Ontology Focusing: Design & Impact

• Ontology focusing is the process of narrowing broad ontologies into application-specific schemas with defined completeness, fixed, and determined query parameters.
• It formalizes a design step that bridges open-world reasoning and closed-world database semantics using description logics and complexity analyses.
• The approach extends to sociotechnical analyses where it critiques AI systems’ implicit world-making assumptions, emphasizing pluralism, groundedness, liveliness, and enactment.

Ontology focusing denotes a family of operations by which a broad ontology is narrowed, reorganized, or rendered operational for a specific purpose. In its explicit formal sense, it is a framework for deriving a schema for a possibly knowledge-enriched database from an ontology together with a specification of scope, completeness, and determinacy conditions (Gogacz et al., 2019). In FOLE, the phrase is not used directly, but a related idea appears in the transformational passage from the classification form of an ontology to its interpretation form in typed relational tables and databases (Kent, 2018). In recent sociotechnical work on LLMs, the term is again not used directly, but ontology becomes the object of deliberate analytical attention: what a system allows one to think, name, or enact, and how design can re-orient that space through pluralism, groundedness, liveliness, and enactment (Haghighi et al., 3 Apr 2025).

1. Meanings and scope of the term

The most precise technical use of ontology focusing comes from the database-theoretic framework in which a background ontology $\varphi$ is not queried in the abstract, but is turned into the backbone of a concrete data-centric system. The central design task is to choose what the system will store, what is assumed complete, what is frozen to the ontology, and which queries must have invariant answers. The result is a schema-plus-semantics configuration rather than a mere extraction of vocabulary (Gogacz et al., 2019).

A second usage is implicit rather than terminological. In FOLE, an ontology is a logical theory over classes, relationships, and properties, represented through the entity-relationship-attribute perspective. The work on FOLE tables develops the interpretation form in which signatures, type domains, signed domains, and keyed tuples realize that theory in relational structures. This suggests a form of focusing in which abstract ontological specification is made concrete as tables and, eventually, databases (Kent, 2018).

A third usage is analytic and sociotechnical. Haghighi and colleagues argue that ontologies concern “what we allow ourselves to talk about” and that LLMs should be examined not only axiologically, through bias or fairness, but ontologically, through the beings, relations, and worlds they make thinkable. Their framework does not define a database-theoretic focusing operator, but it does develop a practice-based way of focusing on ontologies in design (Haghighi et al., 3 Apr 2025).

Strand	What is focused	Main constructs
Knowledge-enriched databases	Ontology into an application-specific schema and semantics	$\Sigma$, $Q_{\mathsf{closed}}$, $Q_{\mathsf{fixed}}$, $Q_{\mathsf{det}}$
FOLE interpretation	Classification form into relational interpretation form	signatures, type domains, signed domains, tables
LLM and design analysis	Ontological assumptions in outputs and architectures	pluralism, groundedness, liveliness, enactment

2. Formal framework in knowledge-enriched databases

The logic-independent framework begins with an ontology $\varphi$, a signature $\Sigma \subseteq Rel$, database instances over $\Sigma$, and query languages used to specify different semantic roles. Certain answers relative to $\varphi$ and an instance $I$ are defined as

$\Sigma$0

where $\Sigma$1 (Gogacz et al., 2019).

A focusing configuration is the tuple

$\Sigma$2

Here $\Sigma$3 is the database schema, $\Sigma$4 are closed queries, $\Sigma$5 are fixed queries, and $\Sigma$6 are determined queries. Closed queries express query-based completeness: $\Sigma$7 Fixed queries express query-based fixing: $\Sigma$8 The intended models are then

$\Sigma$9

A configuration is a focusing solution for $Q_{\mathsf{closed}}$0 when two conditions hold for every legal instance $Q_{\mathsf{closed}}$1 over $Q_{\mathsf{closed}}$2. First, fixing must not introduce inconsistency whenever models already exist under the ontology and the closed queries: $Q_{\mathsf{closed}}$3 Second, determined queries must be invariant across intended models: $Q_{\mathsf{closed}}$4

Within this formalization, ontology focusing is a design step that lies between unrestricted open-world reasoning and ordinary closed-world database semantics. It does not merely prune vocabulary. It selects a schema, commits to explicit completeness and fixing assumptions, and guarantees that the queries regarded as decisive for the application are well-defined across the model class induced by the ontology and the data.

