import type { TClaimCanonicalizationOutput, TCompiledPremise, TConclusionSelectionOutput, TInferenceRelation } from "../stages/schemas.js";
/**
 * The form two titles are compared in when checking for duplicates:
 * surrounding space and letter case are ignored, so "Tacit consent" and
 * " tacit consent" count as the same title.
 */
export declare function titleKey(title: string): string;
/**
 * The conclusion title the model authored, when it is safe to use.
 *
 * The model authors exactly one, describing `conclusionCandidates[0]`.
 * The resolved `conclusionMiniId` is the first candidate that is a known
 * normal claim, or a relation-graph fallback — so it is not necessarily
 * that first candidate. Anything but a strict match falls through to
 * composition, which can be redundant but is never about the wrong
 * claim.
 */
export declare function resolveAuthoredConclusionTitle(conclusion: TConclusionSelectionOutput | undefined, relations: readonly TInferenceRelation[]): string | undefined;
export type TTitleComposerMaps = {
    /** claim miniId → display title (LLM `title`, else `axiom`). */
    claimTitleByMiniId: Map<string, string>;
    /** assigned variable symbol → claim miniId. */
    claimMiniIdBySymbol: Map<string, string>;
    /** claim miniId → assigned variable symbol (defensive fallback). */
    symbolByClaimMiniId: Map<string, string>;
    /** relationId → the relation that produced a premise. */
    relationById: Map<string, TInferenceRelation>;
};
export declare function buildPremiseTitle(premise: TCompiledPremise, maps: TTitleComposerMaps, 
/** Guard-resolved authored conclusion title, if one is usable. */
authoredConclusionTitle: string | undefined, 
/** Title keys (`titleKey`) already given to earlier premises. */
taken: ReadonlySet<string>): string;
export declare function buildClaimTitleByMiniId(canonicalClaims: TClaimCanonicalizationOutput["canonicalClaims"]): Map<string, string>;
export declare function buildArgumentTitle(canonicalClaims: TClaimCanonicalizationOutput["canonicalClaims"], conclusionMiniId: string | null): string;
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