Minimization of the conjunctive normal forms of partially monotonic Boolean functions

TitleMinimization of the conjunctive normal forms of partially monotonic Boolean functions
Publication TypeJournal Article
Year of Publication2017
AuthorsPynko, AP
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
SectionInformation Science and Cybernetics
Date Published3/2017

A Boolean function is said to be partially monotonic provided it is monotonic with respect to some of its arguments, while anti-monotonic with respect to others. We argue that the conjunctive normal forms of partially monotonic Boolean functions can be minimized in a quite effective way with involving just disjuncts possesing the same partial monotonicity.

KeywordsBoolean function, conjunct, conjunctive normal form, disjunct, disjunctive normal form, literal
  1. Yablonskiy, S. V. (1986). Introduction to discrete mathematics. Moscow: Nauka (in Russian).
  2. Quine, W.V. (1959). On cores and prime implicants of truth functions, American Math. Monthly, 66, No. 9, pp. 755-760.
  3. Pynko, A.P. Minimal sequent calculi for monotonic chain finitely-valued logics. Bulletin of the Section of Logic, 2014, 43, No. 1/2, pp. 99-112.
  4. Kapitonova, J.V., Kryvyj, S.L., Letichevskij, O.A., Luckij, G.M., & Pechurin, M.K. (2000). Foundations of discrete mathematics (in 2 volumes), Kiev: LitSoft (vol. 1: Mathematical foundations) (In Ukrainian).