Semantics, Syntax, and Semiotics

Three Lenses on Meaningful Structure

This note clarifies how syntax, semantics, and semiotics relate to each other, and how each one shows up in the Semiotic Publisher and the Semiotic Universe.

It is intentionally practical: the goal is to help you read and write vault content in a way that makes the most of the semiotic tooling.

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1. Syntax: Shape and Well‑Formedness

Syntax is the study of formal shape.

Syntax answers questions like:

• Is this frontmatter valid YAML?
• Is this Markdown well‑formed?
• Does this annotation have the right number of arguments?
• Does this concept ID follow the slug rules?

In this project, syntax shows up in several layers:

1. Markdown + YAML frontmatter

   • Files must parse as Markdown documents with optional YAML frontmatter.
   • The publisher assumes a certain structure (title, tags, status, etc.), but is robust to extras.

2. Annotation terms

   • Internal operators like HasTag, InFolder, LinksTo, Fact all have a syntactic arity.
   • The publisher turns metadata and link structure into these annotation terms.

3. Configuration

   • The config file has its own syntax: keys, lists, maps.
   • Mis‑typed keys or wrong shapes break configuration before any semantics can be computed.

You can think of syntax as the constraint layer: it makes sure the surface structure is coherent enough for downstream processing.

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2. Semantics: Reference, Truth, and Models

Semantics is about what well‑formed expressions are about.

It asks:

• What does this expression refer to?
• In which situations is it true, false, or inapplicable?
• How do different expressions relate in a model (e.g. entailment, equivalence)?

In the formal semiotic-universe.md, semantics is modeled inside a complete Heyting algebra with:

• implication, meet, join, top, bottom;
• a modal closure operator j;
• a comonadic trace G.

In the implementation:

• We approximate semantics via finite feature sets (atoms).
• A concept’s semantic feature set is the result of iterated closure under j and G.
• A simple evaluation score is computed from these semantic features.

This is not full philosophical semantics. It is a practical, computable semantics suitable for:

• ranking concepts by richness or connectedness;
• comparing concepts via semantic deltas;
• querying for “concepts that are semantically similar” using Jaccard similarity.

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3. Semiotics: Practices of Meaning and Use

Semiotics widens the frame.

It includes syntax and semantics, but asks additional questions:

• Who is producing and consuming these concepts?
• In which workflows and infrastructures do they circulate?
• How are annotations used to coordinate work, allocate attention, or make decisions?
• What kinds of stewardship actions are possible and desirable?

The Stewardable Semiotic Concept Universe extends the base universe with:

• a notion of stewardship actions,
• evaluation semantics for fragments and deltas,
• provenance and failure semantics,
• a category‑theoretic view of partial structures and interfaces.

From a semiotic perspective, a concept is not just a statement with a truth value. It is:

• a bundle of signs,
• situated in a history,
• subject to revision and stewardship,
• entangled with other concepts through annotations and use.

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4. How the Publisher Integrates the Three

The Semiotic Publisher is a small engine that brings all three lenses together.

4.1 Syntax in the Publisher

• Frontmatter syntax:

  • keys like title, tags, status, type, aliases, subjects, facts;
  • valid YAML shapes;
  • well‑formed identifiers for concepts.

• Link syntax:

  • Markdown links [text](relative/path.md);
  • wikilinks [[Concept Name]].

• Config syntax:

  • keys like folder_tag_rules, tag_synonyms, type_tag_rules, status_tag_rules.

If syntax is broken, the pipeline stops here.

4.2 Semantics in the Publisher

Once syntax is OK:

1. Metadata and structure are turned into annotation terms.
2. Annotation terms are interpreted as atoms.
3. Atoms are closed under G (trace) and j (graph‑based modality) to produce:
   • fragments: least j,G‑closed sets containing base features;
   • semantic feature sets: one more step of closure.
4. An evaluation score is computed from the semantic features.

This semantic layer enables:

• concept ranking,
• similarity search via Jaccard,
• structured export to JSON, RDF, and OpenAPI.

4.3 Semiotics in the Publisher

Semiotics comes in through:

• the choice of atoms (what we choose to model),
• the choice of closure rules (what we treat as implied by what),
• the evaluation function (what we count as “good” or “rich”),
• the export formats (how concepts become visible and usable).

By changing the configuration, annotations, and evaluation, we are effectively changing the semiotic regime in which our concepts live.

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5. Practical Guidance for Authors

When writing in the vault, you can explicitly think in these three layers:

1. Syntax — Make it parseable.

   • Keep YAML simple and valid.
   • Use consistent keys (tags, status, type).
   • Avoid spaces in IDs; rely on slugification when linking.

2. Semantics — Make it structurally meaningful.

   • Use tags that reflect actual conceptual roles (definition, example, theory, method).
   • Add subjects and facts when you want explicit relational structure.
   • Use consistent folder structures to express coarse domains.

3. Semiotics — Make it stewardable.

   • Use status to indicate readiness (sketch, draft, stable).
   • Use aliases for important alternative names.
   • Use links and references to show how this concept participates in larger stories.

Every time you run the publisher, you are not just generating a site—you are updating a semiotic universe in which these choices matter.

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6. Where This Fits in the Theory

For deeper background:

• [[The Semiotic Universe]] explains the fixed‑point construction in a Heyting–modal–comonadic setting.
• [[The Stewardable Semiotic Concept Universe]] shows how stewardship, failure semantics, and provenance fit into this picture.
• [[The Semiotic Publisher]] documents how the theory is approximated in code.

This note is intentionally informal. It is meant to be an on‑ramp for working concretely with the publisher, not a replacement for the formal papers.