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JOURNALS // Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia // Archive

Dokl. RAN. Math. Inf. Proc. Upr., 2025 Volume 523, Pages 15–20 (Mi danma641)

MATHEMATICS

Type-quantifier calculus of positively-formed formulas with negations

S. N. Vassilyev

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

Abstract: Type quantifier language and calculus as logical positively-constructed means of knowledge representation and automation of deductive inference have been developed. In them, the type conditions of quantifiers can contain negations, and the calculus has completeness with respect to derivability in the classical predicate calculus.

Keywords: knowledge representation, logical inference, automatic proof of theorems.

UDC: 51.01+517.11

Received: 12.05.2025
Revised: 10.06.2025
Accepted: 10.06.2025

DOI: 10.31857/S2686954325030031



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© Steklov Math. Inst. of RAS, 2026