/**
 * @fileoverview Referential Identity Invariant (I2)
 *
 * I2: Entity refs within graph maintain identity.
 *
 * Per SPEC Section 8.2:
 * INVARIANT: For all entity references r1, r2 in graph G:
 *   - If r1 and r2 refer to the same entity, they share a symbolic identity
 *   - Identity is preserved across node boundaries
 *
 * This module provides STRUCTURAL referential identity checking.
 * - Checks that all dependsOn references point to existing nodes
 * - Checks symbolic reference consistency (same ref kind used consistently)
 *
 * Lexicon-based entity type checking is in validate/lexicon.ts.
 */
import type { IntentGraph, IntentNodeId } from "../core/types/intent-graph.js";
/**
 * Result of referential identity check.
 */
export type ReferentialIdentityCheckResult = {
    readonly valid: true;
} | {
    readonly valid: false;
    readonly error: "BROKEN_EDGE" | "SELF_DEPENDENCY";
    readonly nodeId: IntentNodeId;
    readonly details: string;
};
/**
 * Check the I2 (Referential Identity) invariant - STRUCTURAL check.
 *
 * This checks:
 * 1. All dependsOn references point to existing nodes
 * 2. No self-references (node depending on itself)
 *
 * Note: Entity type consistency checking requires Lexicon
 * and is done in validate/lexicon.ts.
 *
 * @param graph - The Intent Graph to check
 * @returns Result with validity and optional error details
 */
export declare function checkReferentialIdentity(graph: IntentGraph): ReferentialIdentityCheckResult;
/**
 * Check if graph passes referential identity check.
 *
 * Convenience wrapper that returns a boolean.
 */
export declare function isReferentialIdentityValid(graph: IntentGraph): boolean;
/**
 * Entity type conflict information.
 */
export type EntityTypeConflict = {
    readonly entityId: string;
    readonly firstType: string;
    readonly firstNode: IntentNodeId;
    readonly secondType: string;
    readonly secondNode: IntentNodeId;
};
/**
 * Result of entity type consistency check.
 */
export type EntityTypeConsistencyResult = {
    readonly valid: boolean;
    readonly conflicts: readonly EntityTypeConflict[];
};
/**
 * Check entity type consistency (I2-S invariant).
 *
 * Per SPEC Invariant I2-S:
 * Same entity ID MUST have the same entityType across all nodes.
 *
 * @param graph - The Intent Graph to check
 * @returns Result with validity and any conflicts found
 */
export declare function checkEntityTypeConsistency(graph: IntentGraph): EntityTypeConsistencyResult;
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