Educational Agential Semioverse Repository

This specification defines what an Agential Semioverse Repository looks like when its content domain is education. It extends the general ASR’s type vocabulary and typed relations with content types and relations specific to educational knowledge.

The general ASR defines types like term, concept, and text that describe what a page is for, but not what makes it valid within a particular domain. Educational content has structural validity requirements that neither the mathematical nor philosophical ASR captures: a lesson without a worked example is a reference document, not a lesson. A curriculum without a dependency structure is a reading list. A skill without testable completion criteria is an aspiration. These requirements are constitutive: the presence or absence of certain structures determines what the content IS.

Validity principle: pedagogical soundness

Educational knowledge is governed by pedagogical soundness. Content is valid when it teaches rather than deposits — when it builds understanding through concrete grounding, honest scope, and active engagement, rather than presenting information for passive reception.

This validity principle is drawn from the education domain’s own critical traditions. Paulo Freire’s distinction between the banking model and problem-posing education is not merely a philosophical preference; it is a constitutive criterion. Content that reproduces the banking model — depositing knowledge into a passive reader without grounding, engagement, or acknowledgment of whose knowledge is centered — fails the domain’s own validity standard, regardless of how accurate its information is.

The dependency graph is a directed acyclic graph at the curriculum and skill level (lessons build on prerequisites; skills depend on other skills), but may contain productive cycles at the conceptual level (a concept taught in one lesson may be deepened and revised in a later lesson that also serves as its prerequisite’s prerequisite in a different learning path). This mirrors experiential learning’s cyclical structure.

Machine verification is partially possible: structural requirements (presence of worked examples, exercises, prerequisite declarations) can be checked automatically. Pedagogical quality (whether a lesson actually builds understanding, whether scope is stated honestly, whether the banking model is reproduced) requires human or agent judgment.

Content types

These extend the general ASR type: field. Each type carries validity requirements expressed as MUST (constitutive — violation means the content is ill-formed or mistyped) and SHOULD (recommended but not constitutive).

lesson

A teaching document that builds understanding of a single core idea through concrete grounding, active engagement, and honest framing.

• MUST focus on a single core idea. If it teaches multiple independent concepts, it is a module, not a lesson.
• MUST include a worked example — a full walkthrough applying the lesson’s concepts to a specific case.
• MUST include exercises or self-check questions that test application, not recall.
• MUST state prerequisites, specifying what the learner needs from each (not “familiarity with X” but “the definition of X and the ability to do Y”).
• MUST introduce concepts concrete-before-abstract: intuitive explanation or example before formal definition.
• SHOULD explain motivation before definitions — why the concept matters, grounded in a concrete scenario.
• SHOULD specify teaches: listing the terms or concepts the lesson covers.
• SHOULD specify requires: linking to prerequisite lessons or terms.
• SHOULD include a “what comes next” section linking forward in the sequence.
• SHOULD cite sources with [@citekey] so learners can trace claims to their origins.

type: lesson
teaches:
  - "backward design"
  - "concrete-before-abstract ordering"
requires:
  - /education/disciplines/pedagogy/curricula/decolonial-pedagogy.md
cites:
  - "Understanding by Design"

curriculum

A structured sequence of lessons organized as a dependency graph with explicit prerequisites, completion criteria, and scope.

• MUST contain a dependency structure — not a numbered list but a graph with explicit prerequisite edges.
• MUST state scope: what it covers, what it excludes, and why the exclusions matter.
• MUST link to actual lesson pages (not descriptions of lessons that do not exist).
• SHOULD specify teaches: listing the skills or competencies the curriculum develops.
• SHOULD specify requires: linking to prerequisite curricula or skills.
• SHOULD identify gaps explicitly — lessons that need to be written.
• MAY use numbered sequences when the dependency structure is genuinely linear, but MUST NOT use numbering to disguise independent lessons as sequential.

type: curriculum
teaches:
  - "pedagogical theory"
  - "lesson design"
requires:
  - /education/disciplines/pedagogy/curricula/decolonial-pedagogy.md

skill

A node in the curriculum dependency graph that defines what a learner can do after completing a set of lessons. Distinguished from lesson by level of abstraction: a skill is a capability; a lesson is a teaching document.

Two sub-kinds:

learn skill (kind: learn): defines a learning outcome.

• MUST specify testable completion criteria — not “understand X” but “given Y, do Z.”
• MUST specify prerequisite skills (or explicitly state “none”).
• MUST link to lessons that develop the skill.
• MUST state scope: what the skill covers and what it does not.
• SHOULD include a verification section describing how to confirm the skill is acquired.

operational skill (kind: operational): defines a repeatable procedure for creating or evaluating content.

• MUST specify inputs and outputs with types.
• MUST include step-by-step instructions.
• SHOULD specify region: declaring what files the skill reads and writes.
• SHOULD specify dependencies on other skills.

type: skill
kind: learn
completion-criteria:
  - "Given a topic, identify the desired learning result before deciding content"
  - "Restructure a definition-first lesson into concrete-before-abstract order"
requires:
  - /education/disciplines/pedagogy/skills/learn-decolonial-pedagogy/SKILL.md

term

A definition page for a concept within the education domain.

• MUST include defines: listing the term(s) being defined.
• MUST provide a clear definition in the body (1-3 paragraphs).
• MUST NOT define more than one independent concept per page. Related aspects of a single concept are acceptable.
• SHOULD include a “Related terms” section linking to connected concepts.
• SHOULD specify cites: for the intellectual sources of the concept.
• SHOULD link to the school or tradition where the term originates.
• MAY specify contested-by: if the term is disputed across traditions.

type: term
defines:
  - "banking model"
cites:
  - "Pedagogy of the Oppressed"
tags:
  - CriticalTheory

school

A page describing a pedagogical tradition or intellectual school.

