Epistemic Dependencies: Logic, Decisions & AI

Updated 19 July 2026

Epistemic Dependencies are formal constructs that delineate how knowledge, knowability, decisions, and disclosures interrelate via syntactic, semantic, and algorithmic constraints.
They are applied across various frameworks, including epistemic logic programming, decision modeling, modal/topological logics, and controlled query evaluation.
By structuring dependencies through graphs, operators, and policy rules, ED frameworks enable efficient solver analysis, secure disclosure strategies, and nuanced AI-mediated epistemic deference.

Epistemic Dependencies (EDs) designate several related but non-identical constructions for representing how knowledge, knowability, disclosure, decision, or justified reliance depends on other epistemic items. In current research, the term ranges from a graph-theoretic abstraction over epistemic literals in epistemic logic programs, to stratified decision rules whose applicability depends on what is known or unknown, to modal operators for partial, functional, continuous, or uniformly continuous dependence, to confidentiality policies of the form $K\,q_b \rightarrow K\,q_h$ in controlled query evaluation, and to broader normative dependence relations in AI-assisted reasoning and multi-agent knowledge ecosystems (Hecher et al., 2020, Marković et al., 2023, Cima et al., 2024, Lange, 23 Oct 2025).

1. Conceptual scope and recurrent structure

A recurring feature across ED formalisms is that they do not treat epistemic states as isolated. Instead, they encode relations of constraint between epistemically salient items: atoms in epistemic literals, decision outputs and knowledge conditions, values of variables across possible worlds, answerable queries under a censor, or human judgments and recognized authorities. The relevant dependency may be syntactic, semantic, topological, modal, or institutional.

Research setting	Core ED object	Dependency intuition
Epistemic logic programs	$\EP_\Pi$	Epistemic atoms linked through non-epistemic program structure
Decision modeling	$K[T][\psi]$ , eDMN, ebd	Decisions depend on what is known or not known
Modal/topological logic	$D_g,D_l$ , $K(C,d)$ , $K(X;Y)$ , $U(X;Y)$	One epistemic item varies with or is knowable from another
Controlled query evaluation	$\forall \vec{x}_1,\vec{x}_2 (K q_b \rightarrow K q_h)$	Disclosure of one query result constrains disclosure of another
AI epistemology	AEAs, total evidence AI deference, informational interdependencies	Human reasoning depends on AI outputs and AI-mediated infrastructures

This suggests a family resemblance rather than a single canonical formalism. In some literatures, EDs are explicit primitives with formal syntax and semantics; in others, they are dependency-like constraints reconstructed from broader epistemic frameworks.

2. Structural EDs in epistemic logic programs

In epistemic logic programming, EDs are introduced as a structural graph abstraction tailored to the epistemic part of an epistemic logic program $\Pi=(A,R)$ . The key restriction is that the graph is built from $atel{\Pi}$ , the atoms occurring in epistemic literals, rather than from all program atoms. The starting point is the primal graph

$\EP_\Pi$0

Two vertices $\EP_\Pi$1 are then called non-epistemically connected if there is a path between them in $\EP_\Pi$2 whose internal vertices all lie in $\EP_\Pi$3. The resulting epistemic primal graph is

$\EP_\Pi$4

The paper explicitly notes that this construction is inspired by the torso graph idea from parameterized complexity (Hecher et al., 2020).

The significance of $\EP_\Pi$5 is algorithmic. It isolates epistemic interaction structure while collapsing away chains of ordinary atoms not appearing epistemically. In the scholarship eligibility example, after instantiation for two students, the graph contains only $\EP_\Pi$6, $\EP_\Pi$7, $\EP_\Pi$8, and $\EP_\Pi$9, with edges only within each student’s pair; hence $K[T][\psi]$ 0 is a forest of treewidth $K[T][\psi]$ 1. This decomposition supports independent or weakly coupled epistemic subproblems.

The operational consequence appears in the bag algorithm EPRIM over a nice tree decomposition of $K[T][\psi]$ 2. The paper states: $K[T][\psi]$ 3 From this, together with linear-size nice tree decompositions and exponential row bounds in bag size, it derives

$K[T][\psi]$ 4

The same work also provides a full dynamic programming algorithm PRIM on the ordinary primal graph $K[T][\psi]$ 5, while emphasizing that $K[T][\psi]$ 6 is the new structural device specifically used for solver-call analysis and epistemic decomposition rather than for the main MSO/Courcelle-style tractability statement on the incidence graph (Hecher et al., 2020).

