Approximation Logic and Strong Bunge Algebra

Abstract

In this paper we give an axiom system of a logic which we call an approximation logic (AL), whose Lindenbaum-Tarski algebra is a strong Bunge algebra (or simply s-Bunge algebra), and show that

For every s-Bunge algebra $B$, a quotient algebra $B^*$ by a maximal filter is isomorphic to the simplest nontrivial s-Bunge algebra $\Omega=\{0,a,1\}$;

The Lindenbaum algebra of AL is an s-Bunge algebra;

AL is complete;

AL is decidable.