GMEOW Notation and Symbolic Systems Module

• IRI: https://blackcatinformatics.ca/gmeow/slices/notation
• Tier: core
• Group: core

What This Slice Covers

This slice owns 42 terms and contributes 7 mapping or projection rows. Use it when its terms match the native fact you want to preserve; use the linkage tables to see how those facts leave GMEOW for consumer vocabularies.

Dependencies

• gmeow:slices/kernel
• gmeow:slices/language
• gmeow:slices/observations
• gmeow:slices/profiles
• gmeow:slices/temporal

Consumers

• Symbolic/notation systems for the language family and the music slice's lossy notation projections.

Local Map

Examples

Notation Systems

• Source: slices/core/notation/examples/notation-systems.ttl
• GMEOW terms: gmeow:NotationSystem, gmeow:WritingSystem, gmeow:langEnglish, gmeow:notationSystemFor, gmeow:notationSystemKind, gmeow:symbolicKindEncoding, gmeow:symbolicKindMusical, gmeow:symbolicKindTranscription, gmeow:writingSystemAsNotation

# SPDX-FileCopyrightText: 2026 Blackcat Informatics® Inc. <paudley@blackcatinformatics.ca>
# SPDX-License-Identifier: CC-BY-4.0
#
# Worked example: notation systems, one machinery for every symbol set . A
# gmeow:NotationSystem is classified by an open gmeow:notationSystemKind
# (musical / mathematical / transcription / encoding / stenographic …), so staff
# notation, IPA, Morse and a math syntax are the SAME kind of object — a symbolic
# system for representing something. A transcription notation declares which
# language it transcribes (gmeow:notationSystemFor); a script is itself a notation
# system, reached from the writing system via gmeow:writingSystemAsNotation.
@prefix gmeow: <https://blackcatinformatics.ca/gmeow/> .
@prefix ex:    <https://blackcatinformatics.ca/gmeow/examples/notation/> .
@prefix rdfs:  <http://www.w3.org/2000/01/rdf-schema#> .

# --- Western staff notation: a musical symbolic system, not tied to a language.
ex:staffNotation a gmeow:NotationSystem ;
    rdfs:label              "Western staff notation"@en ;
    gmeow:notationSystemKind gmeow:symbolicKindMusical .

# --- The IPA: a transcription system FOR a language (here English).
ex:ipa a gmeow:NotationSystem ;
    rdfs:label               "International Phonetic Alphabet"@en ;
    gmeow:notationSystemFor  gmeow:langEnglish ;
    gmeow:notationSystemKind gmeow:symbolicKindTranscription .

# --- A script IS a notation system: the Latin writing system, viewed as the
#     encoding notation it provides.
ex:latin a gmeow:WritingSystem ;
    rdfs:label                  "Latin script"@en ;
    gmeow:writingSystemAsNotation ex:latinNotation .

ex:latinNotation a gmeow:NotationSystem ;
    rdfs:label               "Latin-script encoding"@en ;
    gmeow:notationSystemKind gmeow:symbolicKindEncoding .

Terms

Classes

Properties

Individuals

Linkages

• Rows: 7
• Projection profiles: -
• External vocabularies: schema, wd

Guide

Notation and Symbolic Systems — modelling & interoperability guide

Most vocabularies conflate symbol systems with languages: a musical score is "in English", mathematical notation is "a language", emoji are "characters in a language". GMEOW rejects this collapse. A symbol system is not a language by default; it becomes one only through a standpointed claim (Principle 9).

Governing tenet: neutral symbolic systems

A gmeow:SymbolicSystem is a first-class InformationObject — a system of symbols, signs, or conventions used for communication, representation, or expression. It sits alongside Language and WritingSystem as a sibling under InformationObject, not as a subclass of either.

A gmeow:NotationSystem is a structured symbolic system with defined rules for representing information in a specific domain. It is a SubKind of SymbolicSystem.

Why the sibling approach? Making WritingSystem a subclass of NotationSystem would force all writing systems to carry notation-specific properties (domain, encoding scheme) and all notation systems to carry writing-system properties (ISO 15924 code, text direction). The sibling approach keeps each class minimal and lets explicit bridging properties (hasNotationSystem, writingSystemAsNotation) do the linking.

The boundary: language vs notation vs symbolic system

Decision table

Boundary rules

1. Stenography is usually a notation system for an existing language. It has no independent generative syntax; it encodes an existing language in abbreviated form.

2. Cryptographic ciphers / encodings are not languages by default. They are transform schemes. A standpoint may claim a cipher as a language (e.g. a conlang built on cipher principles), but the default classification is NotationSystem.

3. IPA and Morse code are notation / transcription / encoding systems, not natural languages. They lack independent syntax and semantics.

4. TeX, MathML, OpenMath, MusicXML, MEI, MIDI, LilyPond, and ABC notation may be FormalLanguage instances when treated as grammar-defined encodings. They have parseable syntax and defined semantics. They may ALSO be modeled as NotationSystem via co-modeling — a single entity can carry both classifications from different standpoints (Principle 9).

5. Emoji, gesture, meme, and platform conventions are notation or communication conventions unless modeled as full languages by a standpointed claim. They lack generative syntax and are convention-based.

