Derive an explicit negative by a norm

Intention

I want to derive the absence of a debt from an established discharge.

Correct formFrozen execution sceneBoundary

Incorrect form and why it stays silent

A consumer rule does not itself create its negative premise:

Incorrect form

rule Borrow strict { for p: Person; when registered(p) and not debt(p); then may_borrow(p); }
// Negative отсутствует.

Correct form

Arxo Law

language "law.core" version "0.2";
package recipes.v.r09 version "0.1.0";
namespace "urn:recipe:v-negation:09";

entity Person;
relation registered(p: Person);
relation cleared(p: Person);
relation debt(p: Person);
relation may_borrow(p: Person);
rule Negative strict {
    for p: Person;
    when cleared(p);
    then not debt(p);
}
rule Borrow strict {
    for p: Person;
    when registered(p) and not debt(p);
    then may_borrow(p);
}

Frozen execution scene

Facts	Question	Answer
registered, cleared	debt(a)	FALSE_ONLY
registered, cleared	may_borrow(a)	TRUE_ONLY
registered, cleared, without Negative	may_borrow(a)	NEITHER
registered, cleared, debt	debt(a)	BOTH
same both supports	may_borrow(a)	NEITHER

Counterfactual

evaluates.without removes Negative entirely. Discharge remains a fact, but the bridge to negative support disappears, and Borrow no longer fires.

Boundary

A strict negative head does not cancel a positive fact. Priority of refusal needs defeatable candidates and an explicitly given advantage; consuming a dispute is Use a disputed fact deliberately.

Pitfall

A negative body without a producer stays silent. This page takes the negative from a discharge norm instead, so no complete-registry holder is assumed.