3. Epistemic dependence in decision modeling under incomplete knowledge

A second major use of EDs appears in decision modeling, where the central claim is that decisions should depend on epistemic conditions rather than directly on the objective state of affairs. The formal basis is Ordered Epistemic Logic (OEL), a hierarchy of FO(ID) theories equipped with operators $K[T][\psi]$ 7. The ordering condition is strict: if a theory $K[T][\psi]$ 8 contains $K[T][\psi]$ 9, then $D_g,D_l$ 0. This stratification ensures a bottom theory free of epistemic operators and rules out circular self-reference (Marković et al., 2023).

The semantics is given over partial structures $D_g,D_l$ 1: $D_g,D_l$ 2 Knowledge is therefore truth in all compatible completions of the current partial information. This supports rules whose applicability depends on knownness and unknownness. The salutation example makes the point explicitly: “Mr,” “Ms,” and “Mrs” depend on what is known about gender and marital status, while “Customer” and “Lady” are triggered by ignorance conditions.

The paper formalizes an epistemic decision function as

$D_g,D_l$ 3

a partial map from epistemic states to decision structures, and proves that every DMN decision function and every optimal decision function is an epistemic decision function. The practical language eDMN translates a DMN table with hit policy “Any” into OEL rules of the form

$D_g,D_l$ 4

The extension also adds disjunctions of constraints and an explicit unknownness test $D_g,D_l$ 5, formalized for a variable $D_g,D_l$ 6 over sort $D_g,D_l$ 7 as

$D_g,D_l$ 8

For a more tightly controlled definitional fragment, the paper introduces ebd (Epistemic Body Definitions), where rules have the form

$D_g,D_l$ 9

with every atomic formula in $K(C,d)$ 0 occurring under $K(C,d)$ 1, no defined symbol in the body, and decision symbols separated from environment symbols. The resulting determinacy property is

$K(C,d)$ 2

This makes the decision either uniquely determined or undefined/inconsistent for a given epistemic state. In the interview example, “interview” is triggered not only by factual conditions but by insufficient knowledge itself, which is precisely the epistemic dependency the framework is designed to represent (Marković et al., 2023).

One modal line of work introduces a partial dependency modality into epistemic logic. The language contains

$K(C,d)$ 3

where $K(C,d)$ 4 and $K(C,d)$ 5 express global and local partial dependency between finite sets of variables. The semantics compares worlds agreeing outside $K(C,d)$ 6. For global dependency,

$K(C,d)$ 7

iff there exist $K(C,d)$ 8 in the same $K(C,d)$ 9-class as $K(X;Y)$ 0 such that all variables outside $K(X;Y)$ 1 agree, while both $K(X;Y)$ 2 and $K(X;Y)$ 3 differ between $K(X;Y)$ 4 and $K(X;Y)$ 5. For local dependency, one witness world is anchored at the current world. The logic proves

$K(X;Y)$ 6

and the paper states that $K(X;Y)$ 7 is strictly more expressive than $K(X;Y)$ 8. It also gives a sound and strongly complete axiomatization for the $K(X;Y)$ 9 sublanguage containing $U(X;Y)$ 0 but not $U(X;Y)$ 1 (Wang, 2019).

A second line introduces the functional-dependency operator $U(X;Y)$ 2, read as knowledge of a functional dependency from variables $U(X;Y)$ 3 to variable $U(X;Y)$ 4. Its semantics is

$U(X;Y)$ 5

where $U(X;Y)$ 6 is a designated function domain. This makes EDs sensitive not only to extensional regularity across worlds but to what counts as an admissible explaining function. The framework axiomatizes three single-agent logics by varying $U(X;Y)$ 7: a full function domain validating $U(X;Y)$ 8, a minimal projection-only domain validating $U(X;Y)$ 9 and $\forall \vec{x}_1,\vec{x}_2 (K q_b \rightarrow K q_h)$ 0, and an intermediate domain for which the base system suffices. It then generalizes to a multi-agent setting with agent- and world-relative function domains $\forall \vec{x}_1,\vec{x}_2 (K q_b \rightarrow K q_h)$ 1 (Ding, 2017).

A third line gives a topological account of knowable informational dependence. The central notion is

$\forall \vec{x}_1,\vec{x}_2 (K q_b \rightarrow K q_h)$ 2

This identifies knowable dependence with continuity, and uniformly knowable dependence with uniform continuity: $\forall \vec{x}_1,\vec{x}_2 (K q_b \rightarrow K q_h)$ 3 The paper distinguishes exact dependence, continuous dependence, local dependence, point-continuous dependence, and uniform dependence, and defines a strong epistemic independence condition $\forall \vec{x}_1,\vec{x}_2 (K q_b \rightarrow K q_h)$ 4. A notable theorem-level claim is that $\forall \vec{x}_1,\vec{x}_2 (K q_b \rightarrow K q_h)$ 5 is compatible: exact functional dependence can coexist with epistemic independence when the dependence map is everywhere-surjective and non-continuous in the relevant topological sense. The same work gives complete and decidable proof systems $\forall \vec{x}_1,\vec{x}_2 (K q_b \rightarrow K q_h)$ 6 for continuous dependence and $\forall \vec{x}_1,\vec{x}_2 (K q_b \rightarrow K q_h)$ 7 for uniform dependence (Baltag et al., 2024).

