@article { 5473, title = {On the set of intermediate logics between the truth and degree preserving Lukasiewicz logics}, journal = {Logic Journal of the IGPL}, volume = {24}, year = {2016}, pages = {288-320}, abstract = {The aim of this paper is to explore the class of intermediate logics between the truth-preserving Lukasiewicz logic \L and its degree-preserving companion \L^{\leq}. From a syntactical point of view, we introduce some families of inference rules (that generalize the explosion rule) that are admissible in \L^{\leq} and derivable in \L and we characterize the corresponding intermediate logics. From a semantical point of view, we first consider the family of logics characterized by matrices defined by lattice filters in [0, 1], but we show there are intermediate logics falling outside this family. Finally,we study the case of finite-valued Lukasiewicz logics where we axiomatize a large family of intermediate logics defined by families of matrices (A,F) such that A is a finite MV-algebra and F is a lattice filter.}, URL = { https://doi.org/10.1093/jigpal/jzw006 }, author = {Marcelo Coniglio and Francesc Esteva and Llu\'{\i}s Godo} }