Involutive Uninorm Logic with Fixed Point enjoys finite strong standard completeness

Abstract An algebraic proof is presented for the finite strong standard completeness of Involutive Uninorm Logic with Fixed Point ( $${{\mathbf {IUL}}^{fp}}$$ IUL fp ). It may provide a first step towards settling problem $${\mathbf {IUL}}$$ , posed in G. Metcalfe, F. Montagna. (J Symb Log 72:834–864, 2007)) an manner. The result proved via embedding theorem which based on structural description class odd involutive FL $$_e$$ e -chains have finitely many positive idempotent elements.