The logic of pseudo-uninorms and their residua

Our method of density elimination is generalized to the non-commutative substructural logic GpsUL*. Then the standard completeness of GpsUL* follows as a lemma by virtue of previous work by Metcalfe and Montagna. This result shows that GpsUL* is the logic of pseudo-uninorms and their residua and answered the question posed by Prof. Metcalfe, Olivetti, Gabbay and Tsinakis.Comment: Any comments are welcome prior to formal publication and I would like answer your any question about this work([email protected]). I will upload some materials (such as detailed proofs of some lemmas, examples, etc.) to Arxiv late

Density Elimination for Semilinear Substructural Logics

We present a uniform method of density elimination for several semilinear substructural logics. Especially, the density elimination for the involutive uninorm logic IUL is proved. Then the standard completeness of IUL follows as a lemma by virtue of previous work by Metcalfe and Montagna.Comment: I would like to give you all examples and details of my proof, but I can't provide you with something that I don't have, or something that does not exist in the worl