numeral system
Enable an AI agent to recognise a numeral system, assess whether a representation is valid and interpretable under its rules, and determine which reading, writing, comparison or conversion actions are justified.
Bundle → Layer → Finding → Questions Filled
6 bundles · 11 layers · 11 findings · 21 questions
System identity and variants Establishes which numerical representation conventions the agent is applying.
Identifying conventions
Records the features that distinguish this system from plausible alternatives.
System recognition
Records diagnostic combinations of signs, composition rules and contextual evidence.
- Which combination of signs and composition rules identifies this numeral system rather than a look-alike? definition
- What additional context is required when a numeral is valid in several systems? boundary
Convention profiles
Separates documented variants without assuming they are independent registry things.
Profile applicability
Records where particular numerical conventions apply and the evidence supporting that selection.
- Which sources establish the rules of each historical, regional or specialised profile? provenance
- Which differences change numerical interpretation, and which merely change the written appearance? boundary
Signs and composition Captures the elements of numerals and the rules for combining them.
Numerical signs
Distinguishes value-bearing signs, placeholders, modifiers and separators.
Sign roles
Records each recognised sign's contribution and its dependence on surrounding signs.
- Which signs carry values, mark empty positions, modify other signs or separate numeral components? definition
- Which visually similar or alternate signs may be treated as equivalent under this profile? boundary
Assembly rules
Records how order, repetition, grouping and spatial arrangement construct a numeral.
Numeral formation
Makes permitted combinations and structurally meaningful layout explicit.
- What ordering, repetition, grouping and spatial rules determine whether signs form an admissible numeral? definition
- Which changes to spacing, orientation or layout preserve a numeral, and which change or destroy its interpretation? boundary
Value and expressibility Connects admissible numerals to numbers and establishes representation limits.
Evaluation rules
Records how signs, positions and modifiers jointly determine numerical value.
Value assignment
Specifies the applicable interpretation mechanism without assuming a positional system.
- How do sign values combine through positional weights, addition, subtraction, multiplication or other documented rules? definition
- If position contributes value, what radix or weight sequence applies and how is the reference position established? definition
Representation domain
Records which numbers can be expressed and which extensions are required.
Expressibility limits
Distinguishes core capabilities from optional conventions for zero, signs, fractions and extended forms.
- Can the selected profile express zero, negative numbers and non-integers, and which rules or extensions enable each? boundary
- Which values have exact finite representations, and what bounds or non-finite representation conventions apply? boundary
Validity and equivalence Supports judgments about admissibility, ambiguity and alternative forms of the same number.
Interpretation status
Separates rule compliance from an agent's ability to infer an intended value.
Validity and ambiguity
Records how to assess malformed, incomplete or multiply interpretable representations.
- Which rule violations make a numeral invalid even when its intended value appears recoverable? boundary
- When a representation is incomplete or admits multiple readings, what evidence must an agent obtain before assigning a value? action
Equivalent forms
Records value equivalence and any documented preference among alternate numerals.
Normalisation permission
Determines when a numeral can be rewritten while preserving its value and relevant source information.
- Which distinct admissible numerals represent the same number, and is a preferred form documented? definition
- When may an agent normalise leading placeholders, repeated signs or alternate constructions, and what original-form information must it retain? action
Reading, writing and conversion Defines conditions for applying the system to concrete representations.
Contextual use
Determines whether a sign sequence is being used numerically and whether an output is suitable for its destination.
Use-sensitive actions
Records prerequisites for reading and generating numerals in their actual context.
- What evidence distinguishes a numeral expressing a number from the same signs used as a code, label or identifier? boundary
- Before generating a numeral, which convention profile, representable domain and required layout must the agent establish? action
Cross-system conversion
Records whether another numeral system can preserve the interpreted value and relevant representation properties.
Conversion fidelity
Distinguishes exact value conversion from approximation and loss of written-form information.
- Can the target system express the interpreted number exactly under its permitted representation conventions? boundary
- If conversion requires approximation or discards meaningful source-form information, what authorisation and accompanying record are required? action
Evidence and external alignment What the world already says about this thing, gathered so the model can be checked against it.
Reported evidence
Findings from the breadth pass, kept separate from the structural claims.
Kinds and varieties
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Which of these kinds and varieties hold for the sense of numeral system this model covers, and on what evidence? provenance
Classifiers Filled
- Family
- Thing Registry
- Category
- Information and virtual systems
- Entry kind
- thing
- Plane
- INF
- Domain
- INF.MED
- Other names and narrower kinds
- non-positional numeral system, positional numeral system, residue number system, bijective numeration, redundant binary representation, negative base, non-standard positional numeral system, complex-base system, non-integer representation
What it is Filled
A numeral system is a conventional mapping from written or spoken numeral tokens to abstract numbers, together with the composition rules that determine how those tokens combine to denote a value.
In scope
- Numeral signs, their numerical roles and accepted variants
- Composition rules, including positional, additive, subtractive or combined mechanisms
- Interpretation of numerals and the range of numbers expressible
- Validity, ambiguity and preferred representation conventions
- Conditions for reading, generating, normalising and converting numerals
Out of scope
- Numbers and number structures independently of their representation
- General writing systems, typography and character encoding standards
- Natural-language number names and grammatical number
- Measurement units, currencies and quantity semantics
- Arithmetic algorithms and calculating devices beyond their numeral interpretation requirements
Why it exists Filled
Enable an AI agent to recognise a numeral system, assess whether a representation is valid and interpretable under its rules, and determine which reading, writing, comparison or conversion actions are justified.
Distinguishing features Filled
- It supplies conventions connecting signs and arrangements to numbers; a number itself is independent of those conventions.
- It governs numerical representation; a font or character encoding alone does not determine numerical value.
- Its scope is expressing numbers; a mathematical notation may additionally express operations, relations and propositions.
- A string using numeral signs may instead be an identifier: preserving leading zeros or forbidding arithmetic can indicate identifier use rather than a numerical interpretation.
- A shared digit inventory does not establish a shared system: positional weights, grouping rules or value assignments must also agree.
What robots and AI may and may not do Filled
Must not
- Misread numbers between systems, such as treating a binary or hexadecimal string as decimal.
- Present one culture's numeral system as superior or primitive.
- Hide a change of numeral system in data that others rely on.
- Mix grouping conventions in a way that alters amounts.
Only with a human decision
- Changing the numeral format in shared financial or medical records.
May
- Convert between numeral systems and explain their rules.
- Name the numeral system used when presenting numbers.
Moral aspects Filled
- Confusion between systems causes costly errors.
- Numeral systems are cultural heritage, not a ranking of peoples.
Who is affected
- Users of data
- Students
- Communities with their own numerals
Owners Filled
Steward
Nobody owns them; they are held in common by the communities that use them.
Links to other meta-models Filled
parent
- Q1140046 - registry parent class
- Q17488292 - registry parent class
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.numeral-system
- Wikidata: Q122653 (https://www.wikidata.org/wiki/Q122653)
Direct properties not applicable Not applicable
- Representation mechanism: Positional, additive, subtractive, multiplicative-additive, other documented mechanism, or combination
- Radix or position-weight rule: Fixed radix with specified value; mixed radix with specified sequence; other weight rule; not applicable; unresolved
- Sign inventory: Links to recognised signs, value assignments, modifiers and accepted visual variants
- Representable number domain: Explicitly described number classes, bounds and exclusions
- Zero convention: Zero numeral, positional placeholder, both, neither, or context-dependent
- Interpretation determinacy: Unique under selected conventions; context-dependent; ambiguous; unresolved
- Representation preference: Unique normal form; multiple preferred forms; accepted forms without preference; unresolved
- Applicable convention profile: Links to documented historical, regional, disciplinary or implementation conventions
Plane INF: no invented physical properties.
Recognition not applicable Not applicable
Not applicable
A numeral system is an abstract set of representation rules whose identity cannot be established from visual appearance alone.
Capabilities and actions required Filled
- Identify candidate numeral systems for a representation and request context when identification is ambiguous.
- Validate a numeral against a selected convention profile and explain rule violations.
- Interpret a numeral or generate a representation for a supported number.
- Compare numerical values while preserving distinctions between written forms.
- Normalise or convert a numeral when equivalence is established, recording any approximation or lost representational information.
Hazards and failure modes required Filled
- Misreading base or digit grouping alters amounts and doses.
- Leading zeros or prefixes misinterpreted by software.
Standards and interfaces required Filled
- The Unicode Standard, Unicode Consortium, which encodes digits of many numeral systems.
Context of use required Filled
- Numeral systems are used in writing, speech, education and computing to represent numerical values.
- Their rules allow people and agents to interpret, compare and transform representations across systems such as decimal, binary and Roman numerals.
- Correct interpretation requires knowing the symbol values and any positional or compositional conventions.
Sources Filled
- Numeral system - Core definition distinguishing numeral systems from numbers, and the main practical kinds (positional, additive, hybrid, unary).
- Wikidata item Q122653: numeral system - identity and sense of the item
Open questions
- With no registry definition recorded, does this entry include spoken, signed and tactile numeral systems, or only written numerical notation?
- Which authoritative sources should establish the representation mechanisms and convention profiles covered by the model?
- Where should the boundary fall between a numeral system's core rules and extensions for fractions, exponents, repeating forms or special values?
- How should the model distinguish a variant of one numeral system from a separate system while respecting registry granularity?
- Which documented communities of use recognise preferred forms, tolerate irregular numerals or require preservation of original notation?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q122653/spec.json