3. Decision problems, description logics, and complexity

The framework identifies four principal computational problems. FOCUS asks whether a candidate configuration is a focusing solution for a given ontology. EMPTINESS asks whether every legal database instance yields an empty set of intended models. CONSISTENCY asks, for a given legal instance, whether intended models exist. ENTAILMENT asks whether a Boolean query holds in all intended models (Gogacz et al., 2019).

Two auxiliary problems play a central role. MIXED is a mixed satisfiability or mixed OMQA problem in which selected predicates are required to have finite extensions in models. NULLABILITY asks whether a query can be made empty in some model consistent with the ontology and the closed-query conditions. These are not merely technical conveniences. They isolate variants of classical DL decision problems that the framework uses to analyze focusing solutions.

The paper instantiates the framework mainly with description logics such as $Q_{\mathsf{closed}}$5, $Q_{\mathsf{closed}}$6, and Horn fragments, together with query classes such as instance queries, atomic queries, conjunctive queries, and unions of conjunctive queries. The results are sharply sensitive to the ontology language and to whether closed queries include roles.

Problem or setting	Result
FOCUS over $Q_{\mathsf{closed}}$7 and CQs	$Q_{\mathsf{closed}}$8-complete
ENTAILMENT over $Q_{\mathsf{closed}}$9 and CQs	$Q_{\mathsf{fixed}}$0-complete in combined complexity; coNP-complete in data complexity
MIXED in $Q_{\mathsf{fixed}}$1	NEXPTIME-complete
MIXED in $Q_{\mathsf{fixed}}$2	EXPTIME-complete
EMPTINESS in corresponding settings	coNEXPTIME-complete or EXPTIME-complete accordingly
NULLABILITY with closed roles	undecidable

One of the main negative results is that NULLABILITY becomes undecidable when closed queries can include roles, even for weak DLs and simple queries. One of the main positive results is that, under suitable restrictions, the framework remains decidable and yields exact complexity bounds. The technical machinery includes reductions from FOCUS to MIXED and NULLABILITY, tree-model and type constructions for ENTAILMENT, and tile, mosaic, and enriched integer-programming methods for mixed satisfiability. In Horn settings, cycle reversion yields lower-complexity fragments.

These results clarify that ontology focusing is not an informal scoping heuristic. It is a semantic design problem with a nontrivial complexity landscape, and the feasibility of focusing depends strongly on the expressiveness of the ontology and the way completeness is imposed.

4. FOLE and interpretation-focused ontology representation

In FOLE, an ontology is presented in Gruber’s sense as a specification of primitives for a community of discourse, with classes, relationships, and properties represented by the entity-relationship-attribute model. FOLE’s classification form organizes these primitives through signatures, type domains, and logical axioms; its interpretation form organizes them as relational tables and, in follow-up work, databases (Kent, 2018).

The key schema-level components are a signature

$Q_{\mathsf{fixed}}$3

a type domain

$Q_{\mathsf{fixed}}$4

and a signed domain

$Q_{\mathsf{fixed}}$5

A FOLE table is then defined as

$Q_{\mathsf{fixed}}$6

where $Q_{\mathsf{fixed}}$7 is a set of primary keys and

$Q_{\mathsf{fixed}}$8

maps keys to $Q_{\mathsf{fixed}}$9-tuples. The tuple set is the legal set of tuples for the header and type-domain, canonically

$Q_{\mathsf{det}}$0

The paper places tables in the comma category

$Q_{\mathsf{det}}$1

and develops signature morphisms, type-domain infomorphisms, signed-domain morphisms, and table morphisms. A table morphism satisfies the naturality condition

$Q_{\mathsf{det}}$2

which expresses preservation of typing and integrity across transformations. The paper also states a reflection between tables and relations for a fixed type domain: $Q_{\mathsf{det}}$3

The FOLE paper does not define ontology focusing as such. However, it explicitly describes a transformational passage from the classification form of first-order logic to an equivalent interpretation form, thereby defining the formalism and semantics of first-order logical/relational database systems. This suggests an “interpretive focusing” in which abstract ontological structure is rendered as signed domains, legal tuple sets, keyed tables, and morphisms that preserve classification and information flow (Kent, 2018). The paper further states that FOLE uses a conceptual structures approach completely compatible with formal concept analysis and information flow, situating this passage within a broader categorical and semantic program.

