Alexej P Pynko

Axiomatization of finitely-valued logics Alexej P Pynko

Here, we develop a unversal method of [effective] constructinga [finite] Hilbert-style axiomatization of the logic of a givenfinite disjunctive/implicative matrix with equality determinant[and finitely many connectives](in particular, any/ implicative four-valued expansion of Belnap'sfour-valued logic /[as well as any \L{}ukasiewicz finitely-valued logic]). As a by-product, we also prove that the poset of all disjunctive/axiomaticextensions of the logic is dual to the finite distributive latticeof all relatively-hereditary subsets of the set of allconsistent submatrices of the matrix [to be found effectivelytogether with their finite relative axiomatizations andboth sound and complete matrix semantics]