00 · Hero · Specification v0.4 · February 2026
A formal semantics and rule language for rights, obligations, and governance.
KROG specifies what agents can do, must do, must not do, and how those relationships are governed — in a form that is mathematically precise, machine-checkable, and translatable across domains. It is intended to serve as a substrate under existing rule languages (ODRL, LegalRuleML, OWL) so that rules originating in different formalisms can be reasoned about together.
Guiding principle
Every valid action satisfies Knowledge, Rights, and Obligations — and remains within Governance.
Implemented by Signatu in commercial solutions
01 · Why KROG exists
The problem
Each is solved today by ad-hoc tooling, audit trails, and trust in interpretation. KROG is the formal substrate they share — defining it once allows each to be addressed structurally rather than re-solved per instance.
On whose behalf, under what conditions, against which counterparties — today this is encoded as system prompts, tool definitions, and trust in the model's runtime interpretation. There is no structural separation between the principal's instructions and a counterparty's content, which is what makes prompt injection effective. There is no audit trail of what was permitted versus what was attempted.
Disputes about what a contract requires resolve through litigation rather than verification. The cost of ambiguity is paid downstream — by lawyers, courts, and counterparties — rather than addressed at drafting time.
Each new regulation generates a new interpretation, audit trail, and tooling investment — work done for GDPR does not compose with HIPAA, which does not compose with the AI Act, even though all three encode variations of the same R-type structures (consent, purpose limitation, retention). Beyond regulation, structurally identical patterns across domains face the same problem: a consent-and-purpose-limitation pattern engineered for financial-services data sharing has to be re-derived from scratch when it reappears in healthcare data exchange or AI training data licensing. The shared substructure stays invisible at the engineering layer.
Where authorization is defined at all, post-hoc evaluators — log auditors, behavior-trace analyzers, output classifiers — verify what the agent did after it occurred. None can prevent unauthorized actions before they execute. The temporal asymmetry between detection and action defeats the point in safety-critical contexts: by the time the unauthorized action shows up in the audit trail, it is already done.
02 · Status — published openly
What stage is KROG at?
KROG is an active research and engineering project. Different components are at different maturity levels. Licensing or deploying a framework requires knowing what is solid and what is in progress.
Component
What it is
Status
Formal semantics
Modal operators, capability states, bilateral relationship types, temporal logic, foundational theorems.
Domain skill libraries
Drafted KROG mappings across ~20 domains: social and legal systems (contract law, economics, game theory, cognitive science, AI alignment); computational and information systems (distributed systems, control theory, networks, security & cryptography, machine learning, signal processing, logic); physical and life sciences (physics, chemistry, biochemistry, thermodynamics, quantum mechanics, ecology).
Inference engine
Forward/backward chaining, conflict detection, isomorphism detection.
Multi-format serialization
JSON, YAML, ODRL, OWL/RDF, Solidity, Python, Rust.
KROG Prover
Small language model that extracts capability states, bilateral relationship types, and obligations from legal text via dual symbolic/neural inference.
AI Authorization Gateway
Runtime enforcement layer that gates LLM agent actions against KROG rules before execution.
Short version: the formal semantics is well-developed and stable. Production tooling (reasoner, AI authorization gateway, Prover) is under active development. Signatu is implementing KROG in commercial solutions. We are accepting deployment partners and licensing inquiries.
03 · The four properties
What KROG is engineered to deliver
The substrate primitives — operators, capability states, bilateral relationship types, temporal logic, foundational theorems — are the mechanism. The four properties are what those mechanisms produce.
Knowledge
Queryable, no hidden rules
All rules, agent states, and bilateral relationships are queryable by authorized participants. No hidden rules.
Rights
Permission, formally
Permitted actions are formally specified using the deontic permission operator P() over the bilateral relationship enumeration. Permission is checkable and provable, not implicit.
Obligations
Time-bounded duties
Required actions are formally specified using O() with temporal logic extensions (LTL, CTL, PCTL, QCTL) for deadlines, sequenced duties, and probabilistic time-bounded constraints.
Governance
The rules about rules
A meta-layer for rule creation, modification, and enforcement, using R-type dynamics and phase transitions for state changes — the rules about rules.
Every valid action satisfies all three operational layers and remains within the governance frame.
04 · The technical core
What KROG actually contains
Modal operators
P (permission), O (obligation), F (prohibition), C (claim), L (liberty), W (power, as institutional “counts as”), B (liability), I (immunity), D (disability).
Set T — Capability states
Enumerating the complete space of single-agent capability profiles, from T₁ (full discretion: can act, refrain, or be passive) through T₇ (must prevent: mandatory blocking).
Set R — Bilateral relationships
Covering the complete space of bilateral interactions between two agents. The Induction theorem establishes that 35 bilateral relationship types suffice to express any n-agent topology.
Temporal logic
Patterns for time-bounded obligations, deadlines, sequenced duties, and probabilistic constraints.
Foundational theorems
Five proofs anchor the framework.
Category
KROG forms a category, so category-theoretic tools (Yoneda, limits, adjunctions, monads) apply.
Induction
N-ary multi-agent relationships decompose to bilateral primitives. 35 bilateral relationship types are sufficient for arbitrary agent counts.
Functor
Cross-domain rule transfer is structurally sound. A valid R-type derivation in one domain transfers to any isomorphic structure in another.
Renormalization
R-types flow predictably under coarse-graining. The R7 → R4 emergence pattern is the worked example, explaining how irreversibility appears at macro scale.
Limitations
Structural enforcement is not semantic correctness. The framework documents what it can and cannot guarantee, so users do not assume more than it provides.
Inference capabilities
Forward chaining · backward chaining · transitive inference · conflict detection (identifies unstable R-type combinations before they manifest) · isomorphism detection (recognizes when rules in one domain match a known pattern in another).
05 · Relationship to existing rule languages
Complementary, not a replacement
KROG provides the underlying bilateral semantics under which other formalisms can be expressed, allowing a single reasoner to handle rules originating in different sources.
ODRL
Open Digital Rights Language
Designed for digital rights management. ODRL rulesets can be expressed within KROG; KROG additionally covers bilateral relationship patterns that ODRL does not enumerate natively.
LegalRuleML
Legal-document framing
Encodes legal text with rich legal-document structure. KROG and LegalRuleML compose: LegalRuleML supplies the legal-document framing, KROG supplies the bilateral semantics for the obligations encoded.
OWL / RDF
Ontologies
Describes ontologies. KROG rules serialize to OWL/RDF; conversely, OWL ontologies can be lifted into KROG bilateral relationship types where bilateral relationship semantics are needed.
| Scope | Deontic operators | Bilateral enumeration | Transfer mechanism | Formal anchor | |
|---|---|---|---|---|---|
| ODRL | Digital rights | 3 (Permission, Prohibition, Duty) | None native | Profile-based | W3C standard |
| LegalRuleML | Legal text | Variable (extends RuleML) | None native | Limited (within rule fragments) | RuleML-based |
| KROG | Universal substrate | 9 | 35 (complete enumeration) | Functor (proven sound) | Category-theoretic |
A structural comparison, not a value judgment — each language is well-suited to its scope. KROG's claim is that the substrate underneath generalizes.
06 · Capabilities
What can be built on KROG
The AI Authorization Gateway is a runtime layer between an LLM agent and its tool surface. It evaluates each proposed action against KROG-typed authorizations and either permits, denies, or escalates the action to a human before execution. This converts agent autonomy from a trust question into a structural one.
Can do
Pre-action gating against typed rules. Audit of permitted vs attempted. Human escalation paths.
Cannot do
Replace model-level alignment. Decide policy disputes the rules themselves do not resolve.
Bidirectional translation between contract text and machine-checkable rule structures. The KROG Prover extracts capability states, bilateral relationship types, and obligations directly from legal text, with mathematically grounded confidence scoring that knows when to defer to human review.
Can do
Extract typed obligations and rights. Surface ambiguity with calibrated confidence.
Cannot do
Substitute for licensed legal review. Resolve interpretive disputes about intent.
Pairing of neural pattern recognition with symbolic rule grounding. Decisions are explainable because they trace to formal proofs over KROG rules.
Can do
Produce structured proofs over KROG rules. Explain decisions at the rule level.
Cannot do
Guarantee that the underlying neural component is itself correct.
Approval flows, escalations, and compliance checks expressed as bilateral relationship chains with temporal constraints.
Can do
Express SLAs, escalation, sequencing, and time-bounded duties machine-verifiably.
Cannot do
Replace organisational judgment about risk acceptance.
GDPR-compatible expression of consent, purpose limitation, and data subject rights as machine-verifiable bilateral relationship types.
Can do
Encode consent scope, purpose limitation, retention, and subject rights as typed relationships.
Cannot do
Substitute for the legal lawfulness assessment performed by a controller.
07 · How to engage
Specification, licensing, deployment
The KROG specification, domain skill libraries, reasoner, and serialization tooling are not published openly. They are developed and deployed through Signatu as part of commercial solutions.
Specification
Modal operators, capability states, bilateral relationship types, temporal logic, foundational theorems, inference rules, serialization formats. Available under commercial license for organisations that wish to implement KROG independently.
Domain skill libraries
Drafted mappings across ~20 domains. Available as part of a Signatu engagement or under separate license.
Reasoner
Prototype inference engine. Deployed by Signatu within commercial solutions.
Serialization tooling
Output to JSON, YAML, ODRL, OWL/RDF, Solidity, Python, and Rust. Deployed by Signatu within commercial solutions.
Route 01 · Standard
Signatu is implementing KROG in commercial solutions — AI authorization gateways, contract engineering pipelines, business workflow automation, privacy and consent infrastructure — for clients in regulated and high-assurance sectors.
Route 02 · License
Organisations that wish to implement KROG independently may license the specification under commercial terms. Contact us to discuss scope, sector, and pricing.
Typical engagement
Signatu deploys KROG-based solutions end-to-end — particularly AI authorization gateways, contract engineering pipelines, and regulated-industry workflows.
A typical engagement covers: scoping the rules and authorizations relevant to the client's domain, encoding them as KROG capability states and bilateral relationship types, deploying the runtime enforcement layer, integrating with the client's existing systems, and providing audit and observability tooling. The KROG substrate is the formal core; the deliverable is a working system.
Now · 2026
Domain skill libraries drafted. Prototype reasoner. KROG Prover in early development. Signatu implementing KROG in commercial solutions.
Later
Production-grade tooling. Industry pilots in regulated sectors. Conformance test suite.