/**
 * Types of steps in logical proofs.
 * Defines the different kinds of steps that can appear in a logical proof.
 * @enum {string}
 *
 * @category Proof System Enums
 */
export declare enum Step {
    /** Initial assumption or given statement */
    Premise = "Premise",
    /** Temporary assumption for sub-proof */
    Assumption = "Assumption",
    /** Abbreviated proof step */
    Shortcut = "Shortcut",
    /** Repetition of a previous step */
    Reiteration = "Reiteration",
    /** Step derived from previous steps */
    Derivation = "Derivation",
    /** Basic axiom of the system */
    Axiom = "Axiom"
}
/**
 * Axiom schemas for the Hilbert-style calculus.
 * These represent the fundamental axioms of propositional logic in Hilbert's system.
 * @enum {string}
 *
 * @category Proof System Enums
 */
export declare enum HilbertCalculusSchema {
    /** Implication Introduction */
    II = "II",
    /** Implication Distribution */
    ID = "ID",
    /** Implication Reversal */
    IR = "IR"
}
/** Deduction rules for the Hilbert Calculus.
 * @enum {string}
 *
 * @category Proof System Enums
 */
export declare enum HilbertCalculusRule {
    /** Implication Introduction */
    II = "II",
    /** Implication Distribution */
    ID = "ID",
    /** Implication Reversal */
    IR = "IR",
    /** Implication Elimination */
    IE = "IE"
}
/**
 * Rules for natural deduction system.
 * Defines both introduction and elimination rules for logical connectives.
 * @enum {string}
 *
 * @category Proof System Enums
 */
export declare enum NaturalCalculusRule {
    /** Negation Introduction */
    NI = "NI",
    /** Conjunction Introduction */
    CI = "CI",
    /** Disjunction Introduction */
    DI = "DI",
    /** Implication Introduction */
    II = "II",
    /** Equivalence Introduction */
    EI = "EI",
    /** Negation Elimination */
    NE = "NE",
    /** Conjunction Elimination */
    CE = "CE",
    /** Disjunction Elimination */
    DE = "DE",
    /** Implication Elimination */
    IE = "IE",
    /** Equivalence Elimination */
    EE = "EE"
}
/**
 * Types of formula validation checks.
 * Used to verify the applicability of logical rules and structural equality.
 * @enum {string}
 *
 * @category Proof System Enums
 */
export declare enum PropFormulaCheck {
    /** Check if two formulas are structurally equal */
    areEqual = "areEqual",
    /** Check if Implication Elimination is applicable */
    isIE = "isIE",
    /** Check if Disjunction Elimination is applicable */
    isDE = "isDE",
    /** Check if Conjunction Elimination is applicable */
    isCE = "isCE",
    /** Check if Equivalence Elimination is applicable */
    isEE = "isEE",
    /** Check if Negation Elimination is applicable */
    isNE = "isNE",
    /** Check if Disjunction Introduction is applicable */
    isDI = "isDI",
    /** Check if Conjunction Introduction is applicable */
    isCI = "isCI",
    /** Check if Equivalence Introduction is applicable */
    isEI = "isEI",
    /** Check if Negation Introduction is applicable */
    isNI = "isNI",
    /** Check if Implication Introduction is applicable */
    isII = "isII",
    /** Check if Implication Distribution is applicable */
    isID = "isID",
    /** Check if Implication Reversal is applicable */
    isIR = "isIR"
}