Usage pattern: NotationSystemUsage

The reified relator NotationSystemUsage binds an entity to a notation system with a role and interval, mirroring WritingSystemUsage:

@prefix gmeow: <https://blackcatinformatics.ca/gmeow/> .
@prefix ex:    <https://example.org/notation/> .

ex:english a gmeow:Language .

ex:ipa a gmeow:NotationSystem ;
    gmeow:notationSystemKind gmeow:symbolicKindTranscription .

ex:englishUsesIpa a gmeow:NotationSystemUsage ;
    gmeow:notationUsageTarget ex:english ;
    gmeow:notationUsageNotationSystem ex:ipa ;
    gmeow:notationUsageRole gmeow:notationRoleTranscription ;
    gmeow:notationUsageInterval ex:ipaUsageInterval .

A musical work using staff notation:

ex:beethoven9 a gmeow:CreativeWork .

ex:staffNotation a gmeow:NotationSystem ;
    gmeow:notationSystemKind gmeow:symbolicKindMusical .

ex:beethoven9UsesStaff a gmeow:NotationSystemUsage ;
    gmeow:notationUsageTarget ex:beethoven9 ;
    gmeow:notationUsageNotationSystem ex:staffNotation ;
    gmeow:notationUsageRole gmeow:notationRoleRepresentation ;
    gmeow:notationUsageInterval ex:staffUsageInterval .

Co-modeling: when a system is both language and notation

A system may be classified as both a FormalLanguage and a NotationSystem from different standpoints. GMEOW handles this through co-equal, standpoint-indexed claims (Principle 9), not subclass overlap:

ex:musicxml a gmeow:InformationObject .

# Standpoint A: MusicXML is a formal language (grammar-defined XML)
ex:claimA a gmeow:StandpointClaim ;
    gmeow:vantage ex:softwareEngineer ;
    gmeow:observedFeature ex:musicxml ;
    gmeow:observationResult gmeow:originFormal .

# Standpoint B: MusicXML is a musical notation system
ex:claimB a gmeow:StandpointClaim ;
    gmeow:vantage ex:musicLibrarian ;
    gmeow:observedFeature ex:musicxml ;
    gmeow:observationResult gmeow:symbolicKindMusical .

Projections and lossy drops

Projection framework: NotationProjectionProfile

A gmeow:NotationProjectionProfile is a gmeow:Profile (from the core profiles slice) that describes how a NotationSystem projects canonical, frame-relative content. It is deliberately not the canonical content itself; it is a machine-readable, honest declaration of what survives the projection and what is lost (Principles 4, 11, 12).

Every profile states:

• gmeow:notationSystemOf — exactly one NotationSystem being described.
• gmeow:representableParameter — parameters the notation can carry without loss (range is open in core; domain slices constrain it, e.g. to MusicalParameter in the music extension).
• gmeow:declaredLoss — ProjectionLoss individuals that explain what the notation drops or approximates.
• gmeow:projectionFunction — an FnO function reference that performs the render.

A gmeow:ProjectionLoss is an abstract individual type (value vocabulary; never subclassed). Each loss may gmeow:accountsForParameter one or more parameters so that completeness gates can prove every parameter is either represented or explicitly accounted for.

The core framework intentionally stays domain-agnostic. The music extension provides the concrete MusicalParameter vocabulary, music-domain NotationSystem individuals, and per-system projection profiles.

Terms

gmeow:SymbolicSystem · gmeow:NotationSystem · gmeow:SymbolicSystemKind · gmeow:symbolicSystemKind · gmeow:notationSystemKind

A SymbolicSystem is a first-class InformationObject — a convention-based system of symbols — sitting alongside Language and WritingSystem as a sibling, never a subclass. A NotationSystem is a structured SubKind of it with defined representation rules in a specific domain. SymbolicSystemKind values classify each via symbolicSystemKind / notationSystemKind (transcription, encoding, musical, mathematical, …).

gmeow:hasNotationSystem · gmeow:notationSystemFor · gmeow:writingSystemAsNotation

The explicit bridging properties that do the linking the sibling design keeps out of the class hierarchy: relating an entity to a notation system it uses, its inverse, and the bridge that views a WritingSystem as a NotationSystem.

gmeow:NotationSystemUsage · gmeow:NotationUsageRole · gmeow:notationUsageTarget · gmeow:notationUsageNotationSystem · gmeow:notationUsageRole · gmeow:notationUsageInterval

The reified relator binding an entity to a notation system with a role and an interval, mirroring WritingSystemUsage: notationUsageTarget the entity, notationUsageNotationSystem the system, notationUsageRole a NotationUsageRole value (transcription, representation, …), and notationUsageInterval the span it held.

gmeow:NotationProjectionProfile · gmeow:hasNotationProjectionProfile · gmeow:notationSystemOf · gmeow:representableParameter · gmeow:projectableExpression

A Profile (from the core profiles slice) declaring how a NotationSystem projects canonical, frame-relative content — honestly, not the canonical content itself. notationSystemOf names the one system described, representableParameter the parameters it carries without loss, and projectableExpression the expressions it can render; hasNotationProjectionProfile attaches it.

gmeow:ProjectionLoss · gmeow:declaredLoss · gmeow:accountsForParameter · gmeow:ProjectionFunction · gmeow:projectionFunction

A ProjectionLoss is an abstract value individual (never subclassed) explaining what a notation drops or approximates; declaredLoss lists them on a profile and accountsForParameter ties each to the parameters it covers so completeness gates can prove every parameter is represented or accounted for. A ProjectionFunction referenced by projectionFunction is the FnO function that performs the render.

gmeow:smuflCodepoint

A Unicode codepoint reference in the Standard Music Font Layout (SMuFL) specification identifying a glyph used by a NotationSystem; multiple codepoints may be asserted as multiple triples.