import type { PremiseEngine } from "../core/premise-engine.js";
import type { TCoreArgument, TCorePremise, TCorePropositionalExpression, TCorePropositionalVariable } from "../schemata/index.js";
/**
 * Return `true` iff `pe`'s expression tree is exactly one expression at
 * the root and that expression is of type `variable`. Does NOT inspect
 * the premise type — caller is responsible for any `type === 'derivation'`
 * check.
 *
 * @since 1.0.0
 */
export declare function isNakedQTree<TArg extends TCoreArgument, TPremise extends TCorePremise, TExpr extends TCorePropositionalExpression, TVar extends TCorePropositionalVariable>(pe: PremiseEngine<TArg, TPremise, TExpr, TVar>): boolean;
/**
 * Return `true` iff `pe` is a derivation-typed premise (`type ===
 * 'derivation'`) AND its expression tree is in naked-Q form per
 * `isNakedQTree`.
 *
 * @since 1.0.0
 */
export declare function isNakedQDerivationPremise<TArg extends TCoreArgument, TPremise extends TCorePremise, TExpr extends TCorePropositionalExpression, TVar extends TCorePropositionalVariable>(pe: PremiseEngine<TArg, TPremise, TExpr, TVar>): boolean;
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