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 1. For every s-Bunge algebra B, a quotient algebra B* by a maximal filter is isomorphic to the simplest nontrivial s-Bunge algebra Ω = {0, a, 1}; 2. The Lindenbaum algebra of AL is an s-Bunge algebra; 3. AL is complete; 4. AL is decidable. © 1995, Duke University Press. All Rights Reserved.