Residuated Basic Logic I

Abstract

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.

Extracted Key Phrases

Cite this paper

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