UOR Schema

IRI: https://uor.foundation/schema/
Prefix: schema:
Space: kernel
Comment: Core value types and term language for the UOR ring substrate. Defines Datum (ring element), Term (syntactic expression), and the Ring container.

Imports

https://uor.foundation/u/

Classes

Name	IRI	Subclass Of	Disjoint With	Comment
Datum	`https://uor.foundation/schema/Datum`	`http://www.w3.org/2002/07/owl#Thing`	`https://uor.foundation/schema/Term`	An element of the ring Z/(2^n)Z at a specific quantum level n. The primary semantic value type. Disjoint from Term: datums are values, terms are syntactic expressions that evaluate to datums.
Term	`https://uor.foundation/schema/Term`	`http://www.w3.org/2002/07/owl#Thing`	`https://uor.foundation/schema/Datum`	A syntactic expression in the UOR term language. Terms are evaluated to produce Datums. Disjoint from Datum.
Triad	`https://uor.foundation/schema/Triad`	`http://www.w3.org/2002/07/owl#Thing`		A three-component structure encoding an element's position in the UOR address space: stratum (ring layer), spectrum (bit pattern), and glyph (Braille address).
Literal	`https://uor.foundation/schema/Literal`	`https://uor.foundation/schema/Term`		A term that directly denotes a datum value. A Literal is a leaf node in the term language — it refers to a concrete Datum via schema:denotes without being a Datum itself.
Application	`https://uor.foundation/schema/Application`	`https://uor.foundation/schema/Term`		A term formed by applying an operation to one or more argument terms. The application's value is the result of evaluating the operator on the evaluated arguments.
Ring	`https://uor.foundation/schema/Ring`	`http://www.w3.org/2002/07/owl#Thing`		The ambient ring Z/(2^n)Z at a specific quantum level n. The Ring is the primary data structure of the UOR kernel. Its two generators (negation and complement) produce the dihedral group D_{2^n} that governs the invariance frame.

Properties

Name	Kind	Functional	Domain	Range	Comment
value	Datatype	true	`https://uor.foundation/schema/Datum`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The integer value of a datum element. For a Datum in Z/(2^n)Z, this is an integer in [0, 2^n).
quantum	Datatype	true	`https://uor.foundation/schema/Datum`	`http://www.w3.org/2001/XMLSchema#positiveInteger`	The quantum level n of a datum, where the datum's ring is Z/(2^n)Z. Determines the bit width and modulus of the datum.
stratum	Datatype	true	`https://uor.foundation/schema/Datum`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The ring-layer index of a datum, indicating its position in the stratification of Z/(2^n)Z.
spectrum	Datatype	true	`https://uor.foundation/schema/Datum`	`http://www.w3.org/2001/XMLSchema#string`	The bit-pattern representation of a datum, encoding its position in the hypercube geometry of Z/(2^n)Z.
glyph	Object	true	`https://uor.foundation/schema/Datum`	`https://uor.foundation/u/Address`	The Braille address associated with this datum, linking the algebraic value to its content-addressable identifier.
operator	Object	true	`https://uor.foundation/schema/Application`	`https://uor.foundation/op/Operation`	The operation applied in an Application term.
argument	Object	false	`https://uor.foundation/schema/Application`	`https://uor.foundation/schema/Term`	An argument term in an Application. The ordering of arguments follows rdf:List semantics.
ringQuantum	Datatype	true	`https://uor.foundation/schema/Ring`	`http://www.w3.org/2001/XMLSchema#positiveInteger`	The bit width n of the ring Z/(2^n)Z. Distinct from schema:quantum on Datum — ringQuantum is the container's bit width; datum quantum is a membership property.
modulus	Datatype	true	`https://uor.foundation/schema/Ring`	`http://www.w3.org/2001/XMLSchema#positiveInteger`	The modulus 2^n of the ring. Equals 2 raised to the power of ringQuantum.
generator	Object	true	`https://uor.foundation/schema/Ring`	`https://uor.foundation/schema/Datum`	The generator element π₁ (value = 1) of the ring. Under iterated successor application, π₁ generates all ring elements.
negation	Object	true	`https://uor.foundation/schema/Ring`	`https://uor.foundation/op/Involution`	The ring reflection involution: neg(x) = (-x) mod 2^n. One of the two generators of the dihedral group D_{2^n}.
complement	Object	true	`https://uor.foundation/schema/Ring`	`https://uor.foundation/op/Involution`	The hypercube reflection involution: bnot(x) = (2^n - 1) ⊕ x. The second generator of the dihedral group D_{2^n}.
denotes	Object	true	`https://uor.foundation/schema/Literal`	`https://uor.foundation/schema/Datum`	The datum value that a Literal term denotes. Bridges the Term/Datum disjointness: a Literal refers to a Datum without being one. Evaluation of a Literal produces its denoted Datum.

Named Individuals

Name	Type	Properties	Comment
π₁	`https://uor.foundation/schema/Datum`	`value`: 1	The unique generator of R_n under successor. Value = 1 at every quantum level. Under iterated application of succ, π₁ generates every element of the ring.
zero	`https://uor.foundation/schema/Datum`	`value`: 0	The additive identity of the ring. Value = 0 at every quantum level. op:add(x, zero) = x for all x in R_n.