A remark on functional completeness of binary expansions of Kleene’s strong 3-valued logic
Gemma Robles, José M. Méndez · Logic Journal of IGPL · 2020
Abstract A classical result by Słupecki states that a logic L is functionally complete for the 3-element set of truth-values THREE if, in addition to functionally including Łukasiewicz’s 3-valued logic Ł3, what he names the ‘$T$-function’ is definable in L. By leaning upon this classical result, we prove a general theorem for defining binary expansions (i.e. expansions with a binary connective) of Kleene’s strong logic that are functionally complete for THREE.