An Algebraic Study of the First Order Version of some Implicational Fragments of Three-Valued Łukasiewicz Logic

Aldo Figallo-Orellano, Juan Sebastian Slagter


In this paper, some implicational fragments of trivalent Łukasiewicz logic are studied and the propositional and first-order logic are presented. The maximal consistent theories are studied as Monteiro’s maximal deductive systems of the Lindenbaum-Tarski algebra in both cases. Consequently, the adequacy theorems with respect to the suitable algebraic structures are proven.


Trivalent Hilbert algebras, modals operators, 3-valued godel logic, first-order logics

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