5. Ontology focusing as sociotechnical analysis of LLMs

Haghighi and colleagues shift the locus of ontology from formal schema design to the conditions of thinkability in sociotechnical systems. They distinguish ontology from axiology by arguing that, while value-based analyses of bias and fairness remain crucial, ontological analysis asks what realities a system assumes and reproduces, what beings and relations count as real, and what is erased or rendered unthinkable (Haghighi et al., 3 Apr 2025).

The paper defines ontological harm as “the downstream and often long-term negative impact of systems and practices that constrain or foreclose ways of being in the world, limiting what we enable ourselves to deem possible, or to talk or think about.” On that basis it proposes four orientations for engaging ontologies in design:

• Pluralism: whether outputs or architectures make room for multiple ways of grasping reality rather than a single generalizable entry point.
• Groundedness: whether ontological commitments are situated and specific rather than abstract and essentialized.
• Liveliness: whether ontologies are treated as dynamically taking shape rather than as fixed structures.
• Enactment: how intended ontological commitments are or are not realized in architectures, outputs, and evaluation practices.

These orientations are used in two probing exercises. The first examines four LLM-based chatbots through fourteen open-ended prompts about ontology, dominant ontological assumptions, non-Western ontologies, and the ontology within which answers are valid. The paper reports that the systems can acknowledge multiple philosophical stances, but typically surface a narrow set of ontologies by default; non-Western ontologies often appear as generalized categories such as “Indigenous,” “African,” or “Eastern”; and pluralistic or non-Western ontologies usually require explicit prompting (Haghighi et al., 3 Apr 2025).

The second examines the architecture of Generative Agents. There the ontological commitments are embedded in persona initialization, memory stream, reflection, planning, and evaluation. The architecture assumes agents as discrete cognitive units with internal memories, reflections, and plans; time is decomposed into fixed steps; and evaluation via “believability” privileges coherence, memory completeness, and plan adherence. The paper argues that architecture is therefore a site of ontological design, not just implementation.

In this literature, ontology focusing is best understood as a practice of identifying and deliberately reshaping ontological assumptions in data, model architecture, alignment, interfaces, and evaluation. Unlike the database-theoretic framework, it does not define intended models by logical conditions. Its emphasis is on world-making, on the ontological defaults embedded in systems, and on the gap between declared neutrality and enacted assumptions.

6. Related ideas, distinctions, and open issues

In the knowledge-enriched database setting, ontology focusing is related to OBDA, closed predicates, completeness assertions, module extraction, forgetting, conservative extensions, and non-monotonic restrictions of model classes. The paper explicitly distinguishes focusing from module extraction: module extraction preserves entailments over a signature, whereas focusing may deliberately change the effective meaning of terms within the intended scope by fixing irrelevant predicates or views (Gogacz et al., 2019). It is likewise broader than closed predicates, because it allows closed queries, fixed queries, and determined queries, not only closed atomic predicates.

A common misconception would be to treat focusing as mere schema selection. The formal framework shows that this is too narrow: the core of focusing is the induced class of intended models and the requirement that determined queries have invariant answers. Another misconception would be to identify ontology-focused analysis in LLMs with ordinary bias analysis. Haghighi and colleagues explicitly argue that ontology and axiology are distinct dimensions, even when they interact (Haghighi et al., 3 Apr 2025).

The limitations are also different across strands. In the formal framework, closed roles can trigger undecidability, and several core problems are $Q_{\mathsf{det}}$4-complete or NEXPTIME-complete in expressive DLs (Gogacz et al., 2019). In the sociotechnical framework, the main tensions concern longitudinal tracing, scalability of grounded and pluralistic approaches, institutional pressures toward standardization, and the risk of othering alternative ontologies by treating them as exotic (Haghighi et al., 3 Apr 2025). In FOLE, the work reported is table-level rather than database-level, and the interpretation form is explicitly presented as part of a broader program whose follow-up develops FOLE relational databases (Kent, 2018).

Taken together, these literatures suggest that ontology focusing is not a single doctrine but a recurrent operation across ontology research. In one line of work it is a formal method for producing knowledge-enriched databases on demand; in another it is an interpretive passage from ontological classification to relational realization; in a third it is a practice of exposing and revising the worlds that AI systems presuppose. The shared concern is the same: an ontology becomes operational only when its scope, constraints, and consequences are made explicit.