Taken together, these logics show that EDs need not mean full functional determination. They can represent influence without unique determination, knowledge of admissible explanatory functions, knowability from approximation, or state-independent know-how.

5. EDs as disclosure policies in controlled query evaluation

In ontology-based controlled query evaluation (CQE), EDs are a policy language for regulating what may be disclosed. The basic syntactic form is

$\forall \vec{x}_1,\vec{x}_2 (K q_b \rightarrow K q_h)$ 8

where $\forall \vec{x}_1,\vec{x}_2 (K q_b \rightarrow K q_h)$ 9 is the body conjunctive query, $\Pi=(A,R)$ 0 is the head conjunctive query, and $\Pi=(A,R)$ 1 means that the query result is known or disclosed under the censor. A special case is a denial, obtained when the head is $\Pi=(A,R)$ 2. The intended reading is: if the user can infer the body, then the user must also be able to infer the head; otherwise the disclosure is disallowed (Cima et al., 2024).

The 2024 CQE framework studies instances $\Pi=(A,R)$ 3 with TBox $\Pi=(A,R)$ 4, ABox $\Pi=(A,R)$ 5, and policy $\Pi=(A,R)$ 6. A CQ-censor is a subset $\Pi=(A,R)$ 7 of the entailed information such that $\Pi=(A,R)$ 8. The work distinguishes skeptical entailment over all optimal censors,

$\Pi=(A,R)$ 9

from entailment under the intersection of optimal censors,

$atel{\Pi}$ 0

For DL-Lite $atel{\Pi}$ 1, it proves that SC-entailment preserves confidentiality for BCQs but not for BUCQs, whereas IC-entailment preserves confidentiality for BUCQs. On the complexity side, arbitrary ED policies yield coNP-hardness or coNP-completeness in data complexity, while acyclic EDs admit FO rewritings and hence AC $atel{\Pi}$ 2 data complexity. Acyclicity is defined via a dependency graph $atel{\Pi}$ 3 with P-edges from body predicates to head predicates and T-edges induced by TBox axioms; a policy is acyclic for $atel{\Pi}$ 4 when no cycle in $atel{\Pi}$ 5 contains a P-edge (Cima et al., 2024).

The extended 2025 study shifts to optimal GA censors, maximal sets of entailed ground atoms safe to reveal, and their intersection

$atel{\Pi}$ 6

Its main security result is: $atel{\Pi}$ 7 The paper then shows that IGA-entailment is not FO-rewritable in general: there exists a policy of linear EDs and a one-atom query making IGA-ENT NL-hard in data complexity, and there exists a policy of full EDs and a ground-atom query making IGA-ENT coNP-hard in data complexity. Tractability is recovered for DL-Lite $atel{\Pi}$ 8 TBoxes and policies that are full and expandable with respect to the coupled TBox, yielding FO rewritability and AC $atel{\Pi}$ 9 data complexity via PolicyExp and a detailed first-order rewriting construction (Marconi et al., 23 Jul 2025).

The CQE literature also emphasizes expressiveness. Policies can encode conditional disclosure rather than only denials. One example requires that if the system knows a patient is admitted, then it must also know that the patient gave consent; another requires that salaries may be revealed only for managers. In the extended work, experiments on OWL2Bench use ABoxes $\EP_\Pi$00 with about 325k assertions and $\EP_\Pi$01 with about 710k assertions, reporting that rewriting time was always small, evaluation time was usually acceptable, and the most expensive query was the seventh one, which took several minutes (Cima et al., 2024, Marconi et al., 23 Jul 2025).

6. AI-mediated epistemic dependency, deference, and informational interdependence

Recent AI epistemology treats epistemic dependence not merely as a logical relation but as a normative and socio-technical condition. One account analyzes when users should defer to AI outputs by introducing Artificial Epistemic Authorities (AEAs): AI systems that occupy a superior epistemic position relative to a user in some domain and are therefore correctly recognized as authoritative. The paper contrasts AI Preemptionism,

$\EP_\Pi$02

such that $\EP_\Pi$03 replaces rather than adds to the user’s independent reasons, with Total Evidence AI Deference,

$\EP_\Pi$04

such that $\EP_\Pi$05 is integrated into, rather than replacing, the user’s independent reasons. The argument against preemptionism centers on uncritical deference, epistemic entrenchment, and unhinging epistemic bases, amplified by opacity, self-reinforcing authority, and the lack of human-like failure markers. The positive alternative is a norm of critical deference with oversight, defeasible in at least four cases: domain mismatch, reliability undermining, conflicting authority, and novel evidence. This structure is presented as mitigating expertise atrophy, grounding meaningful human oversight and control on epistemic grounds, and explaining when mistrust of AI is epistemically justified (Lange, 23 Oct 2025).

A related 2026 framework broadens the picture from deference to ecosystem-level dependency. It defines epistemic AI agents as entities capable of (1) autonomously pursuing epistemic goals without sustained human input and (2) actively shaping the external epistemic environment through their actions. Such systems are said to create “new informational interdependencies” and a “complex web of interdependencies created between humans and agentic systems.” The proposed governance framework has three pillars: trustworthiness of epistemic AI agents, alignment with human epistemic goals, and reinforcement of the socio-epistemic infrastructure. Trustworthiness is operationalized by three desiderata: demonstrable epistemic competence, falsifiability, and epistemically virtuous behavior. The surrounding infrastructure includes provenance chains, authorization chains, standardized logging protocols, mutual authentication, least privilege or sandboxing, and “knowledge sanctuaries” as protected repositories of foundational knowledge (Marchal et al., 3 Mar 2026).

The practical stakes are high-stakes domains such as medical diagnostics, finance, and engineering, where AI may outperform humans on narrow tasks but responsible reliance still depends on rigorous validation, domain restriction, continuous auditing, and structures for second-guessing anomalous results. The broader risk vocabulary in this literature includes cognitive deskilling, epistemic drift, epistemic silos, epistemic distortion, verification crisis, epistemic homogenization or monocultures, and collective cognitive atrophy. A plausible implication is that, in AI contexts, EDs increasingly concern the conditions under which dependence remains defeasible and epistemically active rather than becoming uncritical submission or entrenched automation (Lange, 23 Oct 2025, Marchal et al., 3 Mar 2026).

7. Adjacent frameworks and boundary cases

Not every epistemic formalism that tracks informational constraint is an ED framework in the strict sense. In Dynamic Epistemic Logic games with epistemic temporal goals, the formal machinery consists of epistemic models, action models, product update, uniform strategies on indistinguishable histories, and $\EP_\Pi$06 winning conditions. The framework proves undecidability in general, decidability for propositional actions with hierarchical information, $\EP_\Pi$07-completeness for public actions, and $\EP_\Pi$08-completeness for round-robin public announcements under a restricted fragment. However, it “does not define or study EDs as a separate notion”; the relation is indirect, through epistemic indistinguishability and strategy constraints rather than a dedicated ED formalism (Maubert et al., 2020).

Other frameworks recover dependency structure without using the ED label. Justification Epistemic Models (JEMs) make justifications first-class objects and distinguish accepted justifications $\EP_\Pi$09 from knowledge-producing justifications $\EP_\Pi$10. Belief and knowledge are derived: $\EP_\Pi$11

$\EP_\Pi$12

This framework is used to model Russell/Gettier-style cases in which a true proposition is justified and believed but not known because the accepted justification is not the knowledge-producing one. The dependency at issue is evidential rather than graph-theoretic or query-theoretic (Artemov, 2017).

In probabilistic circuits, epistemic dependencies are operationalized as covariances among beta-distributed uncertain probabilities. Leaves are labeled by beta random variables, and the method propagates means and covariance matrices through circuit structure instead of assuming independence. For disjunction nodes,

$\EP_\Pi$13

while conjunction nodes use first-order Taylor approximations for covariances. The paper’s point is that query and evidence terms can be strongly correlated, especially under shared subcomputations, so correct treatment of epistemic uncertainty requires dependency tracking rather than moment matching under independence assumptions (Cerutti et al., 2021).

A further boundary case is quantum computational semantics for epistemic operators. There, sentences are represented by density operators, and understanding and knowledge are quantum operations in an epistemic situation

$\EP_\Pi$14

The framework enforces

$\EP_\Pi$15

and hence

$\EP_\Pi$16

making explicit that knowledge depends on understanding. Knowledge operations are generally irreversible quantum channels, and teleportation is used as a model of memorizing and retrieving information (Beltrametti et al., 2016).

These boundary cases clarify a common misconception: the phrase “epistemic dependency” does not name a single mature standard across logic, knowledge representation, AI, and privacy. In some areas it is a formal primitive; in others it is a reconstruction of how epistemic states are structured by justifications, uncertainty propagation, action observability, or authority relations.