- Published 2014 in ArXiv

We study the residuated basic logic (RBL) of residuated basic algebra in which the basic implication of Visser’s basic propositional logic (BPL) is interpreted as the right residual of a non-associative binary operator · (product). We develop an algebraic system SRBL of residuated basic algebra by which we show that RBL is a conservative extension of BPL. We present the sequent formalization LRBL of SRBL which is an extension of distributive full non-associative Lambek calculus (DFNL), and show that the cut elimination and subformula property hold for it.

@article{Ma2014ResiduatedBL,
title={Residuated Basic Logic I},
author={Minghui Ma and Zhe Lin},
journal={CoRR},
year={2014},
volume={abs/1403.3354}
}