Involutive Uninorm Logic with Fixed Point enjoys finite strong standard completeness

Abstract

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