RT Journal Article
T1 A Completeness Theorem for a Functionally Complete Łukasiewicz Logic
A1 Aranda Utrero, Víctor
AB We present a new axiomatization for a truth-functionally complete version of Ł3, a three-valued propositional logic, using two propositional constants and the Łukasiewicz implication as primitive symbols. We develop a corresponding proof system that incorporates Łukasiewicz’s axioms, a variant of Słupecki’s postulates for a 0-ary connective, and some properties of the Baaz delta operation. Using a weakened Deduction Theorem and adapting Henkin’s method to this three-valued setting, we establish a Completeness Theorem for the system.
PB Uniwersytet Mikołaja Kopernika
SN 1425-3305
YR 2026
FD 2026
LK https://hdl.handle.net/20.500.14352/123833
UL https://hdl.handle.net/20.500.14352/123833
LA eng
NO Aranda, V. (2026) “A Completeness Theorem for a Functionally Complete Łukasiewicz Logic”, Logic and Logical Philosophy, pp. 1–12. doi: 10.12775/LLP.2026.010
NO Comunidad de Madrid
NO Ministerio de Ciencia e Innovación (España)
DS Docta Complutense
RD 8 ago 2026