• MUST state core claims — what the tradition asserts about education.
• MUST identify key texts with authors.
• MUST include a “Relationship to other traditions” section.
• MUST include a “Critiques and limitations” section — honest about the tradition’s blind spots, tensions, and boundaries.
• SHOULD specify tradition: identifying the broader intellectual context.
• SHOULD link to term pages for the tradition’s key concepts.
• MAY specify contested-by: linking to traditions that challenge it.

type: school
tradition: critical-theory
tags:
  - CriticalTheory
  - Decolonial

transmission-mode

A page describing a mode through which knowledge moves between people, generations, or communities.

• MUST include defines: listing the transmission mode.
• MUST describe what the mode preserves and what it transforms or loses.
• MUST address the politics of the mode — whose knowledge it serves, who controls it.
• SHOULD link to traditions that use or depend on this mode.
• SHOULD address what happens when knowledge changes medium (e.g., oral → textual).

type: transmission-mode
defines:
  - "oral transmission"
tags:
  - Indigenous
  - KnowledgeTransmission

Relation vocabulary

These typed relations extend the general ASR’s semantic frontmatter relation set.

These relations carry educational validation requirements intrinsically. When a page uses teaches, the SHACL shapes for that relation validate it. See Domain-Specific Content for how domain-specific relations coexist in a single repository.

Pedagogical dependency graph

The educational dependency graph is a DAG at the structural level:

skill ──requires──► skill ──lessons──► lesson ──requires──► lesson
                                          │
                                     teaches──► term ◄──defines── term page
                                          │
                                     practiced-through──► lesson (cycle at concept level)

Skills depend on skills. Skills point to lessons. Lessons require prerequisite lessons. Lessons teach terms. Terms may link back to lessons where they are practiced, creating productive cycles at the conceptual level — but the structural dependency graph (what must be completed before what) remains acyclic.

The banking model as anti-pattern

The banking model — education as the deposit of information into passive recipients — is not just a pedagogical critique. It is this specification’s primary anti-pattern. Content that reproduces the banking model is ill-formed by the educational ASR’s validity principle, even if it contains accurate information.

Structural indicators of banking model reproduction:

• Definitions without preceding concrete examples
• No worked examples or exercises (the reader is expected to receive, not do)
• Prerequisites stated as “familiarity with X” (assuming passive exposure rather than active capability)
• No scope statement (the content presents itself as complete, universal, and neutral)
• No attribution of intellectual tradition (the content presents its perspective as the only perspective)

These indicators can be checked automatically. The assess-pedagogical-soundness skill codifies this check.

Relationship to other domain ASRs

The educational ASR intersects with both the mathematical and philosophical ASRs:

• Mathematical content that is also educational (curricula teaching mathematics) uses both teaches: and proven-by:. The mathematical ASR validates the proof structure; the educational ASR validates the pedagogical structure.
• Philosophical content that is also educational uses both teaches: and argued-by:. A lesson on critical pedagogy teaches claims that are philosophically argued for; both validation systems apply independently.

A lesson on the banking model is simultaneously educational content (validated by teaches: and structural requirements) and philosophical content (the banking model is a claim argued for by Freire, contestable by objection). The domain-specific relations coexist on the same page, each validated by its own shapes.

Formal artifacts

• Ontology — OWL classes and properties for educational content types
• SHACL Shapes — validation shapes for educational relations

Skills

Operational skills for creating and evaluating educational content:

• write-term-page — create a term definition page
• write-school-page — create a school/tradition page
• write-transmission-mode-page — create a knowledge transmission mode page
• review-curriculum — review a curriculum sequence against pedagogical criteria
• review-skill — review a learn-* skill against structural criteria
• assess-pedagogical-soundness — check content for banking model reproduction
• evaluate-scope-honesty — check whether content honestly states what it covers and excludes
• design-learning-path — design a multi-skill learning path through the vault
• audit-educational-links — check cross-references between education and other domains
• validate-educational-content — validate content frontmatter against educational ASR rules

Lean correspondence

Education is formalizable at the structural level (dependency graphs, prerequisite chains) but its validity principle (pedagogical soundness) includes anti-patterns (banking model reproduction) that require qualitative judgment.

What this domain’s axioms look like formally. The theory for lesson requires teaches: and requires: (SHOULD), a worked example (structural, body-level), and exercises (structural, body- level). The theory for curriculum requires a dependency structure (not just a list) and honest scope. The frontmatter-checkable axioms are a subset of the full theory; the body-level requirements are Layer 1 targets.

What satisfaction means beyond field presence. The current Python approximation checks field presence. Full satisfaction for a lesson would verify that the body contains a worked example, exercises, and a concrete-before-abstract ordering — these are structural patterns in the body text that NLP could detect but that frontmatter alone cannot express.

Current satisfaction data. 40 typed pages checked, 35 satisfied (87.5%), 5 errors, 18 warnings.

Lean target. Formalize the educational dependency graph as a DAG with a well-foundedness proof: every lesson has a finite chain of prerequisites terminating at lessons with no prerequisites. The banking model anti-pattern could be formalized as a structural property: a lesson that has teaches: but no requires: and no outgoing edges to concrete examples lacks the grounding structure that pedagogical soundness demands. Lean could verify that the graph has no such isolated deposit nodes.