Abstract

From a formal point of view, the nihilistic propositional calculi, called in this text „npc”, are such propositional calculi that include three unary propositional conectives: T, F, ~, and one binary propositional connective ≡. They read respectively: true, false, untrue that, if and only if. Their theorems are, mong other things, such expressions as: Tp ≡ p, Fp ≡ ~p, with p being a propositional variable. The four npc are presented in this work, i.e. on two-valued, two three-valued, and one four-valued. Moreover, two of them are also paraconsistent calculi. Npc are constructed by means of the axiomatic method. Following the presentation of npc axioms, the four so called n-algebras are introduced. The npc axioms are proved to be adequate to appropriate n-algebras, i.e. sets of theorems and tautologies of each npc are identical