Engine

Denotational Semantics for ODRL: Knowledge-Based Constraint Conflict Detection