GMEOW Logic

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

What This Slice Covers

This slice owns 0 terms and contributes 0 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.

Consumers

The reasoning layer and every projection consumer: the native logic: solver is the reasoning authority, and OWL/Datalog/SHACL/Prolog/N3 reasoners consume generated views of it (Principle 17). Foundational by Principle 15: it serves every consumer by construction. The foundation vocabulary is now minted; the solver and generators are deferred to later rungs of the logic roadmap.

Design Documents

This slice includes slice-local design notes. They are authored beside the slice and rendered into the docs as part of the same deterministic documentation bundle.

Document	Source
Logic Conformance	`slices/core/logic/design/LOGIC-CONFORMANCE.md`
Logic Migration	`slices/core/logic/design/LOGIC-MIGRATION.md`
Logic References	`slices/core/logic/design/LOGIC-REFERENCES.md`
Logic Runtime	`slices/core/logic/design/LOGIC-RUNTIME.md`
Logic Semantics	`slices/core/logic/design/LOGIC-SEMANTICS.md`
Logic	`slices/core/logic/design/LOGIC.md`

Local Map

logic map

Examples

Projection Loss Ledger

Source: slices/core/logic/examples/projection-loss-ledger.ttl
GMEOW terms: gmeow:InformationObject
External prefixes: logic, xsd

# SPDX-FileCopyrightText: 2026 Blackcat Informatics® Inc. <paudley@blackcatinformatics.ca>
# SPDX-License-Identifier: CC-BY-4.0
#
# Worked example — the logic: foundation surface in use: a rule set declares the
# SEMANTIC PROFILE that governs its reading, a derivation rides the four
# normatively-DISTINCT quantitative axes, and a projection records its
# PRESERVATION POLARITY in the loss ledger (Principle 17).
#
# The shape of the example mirrors the logic doctrine: "sound" is meaningless
# until the profile is named, so every rule set declares one; and a lossy
# projection must say what it GUARANTEES about answers, not only what it omits —
# so each projection carries a logic:preservationKind alongside its complexity
# class. The four axes (probability, confidence, weight, evidenceStrength) are
# carried on the SAME derivation to show they are independent numbers, never
# interchangeable. No Expression-typed value is asserted, so no P11 frame is
# required.

@prefix gmeow: <https://blackcatinformatics.ca/gmeow/> .
@prefix logic: <https://blackcatinformatics.ca/logic/> .
@prefix ex:    <https://blackcatinformatics.ca/gmeow/examples/logic/> .
@prefix rdfs:  <http://www.w3.org/2000/01/rdf-schema#> .
@prefix xsd:   <http://www.w3.org/2001/XMLSchema#> .

# --- A rule set MUST declare the semantic profile that governs it; a rule set
#     with no declared profile is rejected by the compiler. This one is
#     positive (negation-free), so it rides the monotonic Horn least-model
#     semantics (logic:PositiveHornProfile) — the base case against which the
#     richer profiles add cost.  No logic:RuleSet class is minted (the
#     vocabulary is foundation-only); the rule set is modelled as a
#     gmeow:InformationObject and linked to the REAL declared profile individual
#     via rdfs:seeAlso, which is sufficient to make the pedagogical connection
#     without inventing new vocabulary.
ex:mortalityRuleSet a gmeow:InformationObject ;
    rdfs:label "the mortality rule set is read under positive Horn semantics"@en ;
    rdfs:seeAlso logic:PositiveHornProfile .

# --- A single derivation carrying all FOUR quantitative axes at once, to make
#     plain that they are distinct and not interchangeable: a calibrated
#     probability is not an asserter's confidence, a solver ranking weight, or
#     an evidential warrant. A confidence is NOT read as a probability absent an
#     explicit mapping (the named failure mode this surface guards against).
ex:derivation-socratesMortal a gmeow:InformationObject ;
    rdfs:label "derived: Socrates is mortal"@en ;
    logic:probability "0.99"^^xsd:decimal ;       # calibrated, only under the probabilistic profile
    logic:confidence "0.9"^^xsd:decimal ;         # the asserter's epistemic confidence
    logic:weight "1.0"^^xsd:decimal ;             # a solver ranking preference
    logic:evidenceStrength "0.8"^^xsd:decimal .   # provenance-derived evidential warrant

# --- The loss ledger: a projection of the canonical logic: model down to an
#     OWL-EL view records BOTH a complexity class AND a preservation polarity.
#     Overclaiming preservation is a red build, exactly like dropping a fact
#     silently — so the projection honestly declares a SOUND UNDER-APPROXIMATION:
#     anything it entails is canonically valid, but it may miss canonical answers.
ex:elProjectionReport a gmeow:InformationObject ;
    rdfs:label "OWL-EL projection of the mortality rule set"@en ;
    logic:preservationKind logic:SoundUnderApproximation ;
    logic:complexityClass "EL → PTIME" .

# --- A bridge view (e.g. a BFO/DOLCE alignment) constrains but does not reason:
#     the honest label is validation-only — it can flag ill-formedness without
#     computing canonical consequences, never claiming exact preservation.
ex:bridgeViewReport a gmeow:InformationObject ;
    rdfs:label "upper-ontology bridge view of the foundation sorts"@en ;
    logic:preservationKind logic:ValidationOnly ;
    logic:complexityClass "structural validation only" .

Guide

Logic — the `logic:` reasoning layer

Slice: https://blackcatinformatics.ca/gmeow/slices/logic · tier: core The maximally expressive, RDF 1.2-native logic in which GMEOW's model is authored, and of which every prior formalism (OWL, RDFS, SHACL, Datalog, Prolog, N3, SPARQL, and the gUFO/BFO/DOLCE upper ontologies) is a generated lossy projection — Constitution Principle 17.

This slice is the home of GMEOW Logic (logic:). The logic: namespace is registered and the foundation vocabulary is now minted: the UFO⁺ sorts (Kind/SubKind/Phase/Role/Category/Mixin/RoleMixin/PhaseMixin/Relator/Event/Situation), the foundation relations (rigidlyAppliesTo/suppliesIdentity/mediates), the semantic profiles (PositiveHornProfile, StratifiedNAFProfile, WellFoundedProfile, StableModelProfile, ProceduralPrologProfile, ProbabilisticProfile), the world/modal terms (World/accessibleFrom/counterfactualOf), the quantitative axes (probability/confidence/weight/evidenceStrength), and the preservation-polarity vocabulary (PreservationKind/preservationKind/complexityClass and their named individuals) are all declared as bare standalone terms that add no axioms to the reasoned core. The rules, solver, generators, runtime, and full conformance corpus remain deferred to later rungs of the logic roadmap.

The design set

The design is split by genre into five documents under design/, so it can be implemented against rather than only read:

Document	Genre	Contents
`design/LOGIC.md`	manifesto	vision, doctrine, lineage, target architecture
`design/LOGIC-SEMANTICS.md`	formal semantics	the unified core, triple-term/assertion rules, semantic profiles, modality, worlds, decidability
`design/LOGIC-RUNTIME.md`	runtime	solver architecture, the Nemo–Prolog seam, graph versioning, generated artifacts, CLI
`design/LOGIC-MIGRATION.md`	rollout	the MVP ladder, adapter phases, gates, deprecations, the design risk register
`design/LOGIC-CONFORMANCE.md`	contract	the conformance corpus and the loss-ledger preservation contract
`design/LOGIC-REFERENCES.md`	appendix	external standards, theory, and engines cited — staged for the `metadata/references.ttl` ledger

What it commits to

The logic is canonical; OWL is a projection of it, not its ceiling. logic: is RDF 1.2-native and Turing-complete by intent; decidability is a property of a projection or a declared profile, never a cap on what the canonical model may say.
The foundation is authored in logic: (UFO⁺). gUFO is its primary generated down-projection; BFO, DOLCE, and SUMO are generated bridge views, not truth-preserving projections. The OntoUML discipline that lives in external lint becomes actual axioms, with the lints retained as projection-conformance tests.
Verified by construction. A slow, correct Python oracle and a fast Rust core (oxigraph + Nemo + an embedded Prolog, bound by PyO3/wasm — the GTS model) must pass one shared, language-neutral conformance corpus identically (Principle 7).

Status

Foundation vocabulary minted; implementation deferred. The logic: namespace and the foundational surface — 37 bare term declarations — have landed. The reasoned core is unchanged because the minted terms carry no axioms. The solver, generators, runtime, full conformance corpus, and the matching enforcement gates in governance/constitution.ttl land in later rungs of the logic roadmap. Until then, Principle 17 is enforced by design-review practice and surfaces as a warning, never silently.

Terms

The foundation surface is authored in the logic: namespace (https://blackcatinformatics.ca/logic/), standalone by design: logic: is the canonical ground and gmeow: (with gUFO, OWL, SHACL, …) is a generated lossy projection of it (Principle 17), so the foundation terms carry no gmeow: parentage. The logic: UFO⁺ sorts (Kind/SubKind/Phase/Role/Category/Mixin/RoleMixin/PhaseMixin/Relator/Event/Situation), the foundation relations (rigidlyAppliesTo/suppliesIdentity/mediates), the semantic profiles, the world/modal terms (World/accessibleFrom/counterfactualOf), the four quantitative axes (probability/confidence/weight/evidenceStrength), and the preservation-polarity vocabulary (PreservationKind and its individuals) are all documented term-by-term in module.ttl and the design set above.

`gmeow:sharpens`

The one gmeow:-side seam the foundation names: logic:accessibleFrom (the Kripke accessibility relation between worlds) generalizes the standpoint sharpening poset asserted on the gmeow: side via gmeow:sharpens. The specialization is declared on the gmeow: side, never minted as an axiom in this module, so the logic: foundation stays standalone (Principle 17).