Conflict without a winner

Intention

I want to keep both opposite supports when there is no priority.

Without a priority edge the result stays BOTH.

Correct formFrozen execution sceneBoundary

Incorrect form and why it stays silent

Incorrect form

// eligible(p) и refused(q) считаются конфликтом allowed(p).

Different subjects yield different ground atoms. BOTH arises for one head and one argument tuple, not for any pair of opposite rules.

Correct form

Arxo Law

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

entity Person;
relation eligible(p: Person);
relation special(p: Person);
relation allowed(p: Person);
relation refused(p: Person);
rule Allow defeasible { for p: Person; when eligible(p); then allowed(p); }
rule Refuse defeasible { for p: Person; when refused(p); then not allowed(p); }

Frozen execution scene

Facts and choice	Question	Answer
one bearer	truth(allowed(entity_ref("urn:recipe:b-rules:09:p")))	BOTH / COMPUTED
different bearers	truth(allowed(entity_ref("urn:recipe:b-rules:09:p")))	TRUE_ONLY / COMPUTED
refusal only	truth(allowed(entity_ref("urn:recipe:b-rules:09:p")))	FALSE_ONLY / COMPUTED
no data	truth(allowed(entity_ref("urn:recipe:b-rules:09:p")))	NEITHER / COMPUTED

one bearer

Arxo Law

test "one bearer" {
    given {
        context {
            legal_time @2026-09-13;
            decision_time @2026-09-13T09:00:00+05:00;
            knowledge_time @2026-09-13T09:00:00+05:00;
            timezone "Asia/Almaty";
        }
        assert eligible(entity_ref("urn:recipe:b-rules:09:p")); assert refused(entity_ref("urn:recipe:b-rules:09:p"));
    }
    evaluate truth(allowed(entity_ref("urn:recipe:b-rules:09:p")));
    expect truth_status == BOTH;
    expect evaluation_status == COMPUTED;
}

different bearers

Arxo Law

test "different bearers" {
    given {
        context {
            legal_time @2026-09-13;
            decision_time @2026-09-13T09:00:00+05:00;
            knowledge_time @2026-09-13T09:00:00+05:00;
            timezone "Asia/Almaty";
        }
        assert eligible(entity_ref("urn:recipe:b-rules:09:p")); assert refused(entity_ref("urn:recipe:b-rules:09:q"));
    }
    evaluate truth(allowed(entity_ref("urn:recipe:b-rules:09:p")));
    expect truth_status == TRUE_ONLY;
    expect evaluation_status == COMPUTED;
}

refusal only

Arxo Law

test "refusal only" {
    given {
        context {
            legal_time @2026-09-13;
            decision_time @2026-09-13T09:00:00+05:00;
            knowledge_time @2026-09-13T09:00:00+05:00;
            timezone "Asia/Almaty";
        }
        assert refused(entity_ref("urn:recipe:b-rules:09:p"));
    }
    evaluate truth(allowed(entity_ref("urn:recipe:b-rules:09:p")));
    expect truth_status == FALSE_ONLY;
    expect evaluation_status == COMPUTED;
}

no data

Arxo Law

test "no data" {
    given {
        context {
            legal_time @2026-09-13;
            decision_time @2026-09-13T09:00:00+05:00;
            knowledge_time @2026-09-13T09:00:00+05:00;
            timezone "Asia/Almaty";
        }

    }
    evaluate truth(allowed(entity_ref("urn:recipe:b-rules:09:p")));
    expect truth_status == NEITHER;
    expect evaluation_status == COMPUTED;
}

Counterfactual

Mutation: rule Allow defeasible → rule Allow; rejection LDC-E0201. Scenes that delete a fragment are marked explicitly in the table.

Boundary

BOTH at truth is an ordinary COMPUTED answer; a conflict of positions separately carries UNRESOLVED_NORMATIVE_CONFLICT. A kept conflict does not mean logical explosion.

Pitfall

Without a priority edge the result stays BOTH; opposite conclusions about different persons do